ASHRAE Fundamentals of Thermodynamics and Psychrometrics

697 J68f

ASHRAE Continuing Education

Fundamentals of Thernlodynamics & Psychrometries

A Self-Directed Learning Course For Professional Development

Prepared by

Richard R. Johnson, Ph.D. North Carolina State University

American Society of Heating, Refrigerating and Air-Conditioning Engineers Inc. 1791 Tullie Circle NE • Atlanta, GA 30329

Copyright © 1997 by the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE). All rights reserved. No part ofthis book may be reproduced without written permission from ASHRAE, except by a reviewer who may quote brief passages or reproduce illustrations in a review with appropriate credit; nor may any part of this book be reproduced, stored in a retrieval system, or transmitted in any form or by any means (electronic, photocopying, recording or other) without written permission from ASHRAE. ASHRAE has compiled this publication with care, but ASHRAE has not investigated, and ASHRAE expressly disclaims any duty to investigate, any product, service, process, procedure, design or the like that may be described herein. The appearance of any technical data or editorial material in this publication does not constitute endorsement, warranty or guaranty by ASHRAE of any product, service, process, procedure, design or the like. ASHRAE does not warrant that the information in this publication is free of errors. The entire risk of the use of any information in this publication is assumed by the user. Comments, criticism and suggestions regarding the subject matter are invited. Any errors or omissions in the data should be brought to the attention of Martin Kraft, Continuing Education Course Editor. ASHRAE Education Department: Anne Spengler, Director of Education Martin Kraft, Continuing Education Course Editor Laura Tracy, Education Coordinator Marietta Henry, Secretary F or course information or to order additional materials, please contact:

Education Department ASHRAElnc. 1791 Tullie Circle NE Atlanta, GA 30329 Telephone: 404/636-8400 Fax: 404/321-5478

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Table of Contents

Chapter 1 • • • • • • •

Introduction to HVAC

Instructions Study Objectives of Chapter 1 1.1 Introduction 1.2 HV AC: Heating, Ventilating and Air-Conditioning 1.3 The Major Processes of Air-Conditioning 1.4 Thermodynamics and Psychrometries The Next Step

• Summary • Bibliography • Skill Development Exercises for Chapter 1

Chapter 2

Systems, Properties, States and Processes

• Instructions • Study Objectives of Chapter 2 • 2.1 Introduction • 2.2 Closed and Open Systems in Thermodynamics • 2.3 Forms of Energy • 2.4 Properties of a System • 2.5 Equilibrium States • 2.6 Processes and Cycles • The Next Step • Summary • Skill Development Exercises for Chapter 2

Chapter 3

Property Diagrams for Pure Substances

• Instructions • Study Objectives of Chapter 3 • • • • •

3.1 The State Postulate 3.2 Properties 3.3 Phases and Phase Changes for Pure Substances 3.4 Property Diagrams The Next Step

• Summary • Skill Development Exercises for Chapter 3 Fundamentals of Thermodynamics and Psychrometries

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Chapter 4 • • • • • •

Thermodynamic Tables and Charts

Instructions Study Objectives of Chapter 4 4.1 Introduction 4.2 Tables for Saturated Liquid and Vapor 4.3 Tables for Superheated Vapor and Compressed Liquid 4.4 Thermodynamic LiquidlVapor Charts

• The Next Step • Summary • Skill Development Exercises for Chapter 4

Chapter 5 • • • • • • •

Ideal Gas Law and Air Tables

Instructions Study Objectives of Chapter 5 5.1 Ideal Gas and the Ideal Gas Law 5.2 The Ideal Gas Law as an Equation of State 5.3 Constant Specific Heat 5.4 Air Tables The Next Step

• Summary • Skill Development Exercises for Chapter 5

Chapter 6

Heat and Work

• Instructions • Study Objectives of Chapter 6 • 6.1 Introduction • • • •

6.2 Heat 6.3 Work 6.4 Flow Work The Next Step

• Summary • Skill Development Exercises for Chapter 6

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Chapter 7 • • • •

First Law of Thermodynamics Applied to Closed Systems

Instructions Study Objectives of Chapter 7 7.1 Introduction to Controlled Mass Approach 7.2 The First Law of Thermodynamics for a Closed System

• 7.3 • 7.4

Conservation of Energy First Law Applied in Example Cases

• The Next Step • Summary • Skill Development Exercises for Chapter 7

Chapter 8 • • • • •

First Law of Thermodynamics Applied to Open Systems

Instructions Study Objectives of Chapter 8 8.1 Introduction to the Control Volume Approach 8.2 Conservation of Mass 8.3 Conservation of Energy and the First Law for Open Systems

• 8.4 • 8.S

Steady-Flow Processes First Law Applied in Examples of Steady-Flow Processes

• The Next Step • Summary • Skill Development Exercises for Chapter 8

Chapter 9 • • • • •

Applications of the First Law of Thermodynamics

Instructions Study Objectives of Chapter 9 9.1 Compressors, Turbines, Pumps and Fans 9.2 Throttling Valves and Metering Devices 9.3 Heat Exchangers, Condensers and Evaporators

• The Next Step • Summary • Skill Development Exercises for Chapter 9

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Chapter 10

The Carnot Cycle

• Instructions • Study Objectives of Chapter 10 • 10.1 The Second Law of Thennodynamics Heat Engines, Refrigerators and Heat Pumps • 10.2 Reversible and Irreversible Processes • 10.3 • 10.4 The Camot Cycle and the Reversed Camot Cycle • The Next Step • Summary • Skill Development Exercises for Chapter 10

Chapter 11

Refrigeration Cycles

• • • •

Instructions Study Objectives of Chapter 11 11.1 Refrigeration Equipment 11.2 The Ideal Vapor-Compression Refrigeration Cycle Analysis of the Components and Cycle • 11.3 Perfonnance of Ideal Refrigerators and Heat Pumps • 11.4 The Actual Vapor-Compression Refrigeration Cycle • 11.5 Absorption Refrigeration System ·11.6 • 11.7 Gas Refrigeration System • The Next Step • Summary • Skill Development Exercises for Chapter 11

Chapter 12 • • • • • • • • •

Moist Air as a Mixture of Ideal Gases

Instructions Study Objectives of Chapter 12 12.1 Introduction 12.2 Mixtures ofIdeal Gases Mixture of Dry Air and Water Vapor 12.3 12.4 Moist Air Tables The Next Step Summary Skill Development Exercises for Chapter 12

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Chapter 13 • • • • •

Properties of Moist Air

Instructions Study Objectives of Chapter 13 13.1 Humidity Ratio and Relative Humidity 13.2 Dewpoint Temperature 13.3 Adiabatic Saturation and Wet-Bulb Temperatures

• The Next Step • Summary • Skill Development Exercises for Chapter 13

Chapter 14

The Psychrometric Chart

• • • •

Instructions Study Objectives of Chapter 14 14.1 Introduction 14.2 Description ofthe Axes and Lines of the Chart Finding Property Values on the Psychrometric Chart • 14.3 • 14.4 Human Comfort and the Psychrometric Chart • The Next Step • Summary • Skill Development Exercises for Chapter 14

Chapter 15

Air-Conditioning Processes on the Psychrometric Chart

• Instructions • Study Objectives of Chapter 15 • 15.1 Simple Heating or Cooling at Constant Humidity Ratio Heating with Humidification • 15.2 Cooling Coil Dehumidification • 15.3 Evaporative Cooling • 15.4 Adiabatic Mixing • 15.5 • 15.6 Sensible Heat Ratio • Summary • Skill Development Exercises for Chapter 15

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Appendices • Appendix A-I • Appendix A-2 • Appendix B-1 • Appendix C-l • Appendix C-2 • Appendix C-3 • Appendix C-4 • Appendix D-l • Appendix E-l

Table of Contents

Dimensions and Units Used in Air-Conditioning Applications Unit Conversion Factors Thermodynamic Properties of Water at Saturation R-22 Properties of Saturated Liquid and Saturated Vapor Pressure-Enthalpy Diagram for R-22 R-134a Properties of Saturated Liquid and Saturated Vapor Pressure-Enthalpy Diagram for R-134a Thermodynamic Properties of Moist Air at 14.696 psia ASHRAE Psychrometric Chart

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Chapter 1 Introduction to HVAC

Contents of Chapter 1 • Instructions • Study Objectives of Chapter 1 • 1.1 • 1.2

Introduction HV AC: Heating, Ventilating and Air-Conditioning

• 1.3

The Major Processes of Air-Conditioning

• 1.4

Thermodynamics and Psychrometrics

• The Next Step • Summary • Bibliography • Skill Development Exercises for Chapter 1

Instructions Read the material of Chapter 1. Re-read the parts of the chapter that are emphasized in the summary and memorize important definitions. At the end of the chapter, complete all of the skill development exercises without consulting the text.

Study Objectives of Chapter I Chapter 1 is intended to introduce the processes of HVAC and provide substance to the assertion that it is important to study thermodynamics to gain a better understanding of HVAC. Chapter 1 concludes with a definition of thermodynamics and psychrometrics. After studying the chapter, you should be able to: • Define air-conditioning; • Name and describe seven major air-conditioning processes; • Provide a description of thermodynamics as the science of energy; and • List HVAC applications where knowledge of basic thermodynamics is essential.

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1.1

Introduction

Modem air-conditioning systems are part of our everyday life. Whether it is the comfort enjoyed while relaxing at home, or the freedom from discomfort that allows concentration on activities at work, we can appreciate air-conditioning for making our lives healthier, more enjoyable and more productive. The benefits of air-conditioning are also apparent in the wide range of high quality products that are available in the marketplace. Many products and manufacturing processes are improved by air-conditioning because many goods can be produced better, faster and more economically in a properly controlled environment. Air-conditioning allows for the creation of a comfortable environment indoors no matter what the weather is like outdoors. Whether it's a sweltering hot day in August or a bitterly cold night in January, air-conditioning can be a boon. However, there is a cost to air-conditioning, which appears in the form of energy consumption. Systems installed in the United States prior to the energy scare of 1973 were generally designed with little attention to energy conservation because energy was perceived to be plentiful and inexpensive. There was less concern then of the potentially negative environmental impact of energy consumption on a wide scale. Times have changed. Today, energy conservation is a key component in air-conditioning design. Efficiency is the watchword. The results of energy conservation efforts have led to some interesting shifts in the air-conditioning marketplace. There are many more system configurations than ever before as designers try to take advantage of any opportunity to save energy, and there are tradeoffs to be made between energy conservation and performance. This means that it is important to know and understand how to best select components for an HVAC system. Besides the actual redesign of components such as compressors, furnaces, refrigerators and heat exchangers for better efficiency, there has also been a dramatic expansion in the logic and sophistication of electronic controllers used in air-conditioning systems. Properly implemented changes in system control have the potential to lead to significant improvements in performance. Today, buildings often have an energy management system. Besides energy conservation, the issues of health and air quality have drawn a lot of recent attention in air-conditioning systems. For instance, there is a current controversy about the question of ventilation rates and air quality on board large passenger airplanes. Energy considerations call for minimizing the ratio of outside air to recirculated air. In contrast, the ventilation need is for plenty offresh outside air to avoid the build-up of contaminant gases such as carbon dioxide. What constitutes the right balance? There are standards and guidelines for such ventilation requirements, but they must be continually reviewed because of new situations and revised health evidence.

Chapter 1 Introduction to HVAC

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To study the historical record of air-conditioning is to take a fascinating trip through the tremendous technical and scientific record of our society. There are the pioneers such as Robert Boyle, Sadi Carnot, John Dalton, James Watt, Benjamin Franklin, John Gorrie, Lord Kelvin, Ferdinand Carre', Willis Carrier, Thomas Midgley and many others who have brought us to our current state. We can expect that there is further history still to be written. Air-conditioning could not have developed the way it has were it not for all of the accomplishments of science and engineering in this century. Advances in thermodynamics, fluid mechanics, electricity, electronics, construction, materials, medicine, controls and social behavior are the building blocks to better engineered products of air-conditioning. Many of these famous names are connected to the study of thermodynamics. The term thermodynamics was first used by Lord Kelvin in 1849, and the first textbook on thermodynamics was written by William Rankine in 1859. Thermodynamics is the cornerstone to understanding the processes of air-conditioning.

1.2

HVAC: Heating, Ventilating andAir-Conditioning

For a long time, the term air-conditioning was associated with the act of air cooling only. This has changed and the definition of air-conditioning has been broadened to include all of HV AC. HVAC stands for Heating, Ventilating and Air-Conditioning (cooling). This dual meaning of air-conditioning may seem confusing but, when air-conditioning is mentioned by itself in this course, it will stand for both heating and cooling, and when it is used in the context of HVAC, it will mean only cooling. The use of HV AC as a descriptive term continues because of its historical roots. In its modem sense, air-conditioning is the control of temperature, moisture content, cleanliness, air quality and air circulation as required by occupants, a process or a product in the space. This is a definition given by Willis Carrier (1876-1950) in the book, Father ofAirConditioning.! Imbedded in this definition of air-conditioning are many ideas that have been shaped over time about our perceived need for air-conditioning and the changing technology that makes air-conditioning possible. This is a wide ranging definition that gives interpretation to the idea of conditioning the air in a given space for some specific purpose. Air-conditioning is more than an occasional luxury. It is important to our everyday comfort, health and well-being whether we are at home, in the workplace, out shopping or travelling from one place to another. It includes heating, cooling, humidifying, dehumidifying, ventilating and control of air quality year-round. Besides being important for humans and animals, air-conditioning is also essential to many manufacturing processes. For example, precision-engineered products are often made under closely controlled conditions that can only be produced in an air-conditioned environment. Fundamentals ofThermodynamics and Psychrometries

Chapter 1 Introduction to HVAC

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1.3

The Major Processes ofAir-Conditioning

The seven major processes of air-conditioning are heating, cooling, humidifying, dehumidifying, cleaning, ventilating and air movement.

• Heating is the process of adding thermal energy (heat) to the air in the conditioned space for the purposes of raising or maintaining the temperature of the aIr. • Cooling is the process of removing thermal energy (heat) from the air in the conditioned space for the purposes of lowering or maintaining the temperature of the air. • Humidifying is the process of adding water vapor (moisture) to the air in the conditioned space for the purposes of raising or maintaining the moisture content of the air. • Dehumidifying is the process of removing water vapor (moisture) from the air in the conditioned space for the purposes of lowering or maintaining the moisture content of the air. • Cleaning is the process of removing particulate, chemical and biological contaminants from the air in the conditioned space for the purposes of improving or maintaining the air quality. • Ventilating is the process of exchanging air between the outdoors and the conditioned space for the purposes of diluting the gaseous contaminants in the air and improving or maintaining air quality, composition and freshness. • Air Movement (circulation and mixing) is the process of moving air through conditioned spaces in the building for the purposes of achieving the proper ventilation and facilitating the thermal energy transfer, humidification (or dehumidification) and cleaning processes outlined above.

These are the seven major air-conditioning processes used in HVAC systems. Heating and cooling are the most basic and probably the most recognized. If the space is too hot or too cold, then the occupants are unlikely to be comfortable or productive and there is a need to adjust the temperature by adding or removing thermal energy. Heating has been around for a long time and may utilize a variety of heat sources such as the burning of a fuel, electricity or chemical reaction to supply the heat. Cooling is more complicated. It requires a means for removing energy from the air and usually involves a refrigeration cycle or evaporative cooling technique. It takes energy work to drive the refrigeration cycle.

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The term air is used to mean a mixture of dry air and water vapor. Strictly speaking, the term moist air should be used, but it is common in air-conditioning terminology to use air when referring to moist air. There are several standard measures used to describe the proportions of this mixture such as relative humidity, humidity ratio and moisture content. It is important to understand that there is only a limited range of mixture proportions that are considered to be comfortable by humans. The range is also dependent on temperature. The proportion of water vapor to dry air in the mixture is changed by adding water vapor (humidification) or removing water vapor (dehumidification). The study of the properties and processes of moist air at atmospheric pressures is known as psychrometrics and will be discussed in later chapters. Humidification may be accomplished by allowing the air to blow over water on a wet porous surface, by spraying small droplets into the air stream, by misting with an ultrasonic mister, or by steam injection. On the other hand, dehumidification is mostly commonly accomplished by cooling. Cooling removes the energy from the water vapor to convert it to liquid water. There is a limit to the amount of water vapor that can be held by the air. This limit is known as the saturation condition and it decreases with decreasing temperature. If the temperature of saturated air is decreased, then the vapor condenses into water droplets and drips (or rains) out of the mixture. The result is that the air contains less water vapor. The change of state from water vapor to liquid water (condensation) or from liquid water to water vapor (evaporation) involves transfer of substantial amounts of thermal energy known as latent heat. Because heating and cooling are about the management of thermal energy to control temperature, it is clear that the effects of humidification and dehumidification will be interrelated with heating and cooling in air-conditioning. There are many types of airborne pollutants. Particulates such as pollen, dust and smoke are common items that must be removed from a typical conditioned space. Microscopic organisms such as bacteria, fungi and viruses may be important because of health reasons. Some of these pollutants are just irritating, but others may be deadly. The removal of these pollutants is often achieved by filtering or treating the air stream. Heating and dehumidification are powerful deterrents to many small organisms. Air exchange between outdoors and the conditioned space is either by ventilation (intentional) or by infiltration (unintentional). It is important because the outdoor air is often used to dilute pollutants (such as carbon dioxide) and replenish oxygen to the indoor air. Forced ventilation provides for the best control of air exchange rate and air distribution in a building and is usually mandatory in larger buildings where a minimum air exchange rate is required. On the other hand, natural ventilation is driven by wind pressure, indoor-outdoor temperature differences or the opening of a window, and it is not closely controlled. Infil-

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tration refers to air that leaks in through cracks, incomplete seals and unintentional openings. Most residential homes depend on infiltration for an adequate air exchange rate. However, this has become a concern in many modem houses which are purposefully tightly sealed as an energy conservation measure. Air movement, circulation and mixing are all fluid mechanics processes that involve moving the air between and through the conditioned spaces and to places where the other processes of heating, cooling, humidifying, cleaning and ventilating can occur. Air movement may be forced or free. Forced air movement as produced by fans may be carefully controlled. However, free air movement is often driven by temperature gradients in the conditioned space and occurs naturally. Mixing is an important process that occurs when outdoor air is mixed with indoor air as part of ventilation or when newly conditioned air mixes with air already in the conditioned space.

1.4

Thermodynamics and Psychrometries

To better understand and analyze each of the HVAC processes, it is essential to study and develop an appreciation of thermodynamics and psychrometrics. The terms thermodynamics and psychrometries may sound quite formidable at first, but as we shall see, they are descriptive terms for some common-sense ideas. Studying thermodynamics will provide the tools for quantifying, analyzing and interpreting the very practical matters of HV AC. Studying psychrometrics will provide the understanding needed for controlling humidity. Thermodynamics may be defined as the science of energy. Everybody has some feeling for what is generally meant by energy, but a precise definition takes some development. In the next chapter, some specific definitions and derivations will make it clear how thermodynamics describes the relationships between the different forms of energy and the conversion of one form of energy to another. These relationships occur in almost every aspect of our daily lives. For example, how is it possible to convert the electrical energy ofthe power supply into a cooling effect in an air-conditioned room? How can solar energy be effectively captured and put to good use? How are the heating needs for a house calculated for the middle of winter? These and many other questions may be answered by conducting an energy, or thermodynamic, analysis. You may be familiar with the conservation of energy principle. It states that, during an interaction, energy can change from one form to another, but that the total amount of energy remains constant. Said another way, it means that energy is neither destroyed nor created,. but only changes from one form to another. Forms of energy include internal (such as chemical, thermal, nuclear and electrical), potential and kinetic. To effectively use this principle, Chapter 1 Introduction to HVAC

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it is essential to understand the different forms of energy, the conversion of one energy form to another, the flow of energy across boundaries, and the ability to store energy. Thermodynamics is about the conversion of one form of energy to another. Energy conversions are described in terms of the various properties of substances and the changes of the properties that occur as a result of energy transformations. Thermodynamics is based on experimental observations. The observations are then expressed in terms of some basic laws. For example, the First Law of Thermodynamics is an expression of the conservation of energy principle. The observation that some processes occur in one direction, but not the reverse (for example, the flow of heat from a hot object to a cold one, or the generation of heat by friction) is embodied in the Second Law of Thermodynamics. On the other hand, psychrometrics is the branch of thermodynamics that deals with the thermodynamic properties and processes of moist air. The term humidity is used in connection with the proportion of water vapor in the mixture. It is important to study psychrometrics because, in HVAC, we are interested in controlling humidity as well as temperature. There is a comfort envelope that is framed by temperature and humidity constraints. The study of psychrometrics will be aided by a chart of moist air properties known as the psychrometric chart. We will learn how to plot thermodynamic processes of moist air on the chart. The applications for thermodynamics are numerous. In HVAC, the study of thermodynamics is particularly applied to: • Refrigerators and heat pumps • Heat exchangers • Cooling and heating coils • Radiators • Furnaces • Fans • Pumps • Water and air distribution systems • Building load calculations • Human occupation and activity levels

Both thermodynamic and psychrometric principles are applied to these processes: • Air flow over cooling and heating coils • Humidifiers and dehumidifiers • Outdoor weather conditions • Air in conditioned space (with interest in the comfort envelope) • Breathing by humans and animals

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Chapter 1 Introduction to HVAC

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The following chapters of this course will explain the basics of thermodynamics and psychrometries, and then consider the practical applications to many of the areas listed above.

The Next Step This first chapter provided an introduction to HVAC and the importance ofthermodynamics. In the next chapter, we will begin to build an understanding of thermodynamics by starting with the basics. In Chapter 2, we will introduce the concepts of open and closed systems, forms of energy, equilibrium and property definition. Chapter 2 will also include explanations of the state of a substance, and the process of state change shown on a property diagram.

Summary

Chapter 1 has been an introductory chapter. Following an introduction and a definition of air-conditioning, the seven main processes of HVAC were listed as heating, cooling, humidifying, dehumidifying, cleaning, ventilating and air movement. Each of these processes involves equipment for implementation and deals in different forms of energy. The study of thermodynamics (or the science of energy) is all about the relationship between different forms of energy, and is essential to fully understand the processes ofHVAC. The First Law of Thermodynamics was introduced as a statement of the conservation of energy principle. The Second Law of Thermodynamics was said to embody the idea of irreversibility of some naturally occurring events. Psychrometries was introduced as the science of an air and water vapor mixture. After studying this chapter, you should be able to: • Define air-conditioning; • Name and describe the seven major air-conditioning processes; • Provide a description of thermodynamics as the science of energy; and • List HVAC applications where knowledge of basic thermodynamics is essential.

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Bibliography 1. Carrier, W. 1990. Father ofAir-Conditioning. Louisville, KY: Fetter Printing Co.

Skill Development Exercises for Chapter 1 Complete these questions by writing your answers on the worksheets at the back of this book. Be sure to include your name and address. Send your completed questions to the ASBRAE Education Department.

1-01. List the seven main air-conditioning processes, give a one-sentence description of each process, and give another one-sentence reason why the process is likely to be found in a hospital.

1-02. Define what is meant by air-conditioning.

1-03. Name five pieces of normal BVAC equipment for which the application ofthermodynamic principles is essential to predict performance.

1-04. In your own words, state what is meant by the conservation of energy principle.

1-05. Provide two examples of a process that goes in one direction but will not go in the reverse direction without applying an external energy source.

1-06. What is the difference between dry air and moist air?

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Chapter 2 Systems, Properties, States and Processes

Contents of Chapter 2 • Instructions • Study Objectives of Chapter 2 • 2.1

Introduction

• 2.2

Closed and Open Systems in Thermodynamics

• 2.3

Forms of Energy

• 2.4

Properties of a System

• 2.5

Equilibrium States

• 2.6

Processes and Cycles

• The Next Step • Summary • Skill Development Exercises for Chapter 2

Instructions Read the material of Chapter 2. Re-read the parts of the chapter that are emphasized in the summary and memorize important definitions. At the end of the chapter, complete all of the skill development exercises without consulting the text.

Study Objectives of Chapter 2 The building blocks of thermodynamics (such as system, properties, states, processes and cycles) will be introduced in this chapter. Many new terms will be introduced and defined. The definitions may seem far removed from the applications of interest, but this development of a terminology and logic is essential to understanding how to apply the laws of thermodynamics.

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Chapter 2 Systems, Properties, States and Processes

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After studying Chapter 2 you will be able to: • Define and describe open and closed systems; • Define and describe the different forms of energy; • Define and describe properties and states; and • Define and describe processes and cycles.

Chapter 2 Systems, Properties, States and Processes

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2.1

Introduction

Thermodynamics is about the conversion of one form of energy to another. Energy co.nversions, in tum, are described in terms of the various properties of substances and the changes of the properties that occur as a result of energy transformations. Thermodynamics is based on experimental observations. The observations are then expressed in terms of basic laws. For example, the First Law of Thermodynamics is an expression of the conservation of energy principle. The observation that some processes occur in one direction, but not in the reverse direction (for example, the flow of heat from a hot object to a cold one, or the generation of heat by friction) is embodied in the Second Law of Thermodynamics. However, before we can apply these laws as analysis tools to solve practical applications, we must develop a methodology of analysis. This methodology starts with the definitions of systems, properties, states, processes and cycles. The study of thermodynamics is framed around a system identified for analysis, and the interactions between that system and its surroundings. The condition, or equilibrium state, of a system is defined in terms of the values of the system's properties when at that condition. Properties are any characteristics of the system. The dynamics part of thermodynamics suggests the idea of change, and so changes of state are described in terms of processes and paths. Each of these ideas will be more fully explained.

2.2

Closed and Open Systems in Thermodynamics

In thermodynamics, the first step in finding a solution is identifying the system to be analyzed. The term thermodynamic system has a special meaning in this context as any quantity of matter, or any region in space, selected for study. The system is contained within an imagined system boundary, and everything outside the boundary is known as the surroundings. Heat and work (to be defined later) can cross the boundary in a form of interaction between the system and its surroundings, but it depends on the type of system as to whether mass can cross the boundary. There are two types of systems: closed and open. A closed system is one in which a quantity of matter is identified for study. A closed system definition is often called the control mass approach. A quantity of matter means that the mass to be studied will remain the same throughout the analysis. The matter in the system may change form, phase or location in space, but the system is identified as that matter that was originally targeted for study. There is an imaginary boundary drawn to contain the matter. The location of the matter, and therefore the shape of the boundary, may change with time; but to remain a closed system, no mass enters or leaves the system through the

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boundary. Everything outside the boundary is known as the surroundings. Although there is no mass exchange across the boundary in closed systems, there may still be work and heat crossing the boundary as the system interacts with its surroundings. The other type of system is the open system. An open system is one in which a region in space is identified for study rather than a quantity of matter. An open system definition is often called the control volume approach. In an open system, mass can cross the imaginary boundary between the system and its surroundings. This is important because, as we shall see later, the mass crossing the boundary can also be a vehicle for carrying energy across the boundary. The region in space does not have to be fixed in time, although it is often chosen that way for convenience. In a way, the closed system is a special case of an open system, for which there is no mass flow across the boundary. An example of a closed system is shown in Figure 2-1. The object chosen for demonstra-

tion is a piston and cylinder combination with air in the cylinder. The air is trapped in the cylinder and there is no way for the air to escape, or for new air to come into the cylinder. The system is chosen to be the matter (mass of air) that is trapped in the cylinder. The system boundary is shown by the dotted line. The surroundings are then the piston itself, the cylinder wall, the cylinder head and everything else outside the dotted line. As weights are added to the piston and the piston moves to reduce the volume in the cylinder, the system (air in the cylinder) is compressed and changes shape, but it still maintains the same air that was originally targeted as the system.

Piston

I

Weight

I

Piston

Air System

, - - - -- -- -- --I

Ai r 1 1 :I ___________ System 1 J

1

1

After Adding Weight

Before Adding Weight Figure 2-1. Closed System

Chapter 2 Systems, Properties, States and Processes

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Open systems are shown in Figures 2-2 and 2-3. Figure 2-2 shows a piston and cylinder arrangement like before, only now there is an open valve connecting the cylinder head to a storage tank. Once again, the system is identified as the matter (mass of air) that is in the cylinder at any instant in time. However, with the open system, the amount of air in the cylinder will change when a weight is placed on the piston and the piston moves. Some of the mass initially in the system is pushed across the system boundary and into the storage tank that is part of the surroundings. There is mass flow across the boundary. Although the open system analysis is also called a control volume analysis, the volume does not have to remain fixed in time or space. As can be seen in this case, the control volume changes shape and size during the change. Before leaving Figure 2-2, it is worthwhile to note that the case of the cylinder and the storage tank could have been treated as a closed system if the matter in the system had included both the air in the cylinder and the air in the storage tank. It may also be noted that a different choice of open system could have been to draw a boundary to include the piston and the weights in addition to the air. Which boundary is better depends on what is known, what is sought and what processes are occurring during the change.

Piston

------------

I

I

Weight Piston

Air System

r- - - - - - - - - - - -,

1 1 Air 1 I 1 I System 1 1 ______ - - - - _ ...I

------------

1

Storage Tank

Storage Tank

After Adding Weight

Before Adding Weight Figure 2-2. Open System

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Figure 2-3 depicts another example of an open system; in this case, a reciprocating compressor. The system boundary is drawn to include both the compressor and the air inside the compressor. Mass flows in across the boundary at the inlet, and out across the boundary at the outlet. In this open system, the control volume remains the same in time and space.

There are many choices when it comes to selecting the system and system boundary. The skill is in choosing a system that allows the most convenient analysis and calculation of the unknowns. We will return to the topic of system selection once we have introduced the First Law of Thermodynamics. The conceptual model of system, system boundary and surroundings will be used later to apply the laws of thermodynamics in a way that will permit calculation of practical and useful results. There is only one set of laws, but the thermodynamic relations (equations) that are applicable to closed and open systems are different, making it important to be able to recognize the type of system before starting the analysis. Before applying laws (such as the conservation of energy), we must be able to describe the condition of the system, and define what we mean by energy.

Inlet

-i---------------+

Outlet

-

.. _-------------Figure 2-3. Open System Reciprocating Compressor

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2.3

Forms ofEnergy

The different forms of energy (such as thermal, mechanical, kinetic, potential, electric, magnetic, chemical and nuclear) add together to give the total energy of a system, E. The total energy on a unit mass basis, e, is defined as:

e=Elm

In thermodynamic analysis, it is common to group the forms of energy into two broad categories: macroscopic and microscopic. The macroscopic forms of energy are those that a system possesses as a whole with respect to some outside reference frame. Kinetic and potential energies are examples of macroscopic forms of energy because, as we shall see later, they are defined in terms of an outside reference frame. The microscopic forms of energy are those related to the molecular structure of a system and the degree of molecular activity. Microscopic forms are independent of an outside reference frame. The sum of all microscopic forms of energy is known as the internal energy of the system, U. On a unit mass basis, the specific internal energy is:

u=Ulm

Internal energy is measured at the molecular level. The individual molecules of a system are in continuous motion and the motion contributes to translational, rotational and vibrational molecular energy. The portion of the internal energy associated with this molecular motion is known as sensible energy. The degree of molecular activity increases with temperature; therefore, the sensible energy is higher at higher temperatures. The internal energy is also related to the intermolecular forces between molecules of the system. The forces that bind molecules are strongest in solids and weakest in gases. If sufficient energy is added to a solid or liquid, it will change phase and become a gas. The energy added to make the change is known as latent energy. Latent energy is part of internal energy. Sensible and latent energy changes involve no chemical change in the substance of the system. Chemical energy is part of internal energy. Chemical energy is associated with the chemical bonds between different substances. In cases of chemical change (such as occur in combustion or chemical reaction), there is breaking of some bonds and formation of new bonds, resulting in a change in chemical energy of the system.

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Within the nucleus of an atom are strong binding forces that also contribute to the internal energy of a system. These nuclear bonds, and therefore the nuclear energy, are changed only during fission or fusion reactions. Because thermodynamics is about change in energy forms and because HVAC&R does not commonly include nuclear fission or fusion, nuclear energy will not appear in the energy change relations. The macroscopic energy that a system possesses by virtue of its elevation in a gravitational field is called the potential energy. The potential energy, PE, and the potential energy on a unit mass basis,pe, are:

PE=mgz pe=gz where g is the gravitational acceleration (g = 32.2 ftls 2 on earth at sea level), m is the mass in Ibm' and z is the elevation of the center of gravity of a system relative to some arbitrarily chosen reference frame, in ft. There is often a unit conversion required to express the potential energy in the common unit offt·lbj known as gc' The parameter gc is a unit conversion constant, whose value depends on what units are used for mass. When using the units of mass as Ibm' the value is gc = 32.2 (Ibm ·ftls2)/lbj . The use of g and gc with apparently the same numerical value may seem odd, but it is a result of the fact that one lbj will accelerate one Ibm at 32.2 ftls2. To convert ft'lbj to Btu, the conversion factor is 1 Btu = 778 ft·lbj . Thermodynamics is the study of energy change rather than the study in absolute values of energy, and the use of an arbitrary reference, or datum, is acceptable. An example can be seen in analyzing the increase in potential energy when lifting a weight from a chair on to the top of a table. It is only the height difference between the chair and tabletop that matters, and not how high the table and chair are above the floor. In thermodynamics, it is change of energy that is important and the reference level of absolute total energy is chosen at some convenient datum level. As an example of the change of potential energy and the units of energy, consider a mass of214 Ibm lifted 2 ft from the chair to the table:

PE increase

mgz (214 Ibm )(32.2

ftls 2)(2

ft)/ {32.2 (Ibm ·ftls2)/lbj

}

= 428 ft·lbj = 0.55 Btu pe Increase

= 2 ft·lbj/lb m = 0.0026 Btullbm

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The macroscopic energy that a system possesses by virtue of its motion relative to some reference frame is known as the kinetic energy. When all parts of the system move with the same velocity, V (ft/s), then the kinetic energy, KE, and the kinetic energy on a unit mass basis, ke, are:

The units of kinetic energy are handled similarly to those of potential energy and include the unit conversion constant gc' and often the energy conversion factor I Btu = 778 ft·lb!. The magnetic, electric, nuclear and surface tension effects are important in some cases, but are usually not significant in HVAC&R problems and will not be dealt with here. The total energy, E, and the total energy per unit mass, e, may be written as the sum ofthe internal, potential and kinetic energies:

E = U + PE + KE

= U + mgz + m V2 /2 2

e = u + pe + ke = u + gz + V /2

You must be careful about units when doing a calculation involving potential, kinetic and internal energy so as to be sure that they are each in compatible units.

2.4

Properties ofa System

A property of a system is any observable characteristic of the system. Common properties are mass m, temperature t, pressure p, volume V, specific volume v, density p, specific heats Cp and C", internal energy U, enthalpy H, and entropy S. Some of the terms you will immediately recognize, but others we will have to discuss in more detail in the next chapter on properties. Properties that are independent of the size of the system (such as pressure, temperature and density) are known as intensive properties. Properties that vary with the size, or extent of the system (such as mass, volume and total energy) are known as extensive properties. When extensive properties are expressed per unit mass, they become intensive properties and are known as specific properties, such as specific total energy (e = Elm), specific internal energy (u = Ulm), and specific enthalpy (h = Him).

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Common properties will be more fully defined and described in the next chapter. Properties playa key role in conducting a thermodynamic analysis because of the following postulate: The state of a simple compressible system is completely specified by two independent, intensive properties. To fully understand the impact of this postulate, we must further define what is meant by a thermodynamic state, and then elaborate on properties and independent properties.

2.5

Equilibrium States

Consider a system that is not undergoing any change. It is possible to calculate all the properties of the system. This set of properties then completely determines the condition, or state, of the system. Said another way, the thermodynamic state is the condition of a system in which all the properties have a fixed value. If the value of anyone property changes, then the system will be in a different state. The previous paragraph started with the reference to a system not undergoing change. In thermodynamics, this is known as an equilibrium state. Equilibrium conveys a sense of balance. For a system in an equilibrium state, there are no unbalanced driving forces within the system. For thermal equilibrium, there are no internal temperature gradients that will cause heat flow within the system. For mechanical equilibrium, there is no change of pressure in time to cause mass flow. The static pressure distribution does not violate equilibrium conditions because it does not induce an internal mass flow. For phase equilibrium, there is no relative change in the mass of each phase present in the system. For chemical equilibrium, there are no chemical reactions occurring. The equilibrium state of a system is entirely specified by giving the property values of that state, or conversely, the set of values of the properties is entirely set by identifying the state. Properties are independent of the path followed by the system in coming to a given state. In fact, a property can be defined as any quantity that depends on the state of the system and is independent of the prior history by which the system arrived at the given state.

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2.6

Processes and Cycles

A change in equilibrium state, as defined by a change in properties, is known as a process. The series of states passed through by the system during a process is known as the path. The description of a process involves specifying the initial and final equilibrium states, the path, and any interactions that occur between the system and the surroundings at the system boundaries during the process. When a system is undergoing change, it is by definition not in equilibrium. However, when the process proceeds in such a manner that the system remains infinitesimally close to equilibrium state at all times, then the process is called a quasi-static, or quasi-equilibrium, process. A quasi-equilibrium process is an idealization of real processes, but it can be a very powerful tool in helping to analyze systems. Most of the systems in HVAC&R that we want to analyze are reasonably described by this idealization, and are adequately analyzed in this way. A quasi-equilibrium process can be thought of as a process that proceeds slowly enough that the system can adjust internally so that the properties in one part of the system do not change significantly faster than the properties in another part of the system.

Figure 2-4 depicts a quasi-equilibrium process of air being compressed in a cylinder. The piston and cylinder are shown horizontally at the bottom of the diagram. The closed system is the air trapped in the cylinder at any Pressure ®Final time. The piston is ________ State , initially in Position ,,, 1. With the piston in ,,, Position 1, the propp --------l.-----------~---...... G) Initial erties of the system , State (air in cylinder) are ,,I mass m l , pressure ,,, PI' temperature tl' ' - - - - - - - I . - : - 7 ' " - - - - - - - - - ! - : - 7 " " " - -.. Volume V V2 volume VI' specific ,,: V1 volume vI' internal ,-------, energy VI' specific ,, A',r ,, internal energy up , System , ,, ,, entropy S I and spe,--------, cific entropy S I' These property val® CD ues determine the Figure 2-4. Change of State for a Closed System initial state as State 1. The piston is ~

t

Fundamentals ofThermodynamics and Psychrometries

t

Chapter 2 Systems, Properties, States and Processes

2: 12

slowly moved to the left. After some time, it comes to the final Position 2. The properties have changed. We can see that the volume has changed to a new, smaller volume V2• Because this is a closed system and the mass has not changed (m2 = ml ), the specific volume will have changed to v 2• The pressure may have increased to P2.1t is not known if the other properties have changed values, but it is clear the system has gone to State 2 and so the properties are labeled as (2' U2, u2, S2 and S2' Also shown in Figure 2-4 is the property diagram of pressure plotted against volume. The Initial and Final States (1 and 2) are shown as points on the p-V diagram. The process path is shown as the path taken in going from State 1 to State 2. The pressure-specific volume (p-v) diagram for an open system (axial flow fan) is shown in Figure 2-5. The p-v diagram looks very similar to that for the closed system described earlier, but the States 1 and 2 here refer to the inlet and outlet states of the air blowing through the fan. Many of the practical situations we will want to analyze take the form of the open system shown in Figure 2-5. However, there are often multiple inlets and outlets. We will deal with them when we come to applying the mass and energy conservation laws.

Pressure

p

®

~ I I I I I I I

- - - - +- - -- -- - -- - - ---- - ::--=-:-::-=-----0 I I I I I I I

:V1

Specific Volume V

I I

® Figure 2-5. Change of State for an Open System

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There are many different possible process paths depending on the nature of the interaction between the system and its surroundings and the physical make-up of the system. For example, if a container of fixed volume is heated as shown in Figure 2-6, then the temperature and pressure would increase, but the volume would remain constant. Or, if the constant weight piston of Figure 2-7 is allowed to drop as the air is let out of the cylinder, then the pressure would remain constant, even though the volume changes. There are sets of such processes in which one of the properties remains constant that are very useful for approximating actual situations. They are: • Isobaric process:

Constant pressure process, p

• Isothermal process:

Constant temperature process, t = constant

• Isometric process:

Constant volume process, V = constant

• Isochoric process:

Constant specific volume process, v = constant

• Isentropic process:

Constant entropy process, S = constant

• Adiabatic process:

No heat exchange between system and surroundings

=

constant

The last of the process descriptions given above, the adiabatic process, is different from the others because it does not refer to a property, but instead refers to heat exchange between the system and its surroundings. Heat is not a property, and we will provide a very detailed description of what is meant by heat in a later chapter.

,------1

.------1

1

I I

I 1

I

1

I I

V2

1

P2

I

1

1 I t2 lI ______ JI

I I I ______ JI 1

~Heating

State 1 L

State 2

I

Figure 2-6. Constant Volume Process

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I weight I piston ,------

I r------ .. weight piston

I I V1 I I I P1 I I I t1 I L I _______

I I I I I I I

I I I I I I I

-------.1

Closed Valve

!

State 1

Open Valve

I weight I piston ,-----. V2

I I I I I I

P2= P1 t 2

I I I I I I

-------..1

18 Closed Valve

State 2

Figure 2-7. Constant Pressure Process

A system is said to have undergone a cycle if, after having been through a series of processes, the final state is identical to the starting state. The initial and final states for a cycle are identical, which means that the initial and final properties are also identical. Examples of two-process and four-process cycles are shown on the p-V diagrams in Figure 2-8. The four-process cycle is an idealization of the thermodynamics that occur in a gasoline engine.

Chapter 2 Systems, Properties, States and Processes

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Pressure p

Volume V Two-Process Cycle

Pressure p

®

0---+® ®---+@) @)---+(D 0---+0

Isentropic Compression Constant Volume Isentropic Expansion Constant Volume

Volume V Four-Process Cycle Figure 2-8. Property Diagrams for Two- and Four-Process Cycles

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The Next Step In the next chapter, we will further develop the definition and description of the common properties in the thermodynamics of HVAC&R. The properties to be considered are pressure, temperature, specific volume and density, internal energy, enthalpy and entropy. Also, the idea of a pure substance and the phases of a pure substance will be introduced.

Summary

The starting point of a thermodynamic analysis is the identification of a system. The definition of a thermodynamic system and the ideas of system boundaries and the surroundings were introduced for both open and closed systems. Total system energy was introduced as the sum of the macroscopic and microscopic forms of energy. Macroscopic forms (such as potential and kinetic energies) and microscopic forms of internal energy (such as thermal, phase and chemical energies) add together to make the total energy. A property of a system was described as an observable characteristic of the system. There are intensive and extensive properties. Properties that are independent of the size of the system (such as pressure, temperature and density) are known as intensive properties. Properties that vary with the size or extent of the system (such as mass, volume and total energy) are known as extensive properties. When extensive properties are expressed per unit mass, they become intensive properties and are known as specific properties. A set of property values determines the condition, or state, of a system in equilibrium. A process was defined in terms of the path by which a system changes from one state to a different state. Several idealized processes were described. A cycle is a series of processes linked together so that the initial state is identical to the final state. After studying Chapter 2, you should be able to: • Define and describe open and closed systems; • Define and describe the different forms of energy; • Define and describe properties and states; and • Defme and describe processes and cycles.

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Skill Development Exercises for Chapter 2 Complete these questions by writing your answers on the worksheets at the back of this book. Be sure to include your name and address. Send your completed questions to the ASHRAE Education Department.

2-01. Using examples, explain the main difference between open and closed systems. 2-02. Automobile engines are usually cooled by antifreeze that is circulated between the engine and the radiator by a centrifugal pump. Air is blown over the radiator to cool the antifreeze. Sketch the following systems and state whether they are open or closed: • Antifreeze in the pump • Antifreeze in the radiator • Antifreeze in the pump, radiator and engine water jacket • Antifreeze in the radiator and air in the fan

2-03. Describe the differences between thermal, phase, chemical and nuclear energies. 2-04.

Give an expression for the specific total energy of a system in terms of the internal, potential and kinetic energies.

2-05.

Sketch on a p- V diagram what happens when trapped air expands in a closed cylinder with a piston. Be sure to label the initial and final states, the path and the major properties.

2-06.

Sketch on a p- V diagram a four-process cycle that has process 1 to 2 as an isobaric decrease in volume, 2 to 3 as an isometric increase in pressure, 3 to 4 as an isobaric increase in volume, and 4 to 1 as an isometric decrease in pressure.

2-07.

Sketch on a t-p diagram the following four-process cycle: 1 to 2 isothermal; 2 to 3 isobaric; 3 to 4 isothermal; and 4 to 1 isobaric.

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Chapter 3 Property Diagrams for Pure Substances

Contents of Chapter 3 • Instructions • Study Objectives of Chapter 3 • 3.1 The State Postulate • 3.2 Properties • 3.3 Phases and Phase Changes for Pure Substances • 3.4 Property Diagrams • The Next Step • Summary • Skill Development Exercises for Chapter 3

Instructions Read the material of Chapter 3. Re-read the parts of the chapter that are emphasized in the summary and memorize important definitions. At the end of the chapter, complete all of the skill development exercises without consulting the text.

Study Objectives of Chapter 3 Chapter 3 begins with a description of the state postulate and then defines the properties first introduced in the previous chapter. There are descriptions of pressure, specific volume, temperature, internal energy, enthalpy and entropy. The solid, liquid and vapor phases of a pure substance are introduced, including the ideas of phase equilibrium, independent properties, and saturated conditions for liquids and vapors. States and state changes are displayed on property diagrams. After studying Chapter 3, you should be able to: • Describe those properties common to analysis in thermodynamics; • Define a pure substance; • Describe the phases and phase change characteristics of pure substances; and • Explain and give examples of the value of property diagrams in describing the state and state change of a pure substance. Fundamentals ofThernwdynamics and Psychrometries

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3.1

The State Postulate

A property of a system is any observable characteristic of the system. Common properties are mass m, temperature t, pressure p, volume V, specific volume v, density p, specific heats Cp and C", internal energy U, enthalpy H, and entropy S. Properties that are independent of the size of the system (such as pressure, temperature and density) are known as intensive properties. Properties that vary with the size or extent of the system (such as mass, volume and total energy) are known as extensive properties. When extensive properties are expressed per unit mass, they become intensive properties and are known as specific properties, such as specific total energy (e = Elm), specific internal energy (u = Ulm), and specific enthalpy (h = Him). Consider a system that is not undergoing any change. It is possible to calculate all the properties of the system. This set of properties then completely determines the condition, or state, of the system. Said another way, the thermodynamic state is the condition of a system in which all the properties have a fixed value. If the value of anyone property changes, then the system will be in a different state. The equilibrium state of a system is entirely specified by giving the property values of that state or, conversely, the property values are entirely set by identifying the state. Properties are independent of the path followed by the system in coming to a given state. In fact, a property can be defined as any quantity that depends on the state of the system and is independent of the prior history by which the system arrived at the given state. There are many different properties of a system, but not all of the properties are independent in value of one another. For example, consider air at a given pressure p and absolute temperature T. From the ideal gas law (to be introduced later), the specific volume v is given by v = RT/p. R is the gas constant for air. Because of this interdependence between some properties, it raises the question of how many properties must be specified before the state of a system is completely specified. Fortunately, for most of the applications we want to consider, the question is reasonably answered by the following state postulate: The state of a simple compressible system is completely specified by two independent, intensive properties.

There are several terms in this postulate that require careful attention. A simple compressible system is one in which there are no electrical, chemical, magnetic, gravitational or surface tension effects. Often these effects, which are produced by external fields, are not significant to the calculation. However, if they are, then an additional property must be specified for each effect. For example, if gravitational effects are important, it will be necessary to specify an elevation and the two thermodynamic properties to specify the state. Chapter 3 Property Diagramsfor Pure Substances

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An intensive property has already been defined as a property that is independent of the size of the system (such as pressure, temperature and density) or a property that is expressed per unit mass, such as specific total energy (e = Elm), specific internal energy (u = Vim) and specific enthalpy (h = Him). Intensive properties are independent if one property can be varied while the other is held constant. We will examine more closely the question of independence when we discuss phase change in a later section.

3.2

Properties

Pressure. In solid mechanics, force per unit area is known as stress. If the direction of the force is perpendicular to the plane of the area it acts on, it is known as a normal stress. If the force is tangential to the plane ofthe area, it is known as shear stress. In fluids (liquids and gases), there are similar stresses. The normal stress in a fluid is called pressure, and the tangential stress is called shear stress. Pressure is the normal force per unit area in a fluid and is positive when the stress is compressive. For a fluid at rest, the pressure at a given point is equal in all directions. However, the pressure increases with depth because of the weight of the fluid. This is known as the change in hydrostatic pressure. The variation of pressure with depth, while being equal in all directions, is shown in Figure 3.1. When the fluid is in motion, the pressure may vary from point to point anywhere in the fluid .

........ - . . - - - - - - -........- - - - - " - - " ' - - - - - - -.....~----- Water Level

.

-. ..-

t

j ---........--1 Figure 3-1. Hydrostatic Pressure Variation With Depth

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The units of pressure are force per unit area. In the inch-pound (IP) system of units, the pressure is usually given as pound-force per square inch (lb/in2, or psi). In the SI system of units, the unit of pressure is a Pascal, where 1 Pa = 1 N/m2• Because a Pascal is a small unit, pressure is often expressed in kilopascals (kPa = 103 Pa), or megapascals (MPa = 106 Pa). Typical units and unit conversions are given in Appendix A. The units of pressure are'often quoted in terms of the equivalent height of fluid that may be supported by that pressure. In fluids at rest, the hydrostatic pressure varies as the depth according to the relation!J.p = pg!J.z where !J.p is the pressure change corresponding to an elevation change of!J.z. The fluid density is p. For example, consider standard atmospheric pressure of29.921 in. mercury (Hg). The ratio ofthe density of mercury to that of water is 13.6 (known as specific gravity, SG). The density of water is 62.4 Ibm Ift3. A unit conversion factor of 32.2 Ibm·ftI(lbj ·S2) is required. The pressure difference between atmospheric and zero pressure is then: !J.p

=

pg!J.z

=

(13.6 )(62.4lb)ft3)(32.2 ftls 2)(29.921 in.)(ftl12 in.)/{32.2lbm·ftI(lbjs2)}

=

2,1161bj lft2

=

14.7 psi

Similarly, the equivalent height of fluid can be calculated for a given pressure difference. Expressing 14.7 psi in feet of water yields: !J.z

=

!J.pl(pg)

=

(14.7 lbj lin. 2)(144 in. 2/ft2)(32.2 Ibm·ftI(lbj ·S2) )1 {(62.4 Ib)ft3)(32.2 ftls2)}

= 33.9 ft water Absolute pressure is usually used in thermodynamics. However, the pressure is often measured by instruments that give the pressure relative to atmospheric pressure. These instruments read zero when the pressure is atmospheric. To distinguish such pressure from absolute pressure, the measurement is known as gage pressure, and the units are Ibj lin. 2 gage, or psig. Sometimes absolute pressure is given as psia to emphasize the absolute. Figure 3-2 depicts the different terms of pressure measurement to provide a picture of the relationships between absolute, gage and vacuum measures of pressure. Pressure measurements below atmospheric pressure are called vacuum measurements. A standard atmosphere is taken as: 1 atm = 14.696 psi = zero psig = 101.325 kPa = 29.921 in. Hg

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pressure

P gage P atmos

--------- ------------- fo-------

P absolute ---

P vacuum P atmos P absolute

Figure 3-2. Terms of Pressure Measurement Temperature. Temperature is not an easy property to define. We have a feeling for temperature because we are used to expressing whether something is hot or cold. It is perhaps easier to define the equality of temperature as: Two bodies have equal temperatures when no change in any observable property occurs when they are in thermal communication. This is the same as saying that if two bodies are in thermal equilibrium with a third body, then they are also in thermal equilibrium with each other. In the case where a thermometer is used to measure the temperature, this may be further simplified to say that two bodies are in thermal equilibrium if both have the same temperature reading even if they are not in contact. This principle is the basis for establishing a temperature scale. By examining materials that have temperature-dependent characteristics, we can assign an arbitrary temperature scale to the observed effect. The mercury thermometer is such a device. Mercury expands with temperature. By observing the densities of mercury at the freezing and boiling points of water at atmospheric pressure (known as the ice point and steam point, respectively), it is possible to construct a temperature scale by assigning a temperature change proportional to the density change. Two such scales are the Fahrenheit and Celsius scales. For the Fahrenheit scale, the ice and steam points were assigned values of 32°F and 212°F, respectively. On the Celsius scale, the ice and steam points were assigned values ofO°C and 100°C. There has been a slight revision to the Celsius scale by identifying the triple point of water to be O.Ol°C rather than the ice point. The triple point is the state in which all three phases of water coexist in equilibrium with each other.

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A more useful scale for thermodynamics is the absolute temperature scale. For the absolute scale, the temperature is always positive. It is based on the concept that for an ideal gas at constant volume, the temperature is proportional to the pressure. This means that as the pressure approaches zero, the temperature also approaches zero. On the absolute scale, temperatures are measured in degrees Rankine, R, for the IP unit system, and degrees Kelvin, K, for the 81 unit system. Temperatures on the absolute scale are referred to with an upper case T. The relationships between these scales can be summarized as:

t (OF)

1.8 t(OC) + 32

and

t(OC)

=

[t(OF) - 32]/1.8 t(OC) + 273.15

T(R)

=

t(OF) +459.17

and

T(K)

=

T(R)

=

1.8 T(K)

and

T(K)

= T(R)I1.8

and

~T(K) =

~T(R) = ~t(OF)

M(OC)

Temperature is an intensive property.

Specific volume. The specific volume of a substance v is the volume per unit mass. The specific volume is an intensive property and has the unit of ft3/lbm . The inverse of the specific volume is the density p (Ibm Ift3 ). In fluid mechanics, it is common to use density, but in thermodynamics, it is just as common to use specific volume.

Internal energy. In thermodynamic analysis, it is common to group the forms of energy into two broad categories: macroscopic and microscopic. The microscopic forms of energy are those related to the molecular structure of a system and the degree of molecular activity. Microscopic forms are independent of an outside reference frame. The sum of all microscopic forms of energy is known as the internal energy of the system, U. On a unit mass basis, the specific internal energy is:

u=Ulm Internal energy is measured at the molecular level. The individual molecules of a system are in continuous motion and this motion contributes to translational, rotational and vibrational molecular energy. The portion of the internal energy associated with this molecular motion is known as sensible energy. The degree of molecular activity increases with temperature; therefore, the sensible energy is higher at higher temperatures. The internal energy is also related to the intermolecular forces between molecules of the system. The forces that bind molecules are strongest in solids and weakest in gases. If sufficient energy is added to a solid or liquid, it will change phase and become a gas. The energy added to make the change is known as latent heat. Latent heat is part of internal energy. Changes in sensible and latent energy involve no chemical change.

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Chemical energy is part of internal energy. Chemical energy is associated with the chemical bonds between different substances. In cases of chemical change (such as occur in combustion or chemical reactions), there is breaking of some bonds and formation of new bonds, resulting in a change in chemical energy of the system. Within the nucleus of an atom are strong binding forces that also contribute to the internal energy of a system. These nuclear bonds, and therefore the nuclear energy, are changed only during fission or fusion reactions. Because thermodynamics is about change in energy forms, and because HV AC&R does not commonly include nuclear fission or fusion, nuclear energy will not appear in the energy change relations.

Enthalpy. Enthalpy is the name given to the combination of internal energy, pressure and volume. Because it is a combination of properties, enthalpy is a property itself. It is a particularly useful combination, as will be shown when applying the First Law of Thermodynamics to open systems. The enthalpy H, and the specific enthalpy h, are given by the following two expressions: H=U+pV h=u+ pv

The units of specific enthalpy are the same as those of internal energy. If common units of psi and ft3/lb m are used for p and v, then the product pv has to be converted to produce Btu/Ibm as shown by the following: h

=

u (Btu/Ibm) + p (lbj /in. 2) v (ft3/Ib n)(144 in. 2/ft2)(Btu/(778 ft·lbj

))

Enthalpy will become a very convenient property when we apply the First Law of Thermodynamics to open systems. In open systems, enthalpy is a useful descriptor for the internal energy and flow work done by a flow of mass across the system boundary.

Entropy. Entropy is another new property that is not easily measurable or obvious. It is a property that is linked with the Second Law of Thermodynamics. We will not derive the basis for entropy, but we will make use of the tabulated values of entropy to describe certain types of ideal processes. The Second Law of Thermodynamics deals with the fact that many processes proceed in only one direction. For example, hot coffee left out in a cool room will cool to the temperature of the room, but the coffee will not, by itself, become hotter. In another example, when two pieces of wood are rubbed together, there can be enough frictional heating to start a fire, but a hot spot, by itself, will not cause the two pieces of wood to start rubbing against each other. These processes are known as irreversible.

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In contrast, reversible processes can only be imagined (such as frictionless pistons or heat transfer between objects at the same temperature). Although a frictionless piston does not exist, it is useful to consider it as an ideal, and then compare real behavior to the ideal. Similarly, in thermodynamics, it will prove to be very useful to consider ideal reversible processes, and then compare actual, irreversible processes to the reversible idealizations. Entropy is a convenient property for tracking ideal processes, and also for identifying the degree of irreversibility of real processes. The symbols for entropy and specific entropy are Sand s. The units of entropy are energy over absolute temperature. The units of S are BtuIR, and of s are Btu/(lbm R).

3.3

Phases and Phase Changes for Pure Substances

A pure substance is characterized by the requirements that it be homogeneous and of invariable chemical composition. A pure substance can be a single chemical element, a compound, or a mixture of elements and compounds. Water is a pure substance because it always has the composition of H20, although it may have different phases: solid (ice), liquid (water) or gaseous (steam or water vapor). Air in the gas phase is considered a pure substance even though it is made up of several gases. But air will not be considered as a pure substance if it mixed with liquid air because the composition of the gaseous air and liquid air is different when they are in equilibrium with each other. Similarly, the air of combustion is not a pure substance because it is chemically reacting with the burning fuel. We will start our thermodynamics with the discussion of pure substances. The basic laws and principles of thermodynamics do apply to other than pure substances, but it takes more advanced study. The three principle phases of a pure substance are solid, liquid and gas. As we study phase change in thermodynamics, we do not deal with issues of molecular structure, but some description of molecular structure can provide insight into the nature of the three phases. Solids have a crystalline structure. In solids, the molecular bonds are strong and the molecules are fixed in a three-dimensional lattice. Although the molecules do not change location with respect to each other in the lattice, they continually oscillate about their equilibrium position. The oscillation intensity depends on the temperature. If the temperature is raised high enough, the molecules develop enough oscillation energy to overcome the molecular bonds that keep them fixed in the lattice. With additional energy, the solid melts and becomes a liquid. There are still strong intermolecular bonds and neighboring molecules exert a significant influence over each other, but the molecules can move relative to each other. At a higher temperature, the molecules abChapter 3 Property Diagramsfor Pure Substances

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sorb energy, the distances between molecules increase and the molecular order breaks down. The liquid evaporates and changes phase to become a vapor (gas phase). In the gas phase, molecules are far apart and move around at random, colliding into each other and the container walls. Under certain circumstances, a solid may sublimate and go directly from the solid to vapor phase when heated. The phases and phase change processes in pure substances are important in thermodynamics. To illustrate the basics of phases and phase changes of a pure substance, we will describe the behavior of water changing from liquid to vapor. Although the example is water, it should remembered that the same basic explanation applies to all pure substances, and there are similar changes between solid-to-liquid and solid-to-vapor. Consider as a system the water in a piston-cylinder arrangement shown in Figure 3-3. Imagine that the piston has no weight so that, although the piston can travel up and down, the pressure in the system remains constant at 14.7 psia (atmospheric pressure) throughout the series of steps described below. The water is initially all liquid at 60 oP. In this state, the water is known as a sub-cooled, or compressed, liquid.

Piston

Vapor Piston

Piston

Liquid

Liquid

Liquid

State 1 compressed liquid t lsat

State 6 gas 1»1sat

=

Figure 3-3. Stages in the Constant Pressure Change of Phase of Water

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The water in the cylinder is then heated so that the temperature rises. The water expands slightly as the specific volume increases, causing the piston to rise slightly (State 2). The pressure remains constant at 14.7 psia because of the weightless piston and no constraint on piston movement. When the temperature first reaches 212°F, the water is still all liquid and remains liquid unless further heat is added. If further heat is added, then the liquid progressively changes phase from liquid to water vapor or steam (States 3 and 4). The temperature and pressure throughout the whole phase change process remain constant at 212°F and 14.7 psia respectively, but the specific volume increases from 0.0167 ft 3/lb to 27.82 ft3/lb m • The conditions during the phase change are called saturated conditions and the temperature and pressure are known as saturated pressure Psat and saturated temperature tsat • lll

Ifheating continues after the liquid is all converted to vapor, the temperature will rise above tsat" In this case, imagine the temperature to be 250°F and the pressure still 14.7 psia (State 5). The vapor in the system is described as superheated vapor when t> tsat" If the temperature is much greater than the saturated temperature, t >> tsat ' then the vapor is said to behave as a gas (State 6). We will explain this in a later chapter. When the temperature first reached 212°F and the water was all liquid, but before the phase change started to take place, the state of the water is described as saturated liquid (t = 212 of, P = 14.7 psia, and all liquid). When the liquid had just been fully converted to vapor, the state is known as saturated vapor (t = 212°F, P = 14.7 psia, all vapor). Between the saturated liquid and saturated vapor states, both liquid and vapor are in equilibrium with each other. The temperature and pressure are 212 OF and 14.7 psia respectively, but to determine where we are in the phase change, we introduce a new property called the quality. The quality, x, of a pure substance only has meaning during a phase change. The quality during the phase change from liquid to vapor is the ratio of mass of vapor to total mass in the system: x

= mvapor 1m

(1- x)

= mliquid 1m

That means that x is zero when there is only saturated liquid, and 1 when there is only saturated vapor. The quality can easily be related to the specific volumes of saturated liquid and vapor. Let ~ be the volume and Vj be the specific volume of the saturated liquid. Let Vg be the volume and vg be the specific volume of the saturated vapor. The volume of vapor is V g = vg m vapor . The volume of liquid is Vj = Vj mi·IqUi·d'

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The mass is made up of the sum of the liquid and vapor masses, m = m vapor + m."qUid. :

= mliquid V j + mvapor V g =(l-x)mVj +xmVg Divide through by m and get: V

= (l-x)vj +XVg

This is a useful relationship because it determines the specific volume for a mixture of the two phases. Often the difference between the specific volumes of saturated vapor and liquid is given the designation Vjg = (Vg - Vj)' and the above expression can be rewritten as:

Again, this refers to the property called quality, which has meaning for cases where there is a mixture of two phases of a pure substance. During phase change, we have seen that the temperature and pressure are not independent properties. That means that if the mixture is saturated, then setting either the pressure or temperature will fix the other. It is under these saturated mixture conditions that quality can serve as an independent intensive property. The above discussion used water as an example of a pure substance. All pure substances exhibit similar behavior, but at different values of temperature and pressure. Also, there is not only the phase change between liquid and vapor to be considered. There are also phase changes between solid and liquid, and solid and vapor. These issues will be elaborated in the next section, with the help of property diagrams.

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3.4

Property Diagrams

A two-dimensional property diagram is a plot of one property against another. Because the state postulate asserts that it takes only two independent, intensive properties to determine the state of a pure substance, such diagrams are very useful for visualizing states and changes of state. We will start in this section with a temperature versus specific volume (T-v) diagram to illustrate the constant pressure process that was described earlier for water in a cylinder that was heated and changed from compressed liquid to superheated vapor. The process is shown in Figure 3-4. The States 1,2,3,4,5 and 6 correspond to those first depicted in Figure 3-3. State 2 is saturated liquid, State 4 is saturated vapor, and in between are saturated mixtures of vapor and liquid where the state is determined by the quality. The question arises as to what happens if we follow the same process, but at a higher pressure (we can add a weight to the piston in Figure 3-3). The answer is shown in a more general T-v diagram in Figure 3-5. The constant pressure changes of state are shown as dashed lines for two different pressures PI and P 2 ' for a pure substance being heated from compressed liquid to superheated vapor. The conditions that represent the points of saturated liquid can be joined to draw the saturated liquid line that separates the compressed liquid region from the saturated (liquid + vapor) region. Similarly, the conditions that repre-

Temperature

tOF

CD

Gas

400 Saturated Liquid

® 200

Saturated Mixture

Specific Volume V

Figure 3-4. Constant Pressure Boiling of Water on a T-v Diagram

Chapter 3 Property Diagrams for Pure Substances

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sent the points of saturated vapor may be joined to draw the saturated vapor line. The saturated liquid and vapor lines converge at the top of the curve at the critical point. The critical point has special significance because it characterizes the pure substance. It also represents a temperature/pressure combination above which the transition from liquid to vapor happens without a clear distinction between saturated liquid and vapor.

Temperature

tOF

Critical Point

,s.0 ~"

(I:)~ ~0

Compressed Liquid Region

/

/ /

~

Superheated Vapor Region

/ /

(l)

/.s

li-----------'

/ /

/ / /

::;;, .~

/ / I -'

j

/1 / I I I .a / I

e

c3

Saturated (Liquid & Vapor) Region

Specific Volume V

Figure 3-5. The T-v Diagram

We will become very familiar with diagrams such as the T- v diagram in Figure 3-5, and the p-v diagram in Figure 3-6. In the p-v diagram, lines of constant temperature are shown as dashed lines for the temperatures TJ and T2 • The saturated liquid and saturated vapor lines, and the critical point, look very similar to those of the T- v diagram. Again as a reminder, the real power of these diagrams is that the state of a system is easily represented as a point on the diagram. There is more to property diagrams than the two shown in Figures 3-5 and 3-6. We might plot other property combinations. It will later be useful to plot temperature against entropy and temperature against enthalpy. There is also the extension of the diagram to include phase changes between solid, liquid and vapor.

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pressure

p

I I I

Compressep Liquid I Region I

Critical Point

I I I I I

Superheated Vapor Region

' "'"

-

I_~ ____ - - - - - -

~

.S!"

N .a

ciJ

,

"

Saturated (Liquid & Vapor) Region

'. ' ,

~

-..J 1:)

,

~~

'lJe/"qfl '

';/"e .,.

, ,

~"

Grr~/61.

'

Q' U

fel1]~

q..oo 1"1..'IfJe

'<

e/"qfll. ~e

l:

1

Specific Volume V

Figure 3-6. The p-v Diagram

The p- T, or phase, diagram is shown in Figure 3-7, where three lines all converge at one point. This point is known as the triple point because the solid, liquid and vapor phases all co-exist in equilibrium with each other at this state. The three lines that separate the solid, liquid and vapor regions on the diagram are known as the fusion line, vaporization line and sublimation line. The vaporization line is also known as the condensation line, depending on whether the change is from liquid to vapor, or vapor to liquid. The vaporization line represents an edge view of the saturated liquid and vapor lines that were presented in the Tv and p-v diagrams. The fusion, or melting, line separates the solid and liquid regions. The sublimation line separates the solid and vapor regions. To fully illustrate the relationship between the properties of pressure, temperature and specific volume, it is possible to construct the p-v-T surface in a three-dimensional picture. The picture helps to visualize the various phases.

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pressure

p Liquid

Phase

Critical Point

Solid

Phase

Vapor

Phase

Temperature T

Figure 3-7. Phase Diagram of a Pure Substance

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The Next Step In the next chapter, we will discuss the properties of the common pure substance, water, in more detail. We will examine the thermodynamic tables and charts that give values for the properties over a wide range of conditions.

Summary

The state postulate established that the state of a simple compressible system is completely specified by two independent, intensive properties. Descriptions were provided for pressure, temperature, volume, internal energy, enthalpy and entropy, including explanations of the common units of these properties. Enthalpy was introduced as a property equal to the sum of internal energy and the pressure-volume product. Enthalpy will be very useful when applying the First Law of Thermodynamics to an open system. Entropy was introduced as a property of particular significance when dealing with the Second Law of Thermodynamics, and constructing ideal, reversible processes and cycles. The solid, liquid and vapor phases of a pure substance were introduced, including the ideas of phase equilibrium, independent properties and saturated conditions for liquids and vapors. The quality is introduced as an intensive, independent property relating the mass of vapor to total mass of a system when saturated liquid and vapor exist simultaneously in equilibrium with each other. An expression was developed relating the specific volume of a saturated mixture of liquid and vapor to the quality and the specific volumes of the liquid and vapor. States and state changes are displayed on the T-v and p-v property diagrams. The diagrams are used to introduce the ideas of the saturated liquid line, saturated vapor line and the critical point. After studying Chapter 3, you should be able to: • Describe those properties common to analysis in thermodynamics; • Define a pure substance; • Describe the phases and phase change characteristics of pure substances; and • Explain and give examples of the value of property diagrams in describing the state and state change of a pure substance.

Chapter 3 Property Diagramsfor Pure Substances

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Skill Development Exercises for Chapter 3 Complete these questions by writing your answers on the worksheets at the back of this book. Be sure to include your name and address. Send your completed questions to the ASHRAE Education Department.

3-01.

Give the state postulate and explain what a simple compressive substance is.

3-02. Explain the differences between absolute, gage and vacuum pressures. 3-03. Give the typical units for the following properties, and indicate which properties are intensive and which are extensive: specific enthalpy, total volume, pressure, temperature, specific entropy, mass and quality. 3-04.

Give the temperature of212 cP in units of degrees Rankine, degrees Kelvin and cC.

3-05. Sketch a T-v diagram for a pure substance and show the saturated liquid line, the saturated vapor line, the critical point and a constant pressure process line from compressed liquid to superheated vapor. Also include a constant temperature line. 3-06. Sketch a p-v diagram for a pure substance and show the saturated liquid line, the saturated vapor line, the critical point and a constant temperature process line from compressed liquid to superheated vapor. Also include a constant pressure line. 3-07. A saturated mixture of water is at 230 cP and 103 psia. The specific volume of the liquid is vj = 0.0178 ft3/lb11/ and the specific volume ofthe vapor is vg = 4.312 ft3/lb11/ . If the quality is x = 0.5, what is the specific volume of the mixture? 3-08. A fixed volume container initially contains a pure substance in superheated form. The container is cooled until there is a mixture ofliquid and vapor inside. Using T-v and p-v diagrams, describe the changes taking place in this constant volume process as the contents are cooled.

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Chapter 4 Thermodynamic Tables and Charts

Contents of Chapter 4 • Instructions • Study Objectives of Chapter 4 • 4.1

Introduction

• 4.2

Tables for Saturated Liquid and Vapor

• 4.3

Tables for Superheated Vapor and Compressed Liquid

• 4.4

Thermodynamic LiquidN apor Charts

• The Next Step • Summary • Skill Development Exercises for Chapter 4

Instructions Read the material of Chapter 4. Re-read the parts of the chapter that are emphasized in the summary and memorize important definitions. At the end of the chapter, complete all of the skill development exercises without consulting the text.

Study Objectives of Chapter 4 In Chapter 4, you will develop the skill of looking up properties in tables and charts for water (steam) and refrigerants. You willieam how to select the right table, interpolate between entries in the table, and understand the properties normally given in such tables. There are tables for the different phases of a pure substance, and the table format is different for each phase. After studying Chapter 4, you should be able to: • Understand the format and content of the different tables and charts; • Find the values of common properties in the tables; • Interpolate to determine values between the entries in the tables; and • Determine the property values of liquid-vapor mixtures.

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4.1

Introduction

Tables list values of the thermodynamic properties of a pure substance. Charts are property diagrams that have lines of constant property value mapped in on the diagram. The tables and charts for water and refrigerant R-22 will be used in this chapter as the basis for studying how to use tables and charts. Water tables are sometimes referred to as steam tables because of the early development of the science of thermodynamics for steam boilers and steam engines. The tables and charts for water, refrigerants R-22 and R-134a, and moist air are given in Appendices B, C and D at the end of this book. Extracts from these tables will be used extensively in this chapter to illustrate the different operations involving these tables and charts. The tables and charts of Appendices B and C, and thermodynamic tables and charts for many other substances (including many well known refrigerants), are found in the ASHRAE Handbook-Fundamentals, Chapters 6 and 17. R-22 is a cornmon refrigerant used in many appliances, such as horne refrigerators, airconditioners and chillers. Its technical composition is chlorodifluoromethane, and it is one of the CFCs (chlorofluorocarbons). The CFCs have been the subject of extensive discussion in recent years because of the effect that they may have on the ozone layer, high in the earth's atmosphere. The primary refrigerant of concern has been R-12, the CFC that first achieved widespread use and, until recently, was found in applications such as automobile air-conditioning. Production ofR-12 has been discontinued. R-22 is not as potent as R-12 with respect to the ozone question, but even so, there is a proposed agenda to phase out R-22. The CFCs are not naturally occurring substances. As a class of refrigerants, they have been spectacularly successful because of their attractive thermodynamic properties. The concern about the ozone layer has driven a search for non-CFC alternatives. The other older refrigerants (such as ammonia) have important applications, but do not have the full range of attractive properties that were the hallmark of the CFCs. The search has produced some new non-CFC alternatives (such as R-134a) that are very promising. However, of the new alternatives, it is not yet clear as to which ones will be widely adopted by industry as replacements for R-22. In the meantime, R-22 is used in many existing pieces of equipment. Chapter 4 will deal only with property values in the liquid/vapor part of the property diagrams for water and R-22. However, it should be understood that there are also similar tables and charts for the liquid/solid and solid/vapor regions of the property diagram. Except for a short discussion about ice, the tables for solid/liquid and solid/vapor will be left for further study.

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Recalling the introduction of property diagrams in the previous chapter, there are basically three regions of interest for a pure substance undergoing a change from liquid to vapor. These are the compressed liquid, the saturated mixture of liquid and vapor, and the superheated vapor regions as shown in the t-v diagram of Figure 4-1. The regions are separated by the saturated liquid and saturated vapor lines. Each of the three regions is assigned a different table because of the special nature of the three regions. It would seem logical to draw a rectangular grid on the property diagram in Figure 4-1 and then tabulate the values of all properties at each of the grid line intersections. This is what is done for the compressed liquid and superheated vapor tables, except that the grid is drawn on the p-T diagram. However, the technique is different for the mixed liquid/vapor region because the grid is not necessary. The values everywhere in the mixture region can be determined by knowing only the values along the saturated lines. The discussion of tables and charts will be presented in the following order: saturated liquid/vapor tables, superheated vapor and compressed liquid tables, and charts. We will introduce the property values of most interest, and explain how the tables can be used to obtain values for many properties when the state is known. It takes any two independent, intensive, properties to determine the state.

Temperature Critical Point Compressed Liquid Region e«'"

~~"

,

T

I

" .scv ~

, .1:! •••••••••••••• I

I

I

"

I

I I

I I

,

;:,

~

, I

et!O, «~,

I,. .S! I

I

, Superheated Vapor Region

'

"0

cv

.....

EE

.a ~

Saturated (Liquid + Vapor) Region

Specific Volume V

Figure 4-1. Typical t-v Diagram

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4.2

Tables for Saturated Liquid and Vapor

Along either the saturated liquid or saturated vapor lines, and for the region in between, the pressure and temperature are not independent from one another. That means that if we specify the pressure, then the temperature is automatically known. An example was given earlier when we examined boiling water. If the pressure is 14.7 psia, then the water would boil (change phase from liquid to vapor) at a temperature of212°P. The 212°P temperature applies for saturated liquid, saturated vapor and any mixture of saturated liquid and vapor in equilibrium with each other at the 14.7 psia. A similar argument applies for other pressures, and there is a unique temperature corresponding to each pressure at which water will boil. These are known as the saturated valuespsat and t sat. The relationship betweenpsat and t sat can be expressed in mathematical terms by saying that, for a given pure substance, saturated pressure is a function of temperature only: Psat

=/

(tsat)

The question here is what is the function /? Experiments show the function is not a simple function. Mathematical equations for the function/are available, such as those given in the ASHRAE Handbook-Fundamentals (Chapter 6), but the equations are complicated. Therefore, instead of giving the function in mathematical form, the relationship between pressure and temperature is also given in tabulated form. Selected values are taken from the water table of Appendix B and from the R-22 table of Appendix C, and presented in Table 4-1.

Table 4-1. Saturated Pressure and Temperature for Water and R-22 Saturated Water tsat (OF) Psat (psia) 32 62 92 122 152 182 212 242

0.08865 0.27519 0.74394 1.79117 3.91101 7.8589 14.7096 25.9028

Saturated R-22 (OF) Psat (psia) -50.00 11.696 0.00 38.726 50.00 98.799 100.00 210.69 396.32 150.00 200.00 686.11 723.74c 205.06c tsat

The values given in Table 4-1 highlight some features that are common to all saturated property tables. There is usually an entry value and then a value to be found. In this case, the entry value is the temperature and the value to be found is the pressure. The saturated table is sometimes given the other way around, where the temperature is listed for set values of pressure. Whichever way, the basic relationship is the same, and it is only a matter of convenience in which order they appear. Later we will examine the issue of when you wish to find a value that does not correspond exactly to one of the entry values. Chapter" Thermodynamic Tables and Charts

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The values in the table are usually given to at least five-digit accuracy. Because we are relying on the values to describe the functional relationship, they must be accurate. Although the temperature in the water table appears to be only given to a degree, it is also understood to be accurate to five-digit accuracy. The critical value is the last entry in the saturated R-22 table. The critical values for R-22 are 205.06°F and 723.74 psia. The critical values are the property values where the saturated liquid and saturated vapor lines join. For water, the critical values are 705.44°F and 3,204 psia. The values for saturated water given in Table 4-1 include the 212°F, 14.7 psia combination that we have been using as an example. What happens if we need a value between two table entries? Actually, as can be seen from Appendices B and C, the values in the table are given at a much smaller interval, and usually include a full range of useful values. Even so, the question still remains as to how to compute values that are between entries. Usually it is assumed that linear interpolation between entries in the table provides an accurate enough value of the property. Linear interpolation means that iftwo data entries were plotted on a graph, then a straight line joining the two points would reasonably describe the values between the two points. The closer together the data entries, the better the linear approximation. As an example of linear interpolation, consider the values in Table 4-1 and the need to know the saturation pressure when the saturation temperature is 200.5°F. The 200.5°F lies between the temperature entries 182°F and 212°F and between pressure values of 7.8589 psia and 14.7096 psia. These values are shown in Table 4-2 and in the graph in Figure 4-2 along with a notation of PJ'tl and P2' t2 for the known points and p, t for the desired pair.

Table 4-2. Steps to Interpolate Between Two Pressures Saturated Water

tsat COF) tl = 182 t= 200.5

t2 = 212

Fundamentals of Thermodynamics and Psychrometries

Psat (psia) PI-7.8589 p = pI + {(t - 11)/(t2 -tl)x(P2 - pI) = 7.8589 + {(200.5 - 182)/(212 -182)} x (14.7096 - 7.8589) = 12.0835 P2 -14.7096

Chapter 4 Thermodynamic Tables and Charts

4: 6

pressure P2 = 14.7096 psia

p=?

P1

=7.8589 psia

t1

=182°F

t

=200.5°F

t2

=212°F

Temperature

Figure 4-2. Linear Interpolation Between Two Temperatures in Saturation Table

From the graph, it can be seen that there are similar triangles in which:

This can be solved for an unknown p as in Table 4-2 as:

or for an unknown t as:

These are two useful expressions that will be applied over and over again as we find values in tables. The linear interpolation technique will be applied to many different variables, not only pressure and temperature.

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The value obtained for PSal at tsal = 200.5°F, when using values in Table 4-1, is 12.0835 psia. If instead the values in the table given in Appendix B are used, then the linear interpolation gives a more accurate value ofpsal as: p

= P1 + {(t - t1) / (t2 - t1)} X (P2 - PI) = 11.5374 + {(200.5 - 200) / (201- 200)} X (11.7779 -11.5374) = 11.6577 psia

These numbers suggest an error of e% = {(12.0835 - 11.6577)/11.6577) x 100 = 3.6% in the linear interpolation from Table 4-1. This is just an example to demonstrate that the closer the entries are in the table, the more accurate the linear interpolation. If the error is deemed too large, the alternative is to use one of the mathematical equations. For water, find the saturated temperature for a saturated pressure of 5 psia. In Table 4-3, it can be seen that tsal = 160.28°F atPsal = 5 psia.

Table 4-3. Steps to Interpolate Between Two Temperatures Saturated Water tsat (OF) . t} = 152 t = t} + {(P - P/)!(P2 - Pi)} X (t2 - t]) = 152 + {(5 - 3.91101)/(7.8589 - 3.91101)} x (182 - 152) = 160.28 t2 = 182

Psat (psia) p}- 3.91101 p-5

P2 -7.8589

The interpolation relations for P and t are two useful expressions that will be applied over and over again as we look up values in tables. The linear interpolation technique will be applied to many different variables, not only pressure and temperature. The tabulated pressure and temperature values are exactly the same for both the saturated liquid and saturated vapor lines. What then is the difference between the saturated liquid and saturated vapor lines? The difference is that the saturated liquid line represents a quality x = 0 (all liquid) and the saturated vapor line represents a quality of x = 1 (all vapor). Quality, x, is the mass proportion of vapor in a mixture of liquid and vapor. All properties, other than pressure and temperature, have different values for saturated liquid and saturated vapor. It is easy to picture that there is a big difference between specific volume; the liquid is heavy while the vapor is light. To draw the distinction between the specific volume of a saturated liquid and the specific volume of a saturated vapor, we use the subscripts offand g respectively (they are the first letters of the German words for liquid and vapor). There-

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Chapter 4 Thermodynamic Tables and Charts

4: 8

fore, the variable Vj is reserved for the specific volume of a substance that is atpsat ,{sat and has a quality x = 0, and vg is reserved for the specific volume of a substance that is at p t' { and has a quality of x = 1. For a quality of x, the specific volume v of a saturated mixture is given in terms ofvj' Vg and specific volume difference, Vjg = (Vg - Vj j, (see explanation in the previous chapter) as: ~

~

v=vj+XV jg

Values of v j ' Vg and Vjg are given in the saturation table for water as shown in the small subset of Appendix B reproduced in Figure 4-3. Figure 4-3 has column headings that include temperature {sal' pressure Psal' specific volume v j ' Vg and Vjg ' specific enthalpy hj' hg' and h jg , and specific entropy Sj' Sg and Sjg' Enthalpy is a property that will become very useful when applying the the First Law of Thermodynamics to open systems. The enthalpy for any saturated condition can be calculated from: h

=

h j +xhjg

Table 3 Tbermodynamic: Properties of Water at Saturation, Temp. I, of 189 190 191 192 193 194 195 196 197 198 199

Absolute Pressure p psi in.Hg 9.1510 . 9.3493 9.5512 9.7567 9.9659 10.1788 10.3955 10.6160 10.8404 11.0687 11.3010

18.6316 19.0353 ·19.4464 19.8648 20.2907 20.7242 21.1653 21.6143 22.0712 22.5361 23.0091

Specific SaL Uquid

"l 0.01656 0.01657 0.01658 0.01658 0.01659 0.01659 0.01660 0.01661 0.01661 0.01662 0.01663

Volume, Eftp.

ft 3 /1b Sat. Vapor

Enthllpy, Btu/lb Sat. Sit. Uquid Eftp. Vapor

hI

"I,

"t

41.7jO 40.901 40.092 39.301 38.528 37.774 37.035 36.314 35.611 34.923 34.251

41.746 40.918 40.108 39.317 38.544 37.790 37.052 36.331 35.628 34.940 34.268

hl'

. m.07 984.32 158.07 983.71 159.08 983.10 160.08 982.48 161.09 981.87 162.09 981.25 163.10 980.63 164.10 980.02 165.11 979.40 166.11 978.78 167.12 978.16

Entropy, Btu/lb· of SaL Sat. Uquld Eftp. Vapor

h,

I(

1141.39 1141.78 1142.18 1142.57 1142.95 1143.34 1143.73 1144.12 1144.51 1144.89 1145.28

0.2772 0.2787 0.2803 0.2818 0.2834 0.2849 0.2864 0.2880 0.2895 0.2910 0.2926

'l'

't

1.5174 1.7946 1.5141 1.7929 1.5109 1.7911 1.5076 1.7894 1.5043 1.7877 1.5011 1.7860 1.4979 1.7843 1.4946 1.7826 1.4914 1.7809 1.4882 1.7792 1.4850 1.7776

Figure 4-3. Thermodynamic Properties of Saturated Water

Enthalpy is an energy-type property with zero value at some chosen reference state. The reference state can be arbitrarily chosen, so the table is often accompanied by a statement of how the reference state was chosen. For the water table in Appendix B, the reference state is set such that the enthalpy is zero at the triple point of water (32.018°F). In most of the thermodynamic expressions that we will be using, it is the enthalpy difference that is important and not the absolute value of enthalpy, so the choice of reference state is not critical. However, the reference state is critical in topics such as combustion where there is a chemical reaction between components, and enthalpy values have to be brought to a common reference state. The enthalpy difference between saturated vapor and saturated liquid, hjg = (hg - hj ), is also known as the heat of vaporization or the latent heat.

Chapter 4 Thermodynamic Tables and Charts

Fundamentals ofThermodynamics and Psychrometries

4: 9

The tables offer a way of determining the quality if two independent properties are known. For example, assume that saturated water at 212°F has an enthalpy of h = 800 BtU/Ibm' From the table in Appendix B, the saturation pressure is 14.7096 psia. From the same table, hj = 180.20 and hjg = 970.03 Btu/Ibm' Solving the enthalpy equation given earlier for x gives:

x

= (h-hj )/ hjg = (800 -180.20) / 970.03 =

0.6389 (or 63.89%)

The column headings from the saturation table for R-22, as given in Appendix C, are reproduced in Figure 4-4. The specific volume for liquid is replaced by the density (density is the inverse of specific volume). The columns for specific volume, enthalpy and entropy do not list the values of Vjg ' hjg or Sjg' but these values can be derived easily from the differences between listed values. There are additional columns. Columns that will be of interest in a later chapter are those of coefficient of specific heat at constant pressure, Cp , and the ratio of specific heats, k = Cp / Cv .

Refrigerant 11 (cblorodiDuoromethane)· Properties of Saturated Liquid and Saturated Vapor Delsity, \bIuIt, EaIUlpy, EaIlOpJ, Specific Heat ep' VelocIty .r Solid, VIscosity, 1\tnuI eold, Sarface TeIIp,* Prasart, IbIrtl rl31U1 BIIIIII IIIIIII'·F Ila/ll,.°F eple. WI 1II./r... Itl/l.. fl,·F Teuioa, Temp, 9~~~~_~~~~~~~~~~~~9 -lSO.OO 107.37 -63.169 76.604 -0.2191. 0."952 0.1018 1.291. 395. - -2S0.00 106.41 -240.00 -S6.~ n.629 -0.18786 0.42332 0.1033 1.2860 403. - -:MO.OO -230,00 . 105.48 - -51.569 78.669 -0.16605 0.40101 0.1048 1.2807 411. 36.7S - 230.00 -220,00 0.002 IU..58 1680S. -47.705 79.724 -0.14958 0.38211 0.1064 1.27504 419. 35.70 -220.00 -lIO.OO O.~ 103.70 6982.6 - ".426 80.796 -0.13616 0.36538 0.1080 1.2703 .27. 34.67 - lIO.OO

-

Figure 4-4. Thermodynamic Properties of Saturated R-22

4.3

Tablesfor Superheated Vapor and Compressed Liquid

Superheated vapor tables cover the region to the right ofthe saturated vapor line on the t-v diagram shown in Figure 4-1. The term superheated comes from the fact that, for a given pressure, the temperature is greater than the saturation temperature. In an example of water at atmospheric pressure, the vapor is superheated if the temperature is greater than the saturation value of 212°F. In the superheated region, the pressure and temperature are independent properties. Therefore, the superheated vapor table actually consists of a set of many tables, each for a different pressure, in which the entries are made according to temperature.

Fundamentals of Thermodynamics and Psychrometries

Chapter 4 Thermodynamic Tables and Charts

4: 10

The compressed liquid tables cover the region to the left of the saturated liquid line on the t-v diagram in Figure 4-1. The term compressed comes from the fact that, for a given temperature, the pressure is greater than the saturation pressure for that temperature. Pressure and temperature are independent properties in the compressed liquid region. The compressed liquid table is a set of tables, each for a different pressure, in which the entries are made according to temperature. The interval in pressures between tables is usually quite large because liquid properties vary less with pressure than do vapor properties. Liquids are often treated as incompressible.

4.4

Thermodynamic Liquid/Vapor Charts

A chart for R-22 is given in Appendix C. A simplified version of that chart is given in Figure 4-5. Figure 4.5 is simplified only in the sense that there are a limited number of constant property lines shown, so that it is easier to explain the chart's complexity. Reference in the next few paragraphs will be to Figure 4-5, but it is the chart in Appendix C that should be used to obtain values. The chart in Figure 4-5 is a plot of pressure against enthalpy. In this case, the pressure is given a log scale. Lines of constant pressure run horizontally across the chart. Lines of constant enthalpy run vertically up and down the chart. The saturated liquid and saturated vapor lines outline a fairly characteristic dome shape to the central part of the chart. The saturated liquid and saturated vapor lines are lines of constant quality (respectively x = 0 and x = 1). Other lines of constant quality can be drawn as shown for x = 0.02 and x = O.S. Because quality is only defined for equilibrium mixtures of saturated liquid and vapor, these lines of constant quality do not extend outside the region bounded by the saturated liquid and vapor lines. The lines of constant temperature on the chart in Figure 4-5 have three distinct parts. Por example, the line for Soop falls steeply in the compressed liquid region until it reaches the saturated liquid line. It then extends horizontally across from the liquid to the vapor line, following the constant pressure line ofPSOI = 15S.40 psia for tsol = SooP. After reaching the saturated vapor line, the line for Soop once again falls very steeply. The line for 200 0 P follows a similar path, but because it is close to the critical temperature of 205.06°P, it seems to barely enter the dome near the critical point. Lines of constant density (inverse of specific volume) are shown for values of 1.0 Ibm /ft3, 15 Ibm /ft3 and 65 lb m /ft3. Lines of constant entropy are shown for 0.3 Btullbm ·R and 0.16 Btullbm .R.

Chapter" Thermodynamic Tables and Charts

Fundamentals ofThermodynamics and Psychrometries

4: 11

Enthalpy (Btu/Ibm) 2000.25

0

50

25

125

150

~

u.

1000

100

oensi\.'i :;

:£

0

0 GO II

\'oJtt' 1000

-

400

200 2000

175

'\5

'b /ft::::.. ~r-.;

400

~O'<

~~

~ II) -9: 100

:i? II)

/

Density

~

:J

='I Ib

0..

.Ift3

100 -;-

....

:J

II) II) Q)

II) II)

~

e..

40

40

10

10

....

e..

u.

o

o o

4

4

~ 1 -25

~

__

~L-

0

_ _ _ _ _ _ _ _ _ _ _ _ _ _~_ _ _ _2 -_ _ _ _~_ _ _ _- L_ _ _ _ _ _ _ _ _ _ _ _ _ _ J

25

50

75

100

125

150

175

1

200

Enthalpy (Btu/Ibm)

Figure 4-5. Pressure-Enthalpy Diagram for R-12

There are many alternative charts because it is choice of convenience as to which properties are selected for the axes of the chart. The charts plotting enthalpy against either pressure or temperature are useful in vapor-compression refrigeration because the constant enthalpy and constant pressure processes are easily shown. Previously, when introducing property diagrams, we found it convenient to describe the temperature-volume (t-v) and pressurevolume (P-v) charts. Another combination that is partiCUlarly convenient when studying compressors and turbines is the temperature-entropy, or t-s, chart. The Mollier chart, widely used in steam turbine work, is a plot of enthalpy against entropy (h-s) for water. Charts are difficult to read on the scale that is drawn in this text. Much larger versions of these charts are usually used to determine specific property values. A more common use of property charts is to provide a visual map of a sequence of processes, with a clear indication of the path and end states. Another purpose is to use the chart to determine which table is appropriate to use: compressed liquid, saturated or superheated vapor.

Fundamentals of Thermodynamics and Psychrometries

Chapter 4 Thermodynamic Tables and Charts

4: 12

The Next Step In this chapter, the emphasis was on finding the property values for substances in a range that included the phase change from liquid to vapor. In Chapter 5, we will consider what to do for ideal gases and for substances that act like ideal gases in the pressure and temperature range of interest. Air at moderate temperatures and pressures is taken as an example of a real gas approximated as an ideal gas.

Summary

In Chapter 4, we developed the understanding and skill of finding properties in the saturated tables for water and R-12. The saturated tables are shown to provide a relationship between P sat and tsat • Values for properties in the mixed liquid and vapor region can be obtained from the saturated values. The tables included values for pressure, temperature, specific volume, specific enthalpy and specific entropy. The linear interpolation technique is used to determine values between the table entries. A chart ofR-22 is used as an example to demonstrate the use of charts. After studying Chapter 4, you should be able to: • Understand the format and content of the different tables and charts; • Find the value of common properties in the tables; • Interpolate to determine values between the entries in the tables; and • Determine the property values of liquid-vapor mixtures.

Chapter 4 Thermodynamic Tables and Charts

Fundamentals ofThermodynamics and Psychrometries

4: 13

Skill Development Exercises for Chapter 4 Complete these questions by writing your answers on the worksheets at the back of this book. Be sure to include your name and address. Send your completed questions to the ASHRAE Education Department.

4-01. The saturated temperature of water is 100°F. What is the pressure? What are the liquid and vapor values of specific volume, specific enthalpy and specific entropy? (Use the table in Appendix B.)

4-02. The saturated temperature of water is 100°F and the quality is 50%. What is the value of specific volume and specific enthalpy? (Use the table in Appendix B.)

4-03. The saturation pressure for R-22 is 50 psia. What is the saturation temperature? (Use the table in Appendix C)

4-04.

The saturation temperature for water is 231.5°F and the quality is 0.2. What is the pressure and the specific enthalpy? (Use the table in Appendix B.)

4-05. The enthalpy for R-22 is 50 Btu/Ibm and the pressure is 40 psia. Is the refrigerant in the compressed liquid, saturated or superheated vapor state? What is the quality? (U se the chart in Appendix C)

4-06.

The enthalpy for R-22 is 50 Btu/Ibm and the temperature is 100°F. Is the refrigerant in the compressed liquid, saturated or superheated vapor state? What is the pressure and the quality? (Use the table in Appendix C)

4-07.

The enthalpy for R-22 is 150 Btu/Ibm and the pressure is 40 psia. Is the refrigerant in the compressed liquid, saturated or superheated vapor state? What is the value of the density? (Use the chart in Appendix C)

Fundamentals of Thermodynamics and Psychrometries

Chapter 4 Thermodynamic Tables and Charts

5: 1

Chapter 5 Ideal Gas Law and Air Tables

Contents of Chapter 5 • Instructions • Study Objectives of Chapter 5 • 5.1

Ideal Gas and the Ideal Gas Law

• 5.2

The Ideal Gas Law as an Equation of State

• 5.3

Constant Specific Heat

• 5.4

Air Tables

• The Next Step • Summary • Skill Development Exercises for Chapter 5

Instructions Read the material of Chapter 5. Re-read the parts of the chapter that are emphasized in the summary and memorize important definitions. At the end of the chapter, complete all ofthe skill development exercises without consulting the text.

Study Objectives of Chapter 5 The ideal gas law expresses the relationship between pressure, temperature and specific volume for an idealized model of a gas. The study objective for Chapter 5 is to understand how the ideal gas law may be used to determine the state properties of pure substances that can be reasonably assumed to act as an ideal gas. Air at room temperature and pressure can often be treated as an ideal gas. There is an introduction to the use of air tables. After studying Chapter 5, you should be able to: • State the ideal gas law; • Express the limitations to the use of the ideal gas equation; • Describe the use of the ideal gas law in determining state properties; • Describe the coefficients of specific heat as properties; and • Determine the enthalpy for an ideal gas with constant specific heat.

Fundamentals of Thermodynamics and Psychrometries

Chapter 5 Ideal Gas Law and Air Tables

5:2

5.1

Ideal Gas and the Ideal Gas Law

An ideal gas does not exist in reality. The theoretical construction of an ideal gas is one where the molecules that make up the gas are so far apart from each other that they have no influence on each other. It is impossible for molecules to have no influence on each other, but it is possible for a substance oflow enough density to behave approximately as an ideal gas. In fact, many common substances that we describe as gases (such as oxygen, nitrogen, carbon dioxide and air) have low enough densities at atmospheric pressures and temperatures to be reasonably described as ideal gases. This really means they behave as ideal gases to an acceptable limit of error. This does not imply that they will behave as ideal gases at all pressures and temperatures. To the contrary, to be reasonably treated as an ideal gas, the state of the substance must be such that the density is small enough so that individual molecules are far enough apart from each other and that they seldom run into each other. The density is the inverse of the specific volume. Therefore, an ideal gas is a substance in which the specific volume is large enough, and the individual molecules are far enough apart, that the molecules have negligible effect on each other. As described earlier, the specific volume varies depending on the state of the substance. For all pure substances, there are solid, liquid and vapor phases. A substance will not behave as an ideal gas in the solid, liquid or much of the vapor phase areas of the phase diagram. Only in the vapor phase range at low enough pressures and high enough temperatures will the vapor behave as an ideal gas. The vapor behaves less and less like an ideal gas the closer the state is to the critical point or the saturated vapor line. For the theoretical ideal gas, the pressure varies proportionally to the absolute temperature and inversely proportionally to specific volume, leading to the ideal gas law which states:

p=R(Tlv) pv=RT The R in this equation is the constant of proportionality in the relationship and is known as the gas constant. It is important that the temperature in the equation is in absolute units (Rankine or Kelvin). To draw a clear distinction of places where the temperature must be in absolute units, we will use the upper case T. The value of the gas constantR is different for every gas and may be determined by dividing the universal gas constant, Ru ' by the molar mass, M, of the substance (often called molecular weight):

Chapter 5 Ideal Gas Law andAir Tables

Fundamentals ofThermodynamics and Psychrometries

5:3

The units of molar mass are lbmoeI lIb m . The value of the universal gas constant is:

Ru

= 10.73 (psia.fe)/(lb mole .R) = 1.98 Btu I (lb mo1e • R) = 8.314 kJ I (k mo1e .K)

The values for molar mass and gas constants for some common gases are given in Table 5-1. The ideal gas law may be expressed in several different forms. For example, the specific volume may be replaced by the total volume divided by the mass of the system. Another form is to write the gas equation for a given number, N, oflbmo'es of gas rather than a mass in lbm . The various forms are summarized below:

pv=RT pV=mRT pV = NRuT

Table 5-1. Gas Constants for Certain Substances ;

Gas Carbon dioxide , Hydrogen , Nitrogen Oxygen Air , R-22 Water

,

Molar Mass (lb",llb mo1e) 44.0995 2.01594 28.0134 3,1.9988 28.9645 102.92 18.01528

Fundamentals ofThermodynamics and Psychrometries

,

,

Gas 'Constant (psiaxft~/(lbmXR) , 0.2438 5.3224 0.3830 0.3353 0.3704 0.1043 , 0.5956

Chapter 5 Ideal Gas Law andAir Tables

5:4

5.2

The Ideal Gas Law as an Equation ofState

In the previous chapter, we said that the functional relationships between properties such as pressure, temperature and specific volume were mathematically complex enough that these values are tabulated for water and other refrigerants. The tables are cumbersome but necessary. However, in areas where the substance behaves as an ideal gas, the ideal gas equation provides a more convenient alternative. The simple relationship among pressure, temperature and specific volume in the ideal gas law suggests that given any two properties, we can calculate the third. The ideal gas law is an example of an equation of state for substances that obey the ideal gas relationship between pressure, temperature and specific volume. In HVAC, it is fortunate that air, and the water vapor in air, can be treated as ideal gases for typical atmospheric conditions. There will be a more careful evaluation of this statement in the chapters on psychrometrics, but for now, consider some examples applying the ideal gas equation of state to air. How would you determine the mass of air in a room of dimensions 10 ft x 20 ft x 8 ft, where the pressure is 14.7 psia and the temperature is 75°P?

m= pV I RT

= (14.7 psia)(10 x 20 x 8 ft3) I {( 0.3704

(psia. ft3))1 (Ibm· R)(75 +460 R)}

= (118.7 Ibm)

What pressure is required if air at 32°P is to have a density ofO.15 Ibm/ft3 (density, p, is the inverse of the specific volume)?

p= RTlv =pRT

= (0.15 Ibm I ft 3){0.3704(psia. ft3) I (Ibm· R)}(32 +460 R) = 27.3 psia The relationship between two states of an ideal gas can be seen by equating the gas constant when the gas is at State 1 to the same gas constant when the gas is at State 2: p\v\ II;

= P2V 2 IT;

Chapter 5 Ideal Gas Law andAir Tables

Fundamentals of Thermodynamics and Psychrometries

5: 5

This relationship holds as long as the gas can be treated as an ideal gas. It does not depend on the path by which the substance goes from State 1 to State 2. Consider a constant volume process for which the initial pressure and temperature are PI = 14.7 psia and tl = 72°F. What is the final pressure if the substance is air, can be treated as an ideal gas and is cooled to 32°F? V2

= VI; PI = 14.7 psia; ~ = (72 +460) = 532 R;

Tz = (36+460) = 496 R

From the ideal gas law:

P2 = (VI / v2)(Tz / ~)(PI) =(496/532)(14.7) = 13.71 psia It is again worth noting that when working with the ideal gas law, it is important to use

absolute temperatures. In the example above, if absolute temperatures were not used, then the expression would have incorrectly predicted a final pressure of one-half of the initial pressure.

5.3

Constant Specific Heat

The ideal gas equation of state relates pressure, temperature and specific volume, but what about the other properties that were listed in the water and refrigerant tables given earlier? How is the enthalpy, or the entropy, determined for an ideal gas. To answer that, we will introduce another new property, specific heat, and we will make the observation that it is the change of enthalpy that interests us more than the absolute value of enthalpy. The term coefficient ofspecific heat is probably known to you from its application in physics. The coefficient of specific heat of unity for liquid water means that it takes one Btu to heat one lbIII of water by one degree Fahrenheit. For gases, we want to apply a similar idea, but it takes a more careful definition because there are two coefficients of specific heat. One is the coefficient of specific heat at constant volume, cv' and the other is the coefficient of specific heat at constant pressure, cp' Contrary to their names, they are not meant to be used only in cases of constant volume or constant pressure. Rather, they are defined in terms oftheir connection to either internal energy, U, or to enthalpy, h.

Fundamentals of Thermodynamics and Psychrometries

Chapter 5 Ideal Gas Law andAir Tables

5:6

For an ideal gas, the coefficient of specific heat at constant volume is: Change of internal energy = cl' times change in temperature

and, for an ideal gas, the coefficient of specific heat at constant pressure is: Change of enthalpy = cp times change in temperature

Strictly speaking, the expressions above apply for only constant values of specific heat. It is possible for the specific heat to vary with temperature and, in those cases, the changes have to be taken over a small temperature range at a time. The distinction between these two specific heats will be elaborated on later when we have developed the idea of work in thermodynamics. For ideal gases, the specific heats do not depend on pressure. Therefore, there is an important deduction that says: For ideal gases, the internal energy and enthalpy are functions of temperature only_

F or the case of constant specific heat, it is straightforward to construct a table of internal energy or enthalpy values as a function of temperature by applying the relationships given above. The coefficients of specific heat can be related to each other. Because enthalpy is related to to internal energy by h = (u + pV), and because the ideal gas law is pv = RT, we can write:

(~-~)=(U2 -UI )+(P2 V 2 -

P1V I )

cAt2 - tl ) = Cv (t2 - t l ) + R(t2 - t l )

Dividing through by the temperature difference gives the relationship between the specific heats and the gas constant as:

cp =cl' +R

Chapter 5 Ideal Gas Law and Air Tables

Fundamentals ofThermodynamies and Psychrometries

5: 7

Another useful property is the ratio of specific heats, k.

Typical values of the coefficients of specific heat for air treated as an ideal gas at 80°F are: C = 0.240 Btullb .OF and C = 0.171 Btullb .oF, which result in a k value of 1.4. p m v III

To determine the values of entropy for an ideal gas (comparable to the values found in the tables for water and refrigerants given earlier), we must have a better understanding of entropy. We are not going to discuss entropy here, because it first takes the introduction of the Second Law of Thermodynamics, but below are the expressions that are used to determine entropy changes for an ideal gas in the cases of constant specific heat:

(S2 -SI) = cl' In(~ 17;)+ R In(v2 Iv l ) (S2 -

SI) = cp

In(~ 17;) + R In(p2 I PI)

For ideal gases, enthalpy is a function of temperature only, but entropy depends on both pressure and temperature.

5.4

Air Tables

The thermodynamic properties for air can be tabulated the same way as they are done for water and refrigerants. The tabulations take into account the way specific heat changes with temperature. The values are usually listed as a function of temperature for a given pressure. An example of a moist air table is given in Appendix D for a pressure of 14.696 psia. The moist air table includes dry air as one of the cases. The moist air table will be more fully explained during the discussion of psychrometrics.

Fundamentals of Thermodynamics and Psychrometries

Chapter 5 Ideal Gas Law andAir Tables

5: 8

The Next Step Now that we have defined a number of useful properties, and learned how to find numbers for those properties, we are ready to return to the discussion about different forms of energy. In the next chapter, we will introduce the ideas of work and heat in preparation for describing the First Law of Thermodynamics.

Summary The ideal gas law expresses the relationship among pressure, temperature and specific volume for an idealized model of a gas. The relationship is given by pv = RT. The use of the equation is limited to applications where the behavior of the substance can be reasonably approximated by that of an ideal gas. This is usually in the low pressure/high temperature range of the superheated vapor region. Vapors do not behave like an ideal gas near the saturated vapor line, or near the critical point. The use of the ideal gas law as an equation of state permits the determination of the remaining value of the properties pressure, temperature or specific volume, if any two of these properties are known. The properties of specific heat at constant volume and specific heat at constant pressure are introduced as a means for determining internal energy and enthalpy for an ideal gas. For many applications, air at room conditions may be treated as an ideal gas with constant coefficients of specific heat. After studying Chapter 5, you should be able to: • State the ideal gas law; • Express the limitations to the use of the ideal gas equation; • Describe the use of the ideal gas law in determining state properties; • Describe the coefficients of specific heat as properties; and • Determine the enthalpy for an ideal gas with constant specific heat.

Chapter 5 Ideal Gas Law and Air Tables

Fundamentals ofThernwdynamics and Psychrometries

5: 9

Skill Development Exercises for Chapter 5 Complete these questions by writing your answers on the worksheets at the back of this book. Be sure to include your name and address. Send your completed questions to the ASHRAE Education Department.

5-01.

Air is often treated as an ideal gas. For the conditions of p = 14.696 psia and t = 72°F, find the specific volume for dry air, va' in Appendix D, and compare the value read in the table to the value calculated using the Ideal Gas Law. Use T= t + 459.67 to convert from of to R. Use the value of gas constant given in Table 5-1. Express the answer as a percent error by treating the tabulated value as being correct.

5-02.

Water vapor is sometimes treated as an ideal gas. For the condition ofp = 67.0341 psia, find the specific volume for saturated vapor, vg , in Appendix B, and compare the value read in the table to the value caclulated using the Ideal Gas Law. Use T= t + 459.67 to convert from of to R. Use the value of gas constant given in Table 5-1. Express the answer as a percent error by treating the tabulated value as being correct.

5-03.

Repeat Exercise 5-02 except for conditions of saturated vapor at p = 0.3628 psia. Compare the error found with the error determined in Exercise 5-02 and comment on the difference.

5-04. A room of dimensions 10ft x 20 ft x 8 ft at atmospheric pressure contains 120 Ibm of air. Assume an ideal gas and estimate the temperature in the room in of. 5-05. Consider the constant pressure heating of air from 70°F to 200°F. If the pressure is 14.7 psia, what is the ratio of specific volumes before and after the heating? 5-06. Make a table listing the values of internal energy, enthalpy and entropy for air at 14.696 psia, with temperatures ranging from O°F to lOO°F in steps of lOoF, using the coefficients of specific heat suggested for air at 80°F in the text. Use reference values of zero internal energy, zero enthalpy and zero entropy at O°F. 5-07. Find the values of enthalpy for dry air in the table in Appendix D, at the same temperature entries used in the table created in Exercise 5-06 and compare calculated and look-up values. Calculate percent error assuming the tabulated values to be correct.

Fundamentals ofThermotlynamics and Psychrometries

Chapter 5 Ideal Gas Law and Air Tables

6: 1

Chapter 6 Heat and Work

Contents of Chapter 6 • Instructions • Study Objectives of Chapter 6 • 6.1

Introduction

• 6.2

Heat

• 6.3

Work

• 6.4

Flow Work

• The Next Step • Summary • Skill Development Exercises for Chapter 6

Instructions Read the material of Chapter 6. Re-read the parts of the chapter that are emphasized in the summary and memorize important definitions. At the end ofthe chapter, complete all ofthe skill development exercises without consulting the text.

Study Objectives of Chapter 6 There are three ways in which energy can cross a system boundary. It can cross the boundary as heat, as work, or (in the case of an open system) as an item carried by mass flow. The energy forms of heat and work are the topics of study in this chapter. Heat is an expression of the flow of thermal energy. Work may appear as moving boundary work, shaft work, electrical work, gravitational work, acceleration work or flow work. After studying Chapter 6, you should be able to: • Describe the concept of heat as an energy form crossing a system boundary; • Describe the concept of work as an energy form crossing a system boundary; • Describe the different types of mechanical work; and • Understand the termflow work and relate it to enthalpy.

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6.1

Introduction

There are three important ways in which energy can be exchanged between a system and its surroundings that warrant special description in thermodynamics. Energy can cross a system boundary as heat or work, or it can be transported by a flow of mass. Earlier, we introduced the concept of internal energy as a property of a system that could be used to help determine the state of the system. Heat and work are different. They are forms of energy that are not properties of the system and, therefore, do not determine the state of the system. Heat and work can cause the state of a system to be changed (as we shall see later), but they cannot define the state of the system. Heat and work are associated with the mechanisms of energy exchange between the system and its surroundings. They are known as transient forms of energy because they only have meaning as the action of energy exchange is taking place. Another way of stating the difference is to say that although a system may contain a certain amount of energy at a given state (internal energy, potential energy or kinetic energy), the system never contains heat or work. The system gains or loses energy by heat and work as it changes from one state to another. Besides the exchange of energy by work or heat, energy can also be carried in or out of an open system when there is mass flow across the system's boundary. Mass flow at the boundary, and its resulting effect on the energy balance of the system, will be discussed when applying the First Law of Thermodynamics to open systems. Heat and work are both forms of energy, but they differ in their driving mechanisms. Heat exchange occurs because of a difference in temperature between the system and its surroundings. In contrast, work has several manifestations such as boundary work, shaft work, electrical work, gravitational work, acceleration work and flow work, which generally occur because of a difference in forces.

Figure 6.1 shows a closed system with energy exchange with the surroundings in the Chapter 6 Heat and Work

Surroundings

Work, W

r--------------System

Heat, Q Figure 6-1. Closed System With Sign Convention for Heat and Work

Fundamentals of Thermodynamics and Psychrometries

6: 3

form of heat, Q, and work, W. Heat and work can cross the boundary in either direction, in or out, but the sign conventions for the two are different. Heat is positive when it is directed into the system. Work is positive when it is directed out of the system, or when the system is said to do work on the surroundings. The sign convention originates with the idea of a heat engine in which heat is supplied to the system so that it can do work as an output. An automobile is an example of a heat engine because the energy from burning fuel is converted into shaft work to tum the wheels. Heat and work are the topics of the next two sections.

6.2

Heat

Consider a hot potato that has just been taken from the oven. With time, the potato will cool as energy is transferred from it to the surrounding air. The temperature difference between the potato and the air causes the exchange of energy, and when the temperature between the potato and the air becomes negligibly small, the exchange of energy will cease. The direction of the energy exchange is always from the higher temperature body to the one at a lower temperature. Heat is the name given to the transitory form of energy as it crosses a boundary separating systems (or a system and its surroundings) by virtue of a difference in temperature. For the potato example, heat is the energy that passes from the potato to the air. This means that some of the potato's internal energy is converted to heat as it flows across the boundary, and then is converted back to become part of the air's internal energy. We do not speak of either the potato or the air as containing heat. In this sense, the use of the term heat is quite specific in thermodynamics and does not include many everyday references that actually more correctly identify internal energy rather than heat. The expressions heat content offuel and body heat are examples of situations where it is really the internal energy that is referred to. Why make such a strong distinction between heat and internal energy? It is important because internal energy is a property and heat is not. Whereas properties are used to identify states, heat)~~ only help determine the process between states. Heat has the units of energy and is usually given the symbol Q. Because heat is a transitory energy form that often occurs as a system goes from one state to another, the states are added to the symbol designation as JQ2, meaning the heat in going from State 1 to State 2. The heat symbol Q is never given a single state designation, such as QJ' to emphasize that heat is not a property associated with any particular state. The direction of flow of energy across the boundary is important. The sign convention is that a positive value of Q means flow of energy from the surroundings into the system. A negative value of Q means a flow of energy out of the system. Fundamentals ofTilermotiynamics and Psychrometries

Chapter 6 Heat and Work

6:4

This sign convention originates from the idea of a heat engine where heat is added to the system to make the system do work, as with an automobile. Sometimes it is inconvenient to keep up with the positives and negatives, and the alternative is to subscript Q with the labels in or out to indicate the direction of energy flow, and then remember to place the appropriate sign when doing an energy balance. We shall see many examples of energy balances when we discuss the First Law of Thermodynamics in the next chapters. The energy flow as heat into the system is referred to as heat addition, while the energy flow as heat out of the system is known as heat rejection. There are two other ways in which the heat term will commonly appear in thermodynamics equations. There is the heat per unit mass, known as q (Btu/Ibm)' and the heat per unit time, known as

Q(Btu/h).

Consider again the potato taken from the oven (as shown in Figure 6-2). The potato is initially at 260°F and the surrounding air is at 76°F. From our discussions about internal energy and the coefficient of specific heat for solids in Chapter 5, we can estimate the energy content of the potato at any time. Assume a reference datum for internal energy as zero at 32°F (arbitrary choice), amass ofm = 0.5 Ibm ,and a coefficient of specific heat of cp = 1 Btu/Ibm .0F, then the internal energy when the potato is first taken from the oven (State 1), and the internal energy after a long time when the potato has come to equilibrium with the room air (State 2), are respectively:

U\ =mcAt\ -tref )

= (0.5 lbm)(l Btu /lb m •o F)(260 = 114 Btu

32° F)

U 2 =mcAt2 -tref )

= (0.5 lbm)(l Btu /lb m·o F)(76 - 32° F) =22 Btu

The heat crossing the boundary, JQ2 , is: \Q2

=(U2 -U\) = -92 Btu

Chapter 6 Heat and Work

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,'" _.... ~ \\

>. \. ..I

Alternative = 92 Btu

.. Qout

State 1

Process 1- 2

State 2

Figure 6-2. Potato (Closed System) Cooling From 260°F to 76°F

Note that this is a special form of the First Law of Thermodynamics in which the work is zero because there is no change in volume of the potato. Descriptions of work appear in the next section, and the First Law is in Chapter 7. The minus sign means that the heat is being rejected. The arrow is shown in Figure 6-2 flowing into the potato, but the negative value means that it really is in the opposite direction. Alternatively, this could be described as 92 Btu rejected from the system, and be expressed as:

IQ2 oul

= 92 Btu

The arrow pointing out of the system with the positive value of 92 Btu is shown as an alternative (dashed) in Figure 6-2. A process in which there is no heat is known as an adiabatic process. There are two circumstances under which a process may be adiabatic. The system may be well insulated, resulting in negligible energy flow even if there is a temperature difference, or there may be no temperature difference between the system and its surroundings. The temperature in an adiabatic process may, or may not, remain constant, depending on other energy flows taking place, such as work. Therefore, an adiabatic process is not the same as an isothermal process. In an isothermal process, the temperature of the system does not change while going from one state to the next, but there mayor may not be heat transferred.

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6.3

Work

Work is the name given to the transitory fonn of energy as it crosses a boundary separating systems (or a system and its surroundings) by virtue of a difference in pressure or force of any kind. Like heat, work is not a property, and is only defined while the energy interchange is occurring across the system boundary. Work has units of energy and is assigned the symbol W. When the work occurs while going from State 1 to State 2, then the work is specified as 1 W2 • The work per unit mass is w Btu/Ibm' The rate of doing work, W Btu/h, is also known as power, P. Power appears in many different units, and may be given as Btu/h, ft-Ib/s, horsepower hp, or kW. There are many different fonns of mechanical work, each in some way connected to a force being moved over some distance. From physics, work is defined as the product of force and displacement (in the direction of the force). We will use that basic definition and develop the expressions for some common fonns of work.

Moving boundary work. Consider a piston-cylinder arrangement as shown in Figure 6-3. The pressure in the cylinder is p, the piston area is A, and the volume of the air in the cylinder is V. The piston is weightless and frictionless and it takes a force of F = pA to keep the piston in place. If the piston (and therefore the system boundary) moves a small distance f:ls, and the system volume increases by a small amount from V to (V + ~V), then the small amount of work done by the force F moving through distance f:ls is:

,-

, __...>1

~W

= F·f:ls

------------~--------

= (pA)f:ls

=p(Af:ls) =p~V

Pressure p

Volume V Figure 6-3. Boundary Work by a Piston in a Cylinder

Chapter 6 Heat and Work

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The work is given as the product of the pressure and the small change of volume. The small change in volume is emphasized here because to get this result, we actually assumed that the pressure remained constant while the volume was changing. Constant pressure represents only a special case of the more general situation where pressure can vary in a variety of different ways with volume change. A case of air expanding in a cylinder is shown in the p- V diagram of Figure 6-4, where the air is shown starting at State 1 and expanding to a lower pressure at State 2. The path between States 1 and 2 is drawn as an arbitrarily shaped curve. The expression developed above for work as p!1Vapplies for the thin slice shown in Figure 6-4 and is the area of that slice on the p- V diagram. To find the work done in going from State 1 to State 2, it would be necessary to add up the areas of many thin slices from the p- V diagram: I

~

= Area under the p - V diagram =LP!1V

The symbol sigma, ~, is used to indicate the sum of all the small areas p!1V. The boundary work is the area under the p- V curve. In evaluating moving boundary work of a closed system, it is very useful to sketch the p- V diagram to obtain a visual picture of the work done. The results to the example of a piston in a cylinder can be stated more carefully and generally. Moving boundary work for the quasi-equilibrium and reversible movement of the boundary of a closed system can be estimated from the area under the p- V diagram. Quasiequilibrium change was described in Chapter 2 as a change that proceeds in such a manner that the system remains infinitesimally close to an equilibrium state at all times. A quasiequilibrium process is an idealization of a real process. Reversibilty is a concept yet to be introduced and will be an important part of a later chapter. A process is said to be reversible ifboth the system and its surroundings can be restored to their original condition. Effects such as friction, non-quasi-equlibrium or heat transfer through a finite temperature difference render a process irreversible. Therefore, reversibility is also an idealization of a real process because no process can actually meet all of the requirements. The sign convention for work is that it has a positive value when work is done by the system on the surroundings. That is the case for the expansion shown in Figure 6-4. If the piston moved in the opposite direction so as to decrease the volume (as in compression), then work would be done on the system, and the sign would be negative. This is the opposite sign convention to that applied to heat.

Fundamentals of Thermodynamics and Psychrometries

Chapter 6 Heat and Work

6: 8

Pressure

P

I I I I I I ____ _ - __ 1I I

- - - ~ - - - - -~ - - - - - - - -=--....-....-......-.~ ®

~

:

~

1

I

V2

AV=AAS

Volume

AS ~

f

1

l+-

I I

~

l}

I I I I

.

Figure 6-4. Boundary Work as the Area Under the p-V Curve

There are many different paths by which the pressure can change as a system goes from State 1 to State 2. The work done by the moving boundary (area under the p- V curve) for a closed system is given for a list of specific processes below and shown in the p-V diagrams in Figure 6-5: Constant pressure process,p] = P2 ' any substance:

IT¥; = PI(V2 - v;) = P2(V2 - v;) Constant volume process, ~

=

V2 ' any substance:

IT¥; = zero

Chapter 6 Heat and Work

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Isothermal process, T] = T2 ' ideal gas only P V = constant: 1

~

= Pl~ In(V2 I~) = P2 V2 In(~ I~)

Isentropic process, s] I

~ = (P2 ~ -

= S2

PI

,P V" = constant, ideal gas only, P V = mRT:

~) 1(1- k) = mR( 1; -

Polytropic process, P vn = constant, n 1

7;) 1(1 - k)

* 1, ideal gas only, P V = mRT:

~ = (P2~ - pl~)1 (1- n) = mR(1; - 7;)1 (1- n)

Pressure

Pressure Constant Pressure

Constant Pressure

CD ® Volume

Pressure

Volume

Pressure

CD

Isothermal, Ideal Gas

Isentropic, Ideal Gas

pV = constant

V2

Volume

V2

Volume

Figure 6-5. Work as Area Under the p-V Curve for Closed Systems and Different Processes

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This may seem a formidable list, but you do not need to memorize all these expressions. They are given to emphasize that the work is a path-dependent function and that the moving boundary work may be calculated when needed. The above expressions apply to closed systems. The derivations of the above expressions are not shown, but it can be seen that they depend on the type of process and the substance. In the case of an isentropic process with ideal gas, it can be shown that the process is given as p V" = constant, where k is the ratio of specific heats. Often, it is experimentally seen that the compression or expansion follows a process that is not quite isentropic, but where the process can be described with an expression p V" = constant. This is called a polytropic process, and n is the polytropic exponent.

Example 6-1. A frictionless piston-cylinder device contains 10 Ibm of saturated liquid water at 212°F. The fixed weight piston is not attached to a shaft. Heat is added to the water until it is all saturated vapor. Calculate the work done by the system. Solution. The piston-cylinder and p-V diagram are shown in Figure 6-6. Because of the fixed weight piston with no shaft, the pressure remains constant. The pressure may be found for saturated water at 212°F from the saturated water tables in Appendix B-1 as 14.7096 psia. From the same table, the specific volume of saturated water is vj = v J = 0.01671 ft3/lb m and the specific volume for saturated vapor is Vg = v2 = 26.780 ft 3/lb m• The volume is the mass times the specific volume. The rectangular area under the curve gives the work as:

I~

=

Pl m(v2 -VI)

= (14.7096 psia)(10 lb m )[ (26.780- 0.01671) ft3 /lb m ][ (1 Btu) I (5.404 psia· ft3)] = 728.3 Btu The work is positive because the system does work on the surroundings.

Chapter 6 Heat and Work

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6: 11

Pressure

p=

r- - - ---- --

14.7096 pSia

Saturated /VaporLine

,-f,-fl-Vapor

ttttt Liquid

Vg

Vt

ft3

=0.0167116

ft3 =26. 780 16

Specific Volume V

Figure 6-6. p-v Diagram for Constant Pressure Process

ft3

Example 6-2. A piston-cylinder device initially contains 1.0 of air at 20 psia in such a way that the temperature and 76°P. The air is compressed to 0.1 remains constant. Calculate the work done by the system.

ft3

Solution. The piston-cylinder andp-v diagram are shown in Figure 6-7. Assume that air can be treated as an ideal gas, then the relationship PV = mRT = constant applies. The area under the curve gives the work as:

IUS = PIV;

In(~ IV;)

= (20 psia)( 1.0 ft3) In( 0.1 11.0)[(1 Btu) I (5.404 psia· ft3)] = -8.52 Btu

The negative sign indicates that, for compression, work is done on the system.

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Chapter 6 Heat and Work

6: 12

P2 = 200 psi a

P1

= 20 psia

--- -

V

IJ

Figure 6-7. p-VDiagram for Constant Temperature Process of Ideal Gas

In the situation given in Example 6-2, it is also possible to calculate the pressure at the end of the process and the mass in the system. Because it is an ideal gas at constant temperature:

P2 = PI (V; IV;) = (20 psia)[ (1.0 fe I (0.1 fe))] = 200 psia m = (pIV;)(R~)

= (20 psia)(1.0 fe)1 {[0.3704 (psia.fe)/(lb m. R)][(76 + 460)R]} = 0.101 Ibm

Chapter 6 Heat and Work

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6: 13

The moving boundary work for a closed system process is represented by the area under the process curve on the pressure-volume diagram. The sign of the work depends on whether the volume increases or decreases. A cycle is formed by a sequence of processes such that the final state of the final process is the same as the initial state of the initial process. This means that the moving boundary work of the cycle is the net area enclosed within the process curves on the p-V diagram, as shown in Figure 6-8. Shaft work. Shaft work usually refers to the energy transmission by a rotating shaft. If the torque on the shaft is T, and the shaft rotates through an angle q, then the shaft work is:

W=Te s

The angle of rotation is often re-expressed in terms of the number of revolutions as 8 = 2 nN and the work is then: Ws = 2nNT

Pressure p

®

®:1 1

1 1

---t-----1 1 1

---r~------------------

1 1 I

leD I I

1

I

I

I

"---.......1--------------.....,1--... Volume V Figure 6-8. Boundary Work for a Cycle as the Net Area Under the p-V Curve

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Chapter 6 Heat and Work

6: 14

The rate of doing work is:

Ws = (27tnT) / 60 ft ·lbf

/

s

= (27tnT) / 12.97 Btu / h =(27tnT) /33,000 hp =(27tnT) / 44,248 kW where n is the rotational speed in revolutions per minute and T is the torque in ft.lbr Often the shaft work is not given in terms of the torque and speed, but is specified either as a desired output of an engine or the needed power input to run a compressor or chiller. Electrical work. Electrical work appears in two forms in thermodynamics. The first form results from the electrons flowing through a resistance element and doing work at a rate of:

We = VI = 12 R =V2 / R The electrical current is I, the voltage across the element is V, and the resistance of the element is R. If I is in amps, V is in volts and R is in ohms, then the units of W are watts. The other common way of encountering electrical work is through an electrical motor, generator or alternator. The conversion between electrical work and mechanical work is done internally to the device and the result often shows up as shaft work.

6.4

Flow Work

F or open systems, there is also the possibility of mass flow across the boundary. That flow carries a certain amount of internal energy with it as it crosses the boundary, but in addition, the mass flow has to do work at the boundary to either enter or leave the system. A flow stream entering a system has to push its way into the system. This is known as the flow work. The rate of flow work W can be expressed very much as boundary work because it amounts to the boundary being pushed by a force F= pA at a velocity V The pressure,p, is constant at the location where the flow enters the system. The flow work is usually expressed as specific work (work per unit mass flow) so that the work can be identified with the flow

Chapter 6 Heat and Work

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6: 15

stream entering or leaving the system. If the mass flow rate across the boundary is ~ VA/v, then the specific flow work is: Wflow

=

WI m

=

(pA)(V)I (VA I v)

=

=pv The flow work is pv. However, in most cases, the flow work is not identified in a category by itself. It is usually taken care of by considering the enthalpy, instead of the internal energy, that is carried into, or out of, the system by the mass flow. The enthalpy of the system is defined as:

h

= u+ pv

The enthalpy is the sum of the internal energy and the flow work. The units of internal 3 energy and enthalpy are usually given as Btu/Ibm. When p is in psia and v is in ft /lb m, it is necessary to apply the conversion factor 1 Btu = 5.404 psia·ft3/lb mto the pv term. We will see another derivation of the flow work and the enthalpy when we consider the First Law of Thermodynamics for open systems in Chapter 8.

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Chapter 6 Heat and Work

6: 16

The Next Step Now the pieces are in place to discuss the First Law of Thermodynamics. In the next chapter, we will analyze the First Law as applied to closed systems.

Summary Heat and work are transitory forms of energy that exist when energy is crossing a system boundary. Heat is the name given to the transitory form of energy as it crosses a boundary separating systems (or a system and its surroundings) by virtue of a difference in temperature. Work is the name given to the transitory form of energy as it crosses a boundary separating systems (or a system and its surroundings) by virtue of a difference in pressure or force of any kind. Heat and work have many similarities: • Heat and work are not properties; they are associated with a process and not a state. • Heat and work are recognized only at the boundaries of the system as they cross that boundary. • Systems contain energy, but they do not contain heat or work. • Heat and work are path functions because their values depend on the process path as well as the end-states. • Heat and work have direction. The sign convention for heat is that energy addition is positive and the sign convention for work is that work done by the system is positive. Boundary, gravitational and acceleration work may be expressed as: Boundary work for a closed system, ] W2 = Area under the P-V diagram Constant pressure process,p] = P2' any substance:

Constant volume process, V] = V2 ' any substance:

lU;; = zero Isothermal process, T] = T2 ' ideal gas only P V = constant:

1U;; = PI V; In(~ / V;) = P2 ~ In(~ / V;)

Chapter 6 Heat and Work

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Isentropic process, s 1 = I

S2

,p JIk = constant, ideal gas only, P V = mRT:

W; = (P2 V2 - PI ~) / (1 - k) = mR(1; - I;) / (1- k)

Polytropic process, P vn = constant, nil, ideal gas only, P V = mRT:

Also important are shaft work and electrical work. For open systems where there is mass flow into or out of the system, there is work associated with the flow called flow work. Flow work is the product of the pressure and the specific volume and is accounted for in open systems by adding the flow work to the internal energy that is carried across the boundary by the flow. The combination of the internal energy and the flow work is the enthalpy: h = u+ pv

After studying Chapter 6, you should be able to: • Describe the concept of heat as an energy form crossing a system boundary; • Describe the concept of work as an energy form crossing a system boundary; • Describe the different types of mechanical work; and • Understand the termflow work and relate it to enthalpy.

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Chapter 6 Heat and Work

6: 18

Skill Development Exercises for Chapter 6 Complete these questions by writing your answers on the worksheets at the back of this book. Be sure to include your name and address. Send your completed questions to the ASHRAE Education Department.

6-01.

Provide a description of heat, and describe how it is different from internal energy.

6-02. A 0.35 Ibm potato at 70°F is placed in an oven at 350°F. After 45 minutes, the potato temperature is 350°F. Assume the coefficient of specific heat for the potato is cp = 1.0 Btu/lbm·oF. If the reference datum for internal energy is U = 0 at t = OaF, then estimate the internal energy content of the potato at the beginning and end ofthe 45 minutes. What has been the heat during the 45 minutes and is it positive or negative? What was the average rate of heat transfer?

6-03.

Provide a description of work in general, and then give short (one- or two-sentence) descriptions of boundary work and shaft work.

6-04. Provide a description of flow work, and say how it is included in enthalpy.

6-05.

A frictionless piston-cylinder device contains 2 Ibm ofwater at 212°F and quality x = 0.4. The fixed weight piston is not attached to a shaft. Heat is added to the water until it is all saturated vapor. Calculate the work done by the system.

6-06.

A piston-cylinder device initially contains 0.2 ft3 of air at 80 psia and 76°F. The air is expanded to 0.9 ft3 in such a way that the temperature remains constant. Calculate the work done by the system, the final pressure and the mass of air.

6-07. In the isentropic compression of air in a cylinder, the volume is reduced from 1.5 ft3 to 0.5 ft3. The ratio of specific heats for air is k = 1.4. The initial pressure is 14.7 psia and the initial temperature is 45°F. Assume the air acts as an ideal gas. Estimate the final pressure, the final temperature and the work done.

Chapter 6 Heat and Work

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Chapter 7 First Law of Thermodynamics Applied to Closed Systems

Contents of Chapter 7 • Instructions • Study Objectives of Chapter 7 • 7.1

Introduction to Controlled Mass Approach

• 7.2

The First Law of Thermodynamics for a Closed System

• 7.3

Conservation of Energy

• 7.4

First Law Applied in Example Cases

• The Next Step • Summary • Skill Development Exercises for Chapter 7

Instructions Read the material of Chapter 7. Re-read the parts of the chapter that are emphasized in the summary and memorize important definitions. At the end of the chapter, complete all ofthe skill development exercises without consulting the text.

Study Objectives of Chapter 7 The objective of Chapter 7 is to develop an understanding of the First Law of Thermodynamics as applied to closed systems. So far, we have developed the ideas and definitions of properties, states, change of states and cycles, and introduced the concepts of heat and work. It is now time to consider the relationship between work, heat and change of energy as we change from one state to another. The relationship is expressed as the principle of energy conservation (or the First Law of Thermodynamics). Initially, the First Law is applied to a closed system (a system for which no mass crosses the system boundary) because the resulting equations are simpler than for an open system.

Fundamentals ofThermotiynamics and Psychrometries

Chapter 7 First Law and Closed Systems

7:2

However, the principle to be applied is the same for closed and open systems. After studying Chapter 7, you should be able to: • Understand the First Law as an expression of the conservation of energy principle; • Write the First Law in equation form by applying an energy balance to a closed system; and • Apply the First Law to simple cases of closed systems.

Chapter 7 First Law and Closed Systems

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7.1

Introduction to Controlled Mass Approach

In an earlier chapter, it was stated that the first step in finding a solution to a thermodynamics problem is to identify the system to be analyzed. A closed system is one in which a quantity of matter is identified for study. A closed system definition is often called the control mass approach. A quantity of matter means that the mass to be studied will remain the same mass throughout the analysis. The matter in the system may change form, phase or location in space, but the system is identified as that matter that originally was targeted for study. There is an imaginary boundary drawn to contain the matter. The location of the matter and, therefore the shape of the boundary, may change with time, but to remain a closed system, no mass enters or leaves the system through the boundary. Everything outside the boundary is known as the surroundings. Although there is no mass exchange across the boundary in closed systems, there may still be work and heat crossing the boundary as the system interacts with its surroundings. An example of closed system is shown in Figure 7-1. The object chosen for demonstration is a piston-and-cylinder combination with air in the cylinder. The air is trapped in the cylinder and there is no way for the air to escape, or for new air to come into the cylinder. The system is chosen to be the matter (mass of air) that is trapped in the cylinder. The system boundary is shown by the dotted line. The surroundings are then the piston, the cylinder

Piston

r----------------'

I

Weight

I

Piston

Closed System

r----------------j I I I I

Closed System

I I I I

~-----------------

Before Adding Weight

After Adding Weight

Figure 7-1. Closed System

Fundamentals of Thermodynamics and Psychrometries

Chapter 7 First Law and Closed Systems

7:4

wall, the cylinder head and everything else outside the dotted line. As weights are added to the piston and the piston moves to reduce the volume in the cylinder, the system (air in the cylinder) is compressed and changes shape, but still maintains the same air that was originally targeted as the system. A closed system analysis is one in which the mass does not change. The analysis is known as the controlled mass approach, and it is characterized by the absence of mass entering or leaving the system, and no change of mass inside the system.

7.2

The First Law of Thermodynamics for a Closed System

F or a closed system undergoing a small change of state, the increase of total energy of the system is equal to the difference between the heat added to the system and the amount of work done by the system on the surroundings: 11£=oQ-oW

Here 11£ is the increase in total energy of the system due to heat transfer into the system oQ and work going out of the system 0 W. The 11 indicates a small change inside the system while the 0 indicates a small flow across the system boundary. 11 and 0 are both said as delta. A negative change in energy would indicate a decrease of energy while negative flow of heat or work would mean they were in the opposite direction to the above conventions.

7.3

Conservation ofEnergy

The First Law of Thermodynamics states that energy can neither be created nor destroyed, it can only change form. In terms of the universe, this may be difficult to see, but if the universe is divided into two parts (a closed system and its surroundings), then it is possible to consider the implications of the First Law by examining the energy associated with the system and the exchange of energy between the system and its surroundings. Because the system is a well defined mass, m, we can talk about the total energy of the system E as being made up of the sum of the microscopic energy (internal energy U) and the macroscopic energy (potential energy PE and kinetic energy KE):

E=U+PE+KE

=m(u+ pe+ke)

Chapter 7 First Law and Closed Systems

Fundamentals ofTI,ermodynamics and Psychrometries

7: 5

There are two ways that energy can cross the system boundary when there is no mass exchange between the system and its surroundings. Energy can cross the boundary as heat (Q, positive when entering system) and work (W, positive when done by the system on the surroundings). If energy can neither be created nor destroyed, then an energy account for system states that: Net energy transfer to (or from) the system as heat or work = Net increase (or decrease) in the total energy of the system or

where I

Q2

= net heat transfer across the system boundary in going from State 1 to State 2 = L 1Q2 in

I

-

L

1

Q2 out

~ = net heat transfer across the system boundary in going from State 1 to State 2

!:!ill = net change in total energy of system between states 1 and 2

= E2 -E) =!::,U+ME+11KE

=m(u2 -ul )+mg(Z2 -z))+m(V;2 -Vn12 and L = the sum of all components

Therefore the First Law of Thermodynamics (or conservation of energy) for a closed system undergoing a process from State 1 to State 2 may be stated as:

For negligible change in the kinetic and potential energy terms, the equation is:

Fundamentals of Thermodynamics and Psychrometries

Chapter 7 First Law and Closed Systems

7:6

7.4

First Law Applied in Example Cases

To develop an understanding of how the First Law of Thermodynamics may be applied to closed systems, we will consider a series of simplified applications in which it will be assumed that the changes in potential and kinetic energy are negligible. These applications are based on two configurations: a rigid tank in which the volume remains unchanged during the process; and a piston-cylinder configuration in which the volume may change as the piston moves. For each configuration, there will be examples of the working fluid being an ideal gas (such as air) or a liquid-vapor combination (such as steam or a refrigerant). The applications will include actual numbers so that the values of properties can be calculated, or read from tables and charts as appropriate, but the solution technique will emphasize the basic solution in symbols before substituting in for the numbers. For each application, there will be a sketch of the configuration and a property diagram (usually p-v) to show the process. Application 1. A rigid tank with a volume of 3 ft3 is initially filled with air at 352.07 psia and 140°F. The air is cooled to 20°F. Treat the air as an ideal gas. Apply the Ideal Gas Law to determine the mass of air in the tank. Apply the continuity equation to determine the final pressure in the tank. Assuming the air in the tank constitutes a closed system, apply the First Law of Thermodynamics to determine the heat transferred during the process. Solution. The air in the tank is taken as the system. The process is assumed to start when the tank is already full of air at p = 352.07 psi a and t1 = 140°F (State 1). The process ends when the air in the tank is cooled to t2 = 20°F,P2 =? Because no mass enters or leaves the tank during the process, this is a closed system. Because it is a rigid tank, the volume remains constant. The configuration is shown in Figure 7-2 along with the p-v diagram showing the constant volume process from State 1 to State 2.

The mass in the tank may be calculated by applying the Ideal Gas Law to the air at State 1:

m= Pl~ / RT; ForP1 = 352.07 psia; V1= 3 ft3; R = 0.3704 (psia·ft3)/(lbm·R) (see Table 5-1); and T1 = (140 + 460)R, the mass is:

m = (352.07 psia)(3 fe) / ([ 0.3704(psia. ft3) / (Ibm' R)]( 600 R)}

=4.75 Ibm The mass of a closed system remains unchanged. The Ideal Gas Law is applied to State 2 to determine the unknown pressure:

P2

= mRT; /~

Chapter 7 First Law and Closed Systems

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For m = 4.75 Ibm; V2 = VI = 3 ft3 (rigid tank); and T2 = (20 + 460)R, the pressure is:

pz = (4.75 lb n,)[ 0.3704(psia. ft3) / (Ibm' R)](480 R) / (3 ft3) = 281.7 psia The calculation to find the final pressure could also have been done without finding the mass. Consider equating the mass from the Ideal Gas Law applied at States 1 and 2, equating volumes, and canceling the gas constant to get: P2

= (1; / I;)PI = (480/600)(352.07) = 281.7 psia

The First Law of Thermodynamics applied to the process from State 1 to State 2 is:

CQ2 - I Tfi)=m(u2 -u1) There is no change of either potential energy (Z2 - zJ = 0) or kinetic energy (velocity V =0) in this application, and the equation may be solved for the heat transferred as: I

Q2 =1

Tfi + m(u2 -

U1)

r----------, I I I I I I

AIR

I I I I

:

V=3ft'l

:

I I I

t Pressure

p

CD]

PI

= 140°F = 352.07 psia

®

I I I

-----------..1

Specific Volume, v

Figure 7-2. Rigid Tank and p-v Diagram for Application 1

Fundamentals of Thermodynamics and Psychrometries

Chapter 7 First Law and Closed Systems

7:8

There is no shaft work. The boundary work is also zero because there is no change in volume. Recall that the boundary work could be expressed as the area under the curve on the p-V diagram. Because the curve is a vertical straight line, as shown in Figure 7-2, there is no area under the curve and the boundary work is zero:

°

I

U;; = (constant volume process)

I

Q2

= m(U2 - ul )

The change of specific internal energy for an ideal gas can be expressed as the product of the specific heat at constant volume and the change in temperature, so that:

IQ2

= mc.(t2 -tl)

Form =4.75Ibm ; cv =0.171 Btu/lbm .oF;t2 =20°F;andtl =140°F,theheattransferis:

IQ2 =(4.75Ib m)(O.l71 Btu/Ib m·oF)(20-140)o = -97.5 Btu The negative sign indicates that the direction of heat flow was out of the system, which agrees with our sense that cooling the air means to remove heat. Application 2. A rigid tank with a volume of 3 ft3 is initially filled with R-22 in a saturated vapor state at 140°F. The refrigerant is cooled to 20°F. Use the refrigerant tables (in Appendix C-J) to determine the mass of refrigerant in the tank. Determine the final pressure. Assuming the refrigerant in the tank to constitute a closed system, apply the First Law of Thermodynamics and determine the heat transferred during the process. Solution. The refrigerant in the tank is taken as the system. The process is assumed to start when the tank is already full atpI = 352.07 psia and tl = 140°F (State 1). The process ends when the refrigerant in the tank is cooled to t2 = 20°F, P2 = ? Because no mass enters or leaves the tank during the process, this is a closed system. Because it is a rigid tank, the volume remains constant. The configuration is shown in Figure 7-3 along with the p-v diagram showing the constant volume process from State 1 to State 2.

From the refrigerant table in Appendix C-J, the properties of saturated R-22 at 140°F are: PI = 352.07 psia, VI = Vg = 0.1434 ft3/lb m ,and enthalpy hI = hg = 112.784 Btu/Ibm' The mass IS:

m = V;

IVI

=(3 ft3)/(O.l434 ft3 /Ibm) = 20.9 Ibm

Chapter 7 First Law and Closed Systems

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7: 9

r----------

I I

: REFRIGERANT I R-12 I I I I I

t

PI

= 140°F

= 352.07 psia

Pressure p

V=3ft3

® Specific Volume, v

Figure 7-3. Rigid Tank and p-v Diagram for Application 2

From Figure 7-3, it can be seen that State 2 is a saturated mixture of liquid and vapor. At 20°F, the properties as read from Appendix C-J are: P2

=Pg = 57.083 psia; vg2 = 0.9343 ft3/lb m ; density ofliquid p = 81.411bm/ft3 (note

that density is the inverse of the specific volume and vfl = 0.0122 ft3/Ib m ); enthalpy of saturated vapor hg2 = 106.434 Btu/Ibm; and enthalpy of saturated liquid hfl = 16.090 Btu/Ibm

The quality ofthe mixture (ratio of mass vapor to total mass) can be found by recognizing that for the constant volume process v2 = VI = vfl +X/Vg2 - vfl ). Therefore, the quality is: x2

=(V2

-v j2 )/(vg2 -v j2 )

= (0.1434 = 0.1423

0.0122) I (0.9343 - 0.0122)

With this quality, the specific enthalpy at State 2 is:

~

=hj2 +x2 (hg2 -hj2) = 16.090 + 0.1423(106.434 -16.090) = 28.946 Btu I Ibm

Fundamentals ofThermodynamics and Psychrometries

Chapter 7 First Law and Closed Systems

7: 10

The First Law of Thermodynamics applied to the process from State 1 to State 2 is:

CQ2 -, n;) = m(u2 -u,) The changes in kinetic and potential energy are zero. There is no boundary work because it is a constant volume process. The heat transfer is:

,Q2

= m(u2 -u,)

The tabulated values for internal energy are not given in Appendix C-l, but they can be calculated from the enthalpy by remembering the relationships:

u,

= ~ - p,v, = 112.784 -(352.07 Ib j I in.2 )(144 in? Ife)( 0.1434 fe /lb m)(Btul 778 ft ·lb j

)

= 103.4 Btu I Ibm

u2

= ~ - P2 V 2 2

=28.946-(57.803Ib j lin?)(144 in.2 /ft )(0.1434 ft3 Ilb m )(Btu/778 ft.lb j

)

= 27.4 Btullb m

The heat transfer is:

,Q2

= m(u2 -u,) = 20.9 Ib m(27.4-103.4) Btullb m = 1,588.4 Btu

As in the previous application, the negative sign is an indication of the heat removed from the system. The large amount of heat transfer is an indication of the heat released during change of phase from vapor to liquid (condensation).

Application 3. A piston-cylinder device contains 10 Ibm of air which is maintained at a constant pressure of 150 psia by a floating piston of constant weight. as shown in Figure 7-4. A resistance heater within the cylinder is turned on for five minutes and supplies heat at a rate of 1.5 kW. During those five minutes, a heat loss of 200 Btu occurs through heat transfer to the surroundings. If the initial temperature is 20°F, determine the temperature after the five minutes.

Chapter 7 First Law and Closed Systems

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7: 11

Solution. The air and the resistance wire are selected as the system. Even though the piston can move, and the volume can change, there is no mass entering or leaving the closed

system. The First Law of Thermodynamics applied to the process from the initial State 1 to final State 2 is:

The changes in kinetic and potential energy are assumed to be negligibly small. Foran ideal gas, the change in internal energy is expressed as (u 2 - u}) = cv (t2 - t}). There are two forms of work in this problem. The boundary work for the constant pressure process is mp(v2 - v). This may also be seen from the area under the curve on the p-v diagram shown in Figure 7-4. Because the air is treated as an ideal gas, the term pv may be replaced by Rt, so that the boundary work is mR(t2 - t}). The electrical work is negative because it is work done on the system and has a magnitude of the power (1.5 kW) times the time it is on (5 minutes); }W2electrical = - (1.5 kW)(3412 BtuI(hr·kW)(5 minutes)(hr/60 minutes) = 426.5 Btu. The heat transfer ]Q2 is negative 200 Btu because it is a heat loss from the system. The First Law equation now reads:

(IQ2 -I W;) = m(u2 -ul )

[-200-(-426.5)-mR(t2 -tl )]=mc (t 2 -tl ) V

Constant Pressure Process

-----------1 : I I I

AIR P = 150 psi a

I I

Pressure

p

®

CD

... I----~I

I I

: Electrically ~ : I Heated - - - - - ______ 1 Specific Volume, v

Figure 7-4. Piston-Cylinder Arrangement andp-v Diagram for Application 3

Fundamentals ofThermotiynamics and Psychrometries

Chapter 7 First Law and Closed Systems

7: 12

Solving for t2 :

t2

= t, + (226.5) 1meR + c v )

Since cp = (R + c) = 0.240 Btu/(lbm·oF), the final temperature is:

t2

= 20+(226.5)1 [10(0.24)] = 114.4°F

It may be noted here that the First Law was used to find one of the properties rather than the heat transfer as in the previous two examples. It all depends on which information and which is to be determined that dictates what is to be solved for in the First Law equation. What is important is that it takes knowledge of the First Law along with knowledge of the equation of state (as given by Ideal Gas Law, or as a set of values in a table or chart) and knowledge of the type of process (constant volume, constant pressure, etc.) to solve the problem. Application 4. Air is compressed polytropicaUy in a piston-cylinder device, pv" = constant, where n = 1.2. The initial temperature and pressure are 20°F and 15 psia. The volume ratio between the beginning and end of the stroke (compression ratio) is 10. Determine the work and heat transfer per unit mass during the compression stroke. Solution. The air is selected as the system. Even though the piston can move and the volume can change, there is no mass entering or leaving the closed system. The piston-cylinder arrangement is shown with the p-v diagram in Figure 7-5.

Polytropic Process

-----------1 I I I I I I

I I

AIR

I I

I I

I I

!....---- ______ I

Pressure

p

P,= 15 psia

1,

= 20°F

: I

•

WI

I I

hI

+

.-_----I w" = . •

'Q-":AF--....-r-...... I

Condensate Drain

fa

t2

•

4

W3

tl

Figure 15-3. Cooling Coil With Dehumidification

Fundamentals of Thermodynamics and Psychrometries

Chapter 15 Air-Conditioning Processes

15:6

Example 15.2. Outdoor air at 95°F and 60% relative humidity is to be cooled to a final condition of 80°F and 50% relative humidity using a cooling coil and a simple heater. Find the intermediate temperature between the cooling coil and the heater, the specific heat removed in the cooling coil, and the specific heat added in the heater. Solution. The solution is best found by drawing all four processes on the psychrometric chart as shown in Figure 15-3. Start with the initial condition and draw a horizontal line across to the saturation line to describe the cooling process 1 to 2. Next draw a horizontal straight line across from the desired final condition to the saturation line. This is the final heating process from State 3 to State 4. The intermediate temperature can be read as t3 = 60°F. It is worth noting that this is also the dewpoint temperature of the final condition.

From the chart, the enthalpies are: hI = 46.3, h3 = 26.4, and h4 = 31.4 Btu per Ibm dry air. The heat transfer may be found by applying the First Law of Thermodynamics to the cooling coil and heater: qcoil

=~-~

= 26.4-46.3 = -19.9 Btu per Ibm dry air (negative means cooling) qheater

= h4 -

~

= 31.4-26.4

= 5.0 Btu per Ibm dry air (positive means heating) In actual cooling coils, the process does not usually follow the idealized process path of constant humidity ratio from 1 to 2, along the saturation line from 2 to 3, and simple heating from 3 to 4. The more practical path is similar to the dotted line shown in Figure 15-3. In the air stream, only the air closest to the coils or fins is cooled to saturation. The state leaving the coil is not on the saturation line because it is a mixture of the parts of the air stream that reach saturation and parts that do not. A reasonable rule of thumb is to assume 90% relative humidity. The air stream is then heated or mixed with another stream to achieve the desired final state.

Chapter 15 Air-Conditioning Processes

Fundamentals ofTllermodynamics and Psychrometries

15: 7

15.4 Evaporative Cooling Evaporative cooling is the process that occurs when water is sprayed into an air stream or when air blows over a wet surface. The energy required to evaporate the water must come from somewhere, and if the process is adiabatic, then that energy is taken out of the air stream. It is the same process that was described earlier as happening in an adiabatic saturator. It is a practical cooling method if the air is initially quite dry (low relative humidity) as is often the case in semi-arid areas. It can be used for space cooling provided the final state is not too humid. Conservation of mass applied to the evaporative cooling process is:

mv1 = mw +mv2 mw =mv2 -mv1

Therefore the mass ratio is:

The First Law of Thermodynamics applied to the adiabatic evaporative cooling process is: ma~

= mwhw + ma~ hw = (ma I mw)(~ -~) =(~ -~)/(n;

-ffn

=l:!.hll:!.W That means that evaporative cooling is a process in which the ratio of the enthalpy change to humidity change is constant and equal to the enthalpy of the water being sprayed into the air stream. On the psychrometric chart, the evaporative cooling process is represented by a straight line with its slope determined from the protractor as shown in Figure 15-4. The protractor can be seen to have I:!.hll:!. W printed as a scale around its perimeter. The line drawn by connecting the center of the protractor to the point on the perimeter corresponding to the value of hw has the same slope as a line drawn on the psychrometric chart itself that goes from State 1 to State 2. The slope of the line is fixed by the enthalpy ofthe added water, and the actual location of State 2 along that line is determined by the mass flow rate of added water. There is an upper limit to the evaporative cooling effect when the outlet condition reaches the adiabatic saturation temperature.

Fundamentals of Thermodynamics and Psychrometries

Chapter 15 Air-Conditioning Processes

15: 8

t

Water spray hwaler

~ ... M1 = hwater

tlw

'Q'lf ,

'0'

_____ ___

2~':::" ~ •

,

#'

o.

I

fiII'It

:

-:'.....

,',

!It

,. ;1'"-..""""-tj£fl11e/

,. • •

W 2

•

w,

~i

0

Figure 15-4. Evaporative Cooling With Water Spray

15.5 Adiabatic Mixing Mixing of two air streams is a common situation in HVAC systems. The air-conditioning of buildings requires a certain amount of mixing of conditioned air with fresh outdoor ventilated air. The physical means of mixing may be brought about in many different ways, but the case of two air streams merging into one is shown in Figure 15-5. There are three states involved: the flow streams are at States I and 2 respectively, and the mixture state is State 3. It is common to assume that mixing is an adiabatic process. The conservation of mass equation can be applied to the dry air and to the water vapor:

mal + ma2 = ma3 W;mal + ~ma2 = W; ma3 The First Law of Thermodynamics applied to the mixing process is:

After substituting for

ma3 from the first equation into each of the other two equations and

then dividing through by

ma2 and solving for mal I ma2 the result is:

mal Ima2 =(~ -W;)/(W; -W;) =(~ -~)/(~ -~)

Chapter 15 Air-Conditioning Processes

Fundamentals of Thermodynamics and Psychrometries

15:9

The geometrical interpretation of this result is shown on the psychrometric chart in Figure 15-5. State 3 lies on a straight line connecting States 1 and 2, such that the relative distances between the mixed state and each ofthe original unmixed states are proportional to the ratio of the air stream flow rates. Although not exact because there is a slight change in specific heat with humidity ratio, the flow ratio can be reasonably estimated from the rule of proportionalities applied to the dry-bulb temperature differences:

= (t2 -t3)1 (t3 -tl )

mall ma2

Example 15.3. Saturated air leaving the cooling section of an air-conditioning system at 55°F at a rate of 200 Ibm per minute is mixed with outside air at 95°F and 40% relative humidity at a rate of 100 Ibm per minute. Determine the temperature and relative humidity of the mixture.

Solution. The mixed State 3 is most easily located by drawing a straight line between air stream States 1 and 2 and using the dry-bulb temperature calculated from proportionality to locate State 3 on the straight line. From proportionality: mal Ima2 =(t2 -t3)/(t2 -tl ) 2001100 = (95 - t3) 1(t3 - 55) Solving for the temperature results in a mixed temperature of t3 relative humidity is ~ = 63%.

75°F. From the chart, the

=

I

\').

> ,, ,

~').~\ ~').

'(\').

,

..

~

').

·· .. .. .. ·· ..

1I

-- •• ~ ••• ~ •••••••• Wi I

•

Figure 15-5. Adiabatic Mixing of Two Streams of Moist Air

Fundamentals ofThermodynamics and Psychrometries

Chapter 15 Air-Conditioning Processes

15: 10

15.6 Sensible Heat Ratio In air-conditioning applications, the object is to maintain the temperature and humidity of the conditioned space within certain comfort limits. To maintain steady conditions means removing the heat load due to people, appliances, conduction through walls, solar gain and other various heat and moisture sources. Because both temperature and humidity are important, it is sometimes useful to think of the total load as being made up of two components: the sensible load and the latent load. The sensible load is the heat to be removed to maintain the dry-bulb temperature without changing the humidity ratio. The latent load is the heat to be removed to change the humidity ratio without changing the dry-bulb temperature. The ratio of the sensible heat to total heat (sensible plus latent) is known as the sensible heat ratio (SHR). This idea can also be related to the psychrometric chart. Consider the change of state shown in Figure 15-6. The line may be thought of as a line of constant SHR. By looking at the protractor, it can be seen that the slope of the line on the psychrometric chart is the same as a line drawn from the center of the protractor to a point on the perimeter corresponding to a value of the SHR. In practice, the idea of the SHR may be useful when approached from the perspective that typical values for SHR may be known Figure 15-6. Sensible Heat Ratio from the desired design conditions. With the known value of SHR and using the slope from a line on the protractor, a line can be drawn through the desired setpoint on the psychrometric chart. Any air delivered to the conditioned space with conditions along this lirie will remove heat in the right ratio of sensible to latent change. Example 15.5. The sensible heat load ratio for a cooling problem is known to be SHR = +2.0. The setpoint condition for the conditioned space is 72°F and 50% relative humidity. Find the relative humidity of the 60°F cooling air if the correct ratio of sensible to latent heat is to be removed from the conditioned space.

Chapter 15 Air-Conditioning Processes

Fundamentals of Thermodynamics and Psychrometries

15: 11

Solution. The positive sign on SHR means that the sensible enthalpy change and the total enthalpy change have the same sign. On the protractor, draw a line from the center to the value of SHR = 2.0 on the perimeter. Draw a parallel line on the psychrometric chart that goes through the state point tdb = 72°F, ~ = 50%. Read the relative humidity for a point on this line at a dry-bulb temperature of 60°F. The relative humidity of the supply air should be ~ = 87%.

Summary Simple heating or cooling at constant humidity ratio is a horizontal straight line on the psychrometric chart for which the heat transfer is given as:

Cooling coil operation with dehumidification is idealized as a two-step process. First there is simple cooling at constant humidity ratio from State 1 to State 2 as the relative humidity increases to 100%, followed by a path along the saturation line from State 2 to State 3 as water vapor is condensed to liquid and the humidity ratio decreases. Applications usually call for a final moist air condition that is in the comfort zone and not on the saturation line. Therefore, the overall cooling path includes a final process during which the relative humidity is reduced to the desired level either by heating or by mixing the saturated air with warmer, non-saturated air. In actual cooling coils, a more practical process path does not reach the saturated condition because there is a mixture of the parts of the air stream that reach saturation and the parts that do not. A reasonable rule of thumb is to assume 90% relative humidity. Evaporative cooling is the process that occurs when water is sprayed into an air stream or when air blows over a wet surface. Adiabatic evaporative cooling is characterized on the psychrometric chart by:

hw = (~-~)/(Wz -~)

=I:1h / I:1W This means that evaporative cooling is a process in which the ratio ofthe enthalpy change to humidity change is constant and equal to the enthalpy ofthe water being sprayed into the air stream. On the psychrometric chart, the evaporative cooling process is represented by a straight line with its slope determined from the protractor.

Fundamentals ofThermodynamics and Psychrometries

Chapter 15 Air-Conditioning Processes

15: 12

Mixing of two air streams is a common situation in HVAC systems. If the flow streams are at States 1 and 2, respectively, and the mixture is at State 3, then for adiabatic mixing, the mass ratio may be expressed as:

mal Ima2

=(W; -U;;)/(U;; -~) =(hz-~)/(~-~)

=(t2 - t3) I (t3 - t l ) The geometrical interpretation of this result on the psychrometric chart is that State 3 lies on a straight line connecting States 1 and 2, such that the relative distances between the mixed state and each of the original unmixed states are proportional to the ratio of the air stream flow rates. In air-conditioning applications, the object is to maintain the temperature and humidity of the conditioned space within certain comfort limits. To maintain that relatively steady state means removing the heat load due to people, appliances, conduction through walls, solar gain and other heat and moisture sources. The total load may be considered as being the sensible load plus the latent load. The sensible load is the heat to be removed to maintain the dry-bulb temperature without changing the humidity ratio. The latent load is the heat to be removed to change the humidity ratio without changing the dry-bulb temperature. The ratio of the sensible heat to total heat (sensible plus latent) is known as the sensible heat ratio (SHR). With a known value ofSHR and using the slope from a line on the protractor, a line can be drawn through the desired setpoint on the psychrometric chart. Any air delivered to the conditioned space with conditions along this line will remove heat in the right ratio of sensible to latent change to satisfy the load.

Chapter 15 Air-Conditioning Processes

Fundamentals of Thermodynamics and Psychrometries

15: 13 .

Skill Development Exercises for Chapter 15 Complete these questions by writing your answers on the worksheets at the back of this book. Be sure to include your name and address. Send your completed questions to the ASHRAE Education Department.

15-01. Moist air is cooled from 80°F, 50% relative humidity to 70°F with no moisture added or removed. What is the final relative humidity and the heat removed perlbm of dry air? 15-02. Moist air is cooled from 80°F, 50% relative humidity to 50°F. What is the final relative humidity, humidity ratio and change of enthalpy? 15-03. 1,000 cfm of outdoor air at 40°F and 20% relative humidity is to be heated and humidified to a final condition of 72°F and 50% relative humidity with a heater followed by a steam humidifier. The temperature after the heater is 64°F. Find the following: the heat added in the heater section; the mass flow rate of steam; and the enthalpy of the steam. 15-04. Outdoor air at 95°F and 50% relative humidity is to be cooled to a final condition of 72°F and 50% relative humidity using a cooling coil and a simple heater. Find the intermediate temperature between the cooling coil and the heater, the specific heat removed in the cooling coil, and the specific heat added in the heater. 15-05. Outdoor air at 95°F and 20% relative humidity is cooled in an evaporative cooler by spraying with saturated liquid water at 70°F. What is the final temperature if the final relative humidity is 60%? (Hint: use the protractor to get the slope of the process line.) How much water will it take per Ibm of dry air? (Hint: use the change in humidity ratio.) 15-06. 20 Ibm per minute of air at 40°F and 90% relative humidity is adiabatically mixed with moist air at 80°F, but unknown relative humidity. The final mixture is at 72°F and 50% relative humidity. What is the relative humidity and mass flow rate ofthe second air stream? 15-07. The sensible heat load ratio for a heating problem is known to be SHR = -2.0. The setpoint condition for the conditioned space is 72°F and 50% relative humidity. Find the relative humidity of the 80°F heating air if the correct ratio of sensible to latent heat is to be removed from the conditioned space.

Fundamentals of Thermodynamics and Psychrometries

Chapter 15 Air-Conditioning Processes

A:1

Appendix A-I: Dimensions and Units Used in Air-Conditioning Applications

Dimension

SI Unit

IP Unit

Acceleration

mls2

ftlsec 2

Area

m2

ft2

Density

kg/m3

lb m Ift3

Energy

N-m, Joule (J)

Btu, ft-Ib

Force

(kg-m)/s2, Newton (N)

pound (Ibj

Length

m, meter (m)

foot (ft)

Mass

kg, kilogram (kg)

pound mass (Ibm)

Power

J/s, Watt (W)

Btu/h

Pressure

N/m2, Pascal (P)

pSI

Specific Heat

J/(kgeOC)

Btu/(IbmeOF)

Time

second (s)

second (sec)

Temperature (absolute)

degree Kelvin (K)

degree Rankine (R)

Temperature

degree Celsius (OC)

degree Fahrenheit eF)

Thermal Conductivity

W/(meOC) W/m2

Btu/(hefteOF)

ft/sec, ftlmin, fpm

Volume

mls m3

Volume Flow Rate

m 3/s

ft3/sec, ft 3/min, cfm

Thermal Flux Density Velocity

Fundamentals of Thermodynamics and Psychrometries

)

Btu/(heft2) ft3

Appendix A

A:2

Appendix A-2: Unit Conversion Factors

Dimension

SI Unit

IP Unit

Length

1 ft = 0.305 m

Area

1 m = 3.281 ft 1 m2= 10.76 ft2

Volume

1 m3= 35.32 ft3

1 ft2 = 0.0929 m2 1 ft3 = 0.0929 m3

Mass

1 kg = 2.205 Ibm

1 Ibm = 0.435 kg

Force

1 N = 0.2248 lbf

1 lbf = 4.448 N

Energy

1 kJ = 0.9478 Btu 1 J = 0.7376 ft-Ibf 1 kWh = 3.412 X 103Btu

1 Btu = 778.2 ft-Ibf = 1.055 kJ 1 ft-Ibf = 1.356 J 1 Btu = 3.183 x 10-2kWh

Specific Energy Specific Enthalpy

1 kJ/kg = 0.4298 Btu/Ibm

1 Btu/Ibm = 2.326 kJ/kg

Power

1 W = 3.412 Btu/h 1 kW = 1.341 hp 1 kW = 0.2844 ton refrigeration

Pressure

1 Pa = 1.450 x 10-4 psi 1 atm = 101 kPa

1 Btu/h = 0.318 W 1 hp = 2545 Btu/h = 0.746 kW 1 ton = 12,000 Btu/h = 3.516 kW 1 psi = 6.897 x 103Pa 1 atm = 14.7 psi = 29.921 in. Hg

1°C diff. = 9/5°F diff. tC = [(9/5)y + 32]OF K = °c + 273.15 Velocity 1 mls = 1.969 x 102ftlmin 1 kglm3= 6.243 x 1O-2Ib m/ft3 Mass Density Mass Flow Rate 1 kgls = 2.205 Ibm/sec 1 kgls = 7.937 x 1031b)h Volume Flow Rate 1 m3/s = 2.119 x 103cfin 1 m3/s = 1.585 x 104 gal/min 1 W/(moOC) = Thermal Temperature

Conductivity Heat Transfer Coefficient Specific Heat

Appendix A

1°F diff. = 5/9°C diff. tF = (y - 32)(5/9)OC R = OF + 459.67 1 ftlmin = 1.602 x 10-3mls Ilbm/ft3 = 1.602 x 103kglm3 1 Ibm/sec = 0.4535 kgls Ilbmlh = 1.260 x lO-4kgls 1 cfm = 4.719 x 10-4 m3/s 1 gal/min = 6.309 x 10-5 m3/s 1 Btu/(hoftoOF) =

0.5778 Btu/(hoftoOF) 1 W/(m2oOC) = 0.1761 Btu/(hoft2 0F)

1.731 W/(mo°C) 1 Btu/(hoft2 0F) = 5.679 W/(m2o°C)

1 J/(kgoOC) = 2.389 x 10-4 Btu/(lbmoaF)

1 Btu/(lbmoOF) = 4.186 x 10-5 J/(kgoOC)

0

0

Fundamentals of Thermodynamics and Psychrometries

B: 1

Appendix B-1: Thermodynamic Properties of Water at Saturation Specific Volume, ft311b Temp. t, of

Absolute Pressure p

Sat. SolidILiq.

Evap.

Sat. Vapor

Entropy, Btullb·oF

Enthalpy, Btullb Sat. SolidILiq. hi

Evap.

Sat. Vapor

Sat. SolidILiq.

Evap.

Sat. Vapor

h jg

hg

si

Sig

Sg

Temp., of

psi

in.Hg

vi

Vig

Vg

-80 -79 -78 -77 -76 -75 -74 -73 -72 -71

0.000116 0.000125 0.000135 0.000145 0.000157 0.000169 0.000182 0.000196 0.000211 0.000227

0.000236 0.000254 0.000275 0.000296 0.000319 0.000344 0.000371 0.000399 0.000430 0.000463

0.01732 0.01732 0.01732 0.01732 0.01732 0.01733 0.01733 0.01733 0.01733 0.01733

1953234 1814052 1685445 1566663 1456752 1355059 1260977 1173848 1093149 1018381

1953234 1814052 1685445 1566663 1456752 1355059 1260977 1173848 1093149 1018381

-193.50 -193.11 -192.71 -192.31 -191.92 -191.52 -191.12 -190.72 -190.32 -189.92

1219.19 1219.24 1219.28 1219.33 1219.38 1219.42 1219.47 1219.51 1219.55 1219.59

1025.69 1026.13 1026.57 1027.02 1027.46 1027.90 1028.34 1028.79 1029.23 1029.67

-0.4067 -0.4056 -0.4046 -0.4036 -0.4025 -0.4015 -0.4005 -0.3994 -0.3984 -0.3974

3.2112 3.2029 3.1946 3.1964 3.1782 3.1701 3.1619 3.1539 3.1459 3.1379

2.8045 2.7972 2.7900 2.7828 2.7757 2.7685 2.7615 2.7544 2.7475 2.7405

-80 -79 -78 -77 -76 -75 -74 -73 -72 -71

-70 -69 -68 -67 -66 -65 -64 -63 -62 -61

0.000245 0.000263 0.000283 0.000304 0.000326 0.000350 0.000376 0.000404 0.000433 0.000464

0.000498 0.000536 0.000576 0.000619 0.000664 0.000714 0.000766 0.000822 0.000882 0.000945

0.01733 0.01733 0.01733 0.01734 0.01734 0.01734 0.01734 0.01734 0.01734 0.01734

949067 884803 825187 769864 718508 670800 626503 585316 548041 511446

949067 884803 825187 769864 718508 670800 626503 585316 547041 511446

-189.52 -189.11 -188.71 -188.30 -187.90 -187.49 -187.08 -186.67 -186.26 -185.85

1219.63 1219.67 1219.71 1219.74 1219.78 1219.82 1219.85 1219.88 1219.91 1219.95

1030.11 1030.55 1031.00 1031.44 1031.88 1032.32 1032.77 1033.21 1033.65 1034.09

-0.3963 -0.3953 -0.3943 -0.3932 -0.3922 -0.3912 -0.3901 -0.3891 -0.3881 -0.3870

3.1299 3.1220 3.1141 3.1063 3.0985 3.0907 3.0830 3.0753 3.0677 3.0601

2.7336 2.7267 2.7199 2.7131 2.7063 2.6996 2.6929 2.6862 2.6730 2.6730

-70 -69 -68 -67 -66 -65 -64 -63 -62 -61

-60 -59 -58 -57 -56 -55 -54 -53 -52 -51

0.000498 0.000533 0.000571 0.000612 0.000655 0.000701 0.000750 0.000802 0.000857 0.000916

0.001013 0.001086 0.001163 0.001246 0.001333 0.001427 0.001526 0.001632 0.001745 0.001865

0.01734 0.01735 0.01735 0.01735 0.01735 0.01735 0.01735 0.01735 0.01735 0.01736

478317 447495 418803 392068 367172 343970 322336 302157 283335 265773

478317 447495 418803 392068 367172 343970 322336 302157 283335 265773

-185.44 -185.03 -184.61 -184.20 -183.78 -183.37 -182.95 -182.53 -182.11 -181.69

1219.98 1220.01 1220.03 1220.06 1220.09 1220.11 1220.14 1220.16 1220.18 1220.21

1034.54 1034.98 1035.42 1035.86 1036.30 1036.75 1037.19 1037.63 1038.07 1038.52

-0.3860 -0.3850 -0.3839 -0.3829 -0.3819 -0.3808 -0.3798 -0.3788 -0.3778 -0.3767

3.0525 3.0449 3.0374 3.0299 3.0225 3.0151 3.0077 3.0004 2.9931 2.9858

2.6665 2.6600 2.6535 2.6470 2.6406 2.6342 2.6279 2.6216 2.6153 2.6091

-60 -59 -58 -57 -56 -55 -54 -53 -52 -51

-50 -49 -48 -47 -46 -45

0.001992 0.002128 0.002272 0.002425 0.002587 0.002760 0.002943 0.003137 0.003343 0.003562

0.01736 0.01736 0.01736 0.01736 0.01736 0.01736 0.01736 0.01737 0.01737 0.01737

249381 234067 219766 206398 193909 182231 171304 161084 151518 142566

249381 234067 219766 206398 193909 182231 171304 161084 151518 142566

-181.27 -180.85 -180.42 -180.00 -179.57 -179.14 -178.72 -178.79 -177.86 -177.43

1220.23 1220.25 1220.26 1220.28 1220.30 1220.31 1220.33 1220.34 1220.36 1220.37

1038.96 1039.40 1039.84 1040.28 1040.73 1041.17 1041.61 1042.05 1042.50 1042.94

-0.3757 -0.3747 -0.3736 -0.3726 -0.3716 -0.3705 -0.3695 -0.3685 -0.3675 -0.3664

2.9786 2.9714 2.9642 2.9570 2.9499 2.9429 2.9358 2.9288 2.9218 2.9149

2.6029 2.5967 2.5906 2.5844 2.5784 2.5723 2.5663 2.5603 2.5544 2.5485

-50 -49 -48 -47 -46 -45

-43 -42 -41

0.000979 0.001045 0.001116 0.001191 0.001271 0.001355 0.001445 0.001541 0.001642 0.001749

-40 -39 -38 -37 -36 -35 -34 -33 -32 -31

0.001863 0.001984 0.002111 0.002247 0.002390 0.002542 0.002702 0.002872 0.003052 0.003242

0.003793 0.004039 0.004299 0.004574 0.004866 0.005175 0.005502 0.005848 0.006213 0.006600

0.01737 0.01737 0.01737 0.01737 0.01738 0.01738 0.01738 0.01738 0.01738 0.01738

134176 126322 118959 112058 105592 99522 93828 88489 83474 78763

134176 126322 118959 112058 105592 99522 93828 88489 83474 78763

-177.00 -176.57 -176.13 -175.70 -175.26 -174.83 -174.39 -173.95 -173.51 -173.07

1220.38 1220.39 1220.40 1220.40 1220.41 1220.42 1220.42 1220.43 1220.43 1220.43

1043.38 1043.82 1044.27 1044.71 1045.15 1045.59 1046.03 1046.48 1046.92 1047.36

-0.3654 -0.3644 -0.3633 -0.3623 -0.3613 -0.3603 -0.3592 -0.3582 -0.3572 -0.3561

2.9080 2.9011 2.8942 2.8874 2.8806 2.8738 2.8671 2.8604 2.8537 2.8470

2.5426 2.5367 2.5309 2.5251 2.5193 2.5136 2.5078 2.5022 2.4965 2.4909

-40 -39 -38 -37 -36 -35 -34 -33 -32 -31

-30 -29 -28 -27 -26 -25 -24 -23 -22 -21

0.003443 0.003655 0.003879 0.004116 0.004366 0.004630 0.004909 0.005203 0.005514 0.005841

0.007009 0.007441 0.007898 0.008380 0.008890 0.009428 0.009995 0.010594 0.011226 0.011892

0.01738 0.01738 0.01739 0.01739 0.01739 0.01739 0.01739 0.01739 0.01739 0.01740

74341 70187 66282 62613 59161 55915 52861 49986 47281 44733

74341 70187 66282 62613 59161 55915 52861 49986 47281 44733

-172.63 -172.19 -171.74 -171.30 -170.86 -170.41 -169.96 -169.51 -169.07 -168.62

1220.43 1220.43 1220.43 1220.43 1220.43 1220.42 1220.42 1220.41 1220.41 1220.40

1047.80 1048.25 1048.69 1049.13 1049.57 1050.01 1050.46 1050.90 1051.34 1051.78

-0.3551 -0.3541 -0.3531 -0.3520 -0.3510 -0.3500 -0.3489 -0.3479 -0.3469 -0.3459

2.8404 2.8338 2.8272 2.8207 2.8142 2.8077 2.8013 2.7948 2.7884 2.7820

2.4853 2.4797 2.4742 2.4687 2.4632 2.4577 2.4523 2.4469 2.4415 2.4362

-30 -29 -28 -27 -26 -25 -24 -23 -22 -21

-20 -19 -18 -17 -16 -15 -14

0.006186 0.006550 0.006933 0.007337 0.007763 0.008211 0.008683

0.012595 0.013336 0.014117 0.014939 0.015806 0.016718 0.017678

0.01740 0.01740 0.01740 0.01740 0.01740 0.01740 0.01741

42333 40073 37943 35934 34041 32256 30572

42333 40073 37943 35934 34041 32256 30572

-168.16 -167.71 -167.26 -166.81 -166.35 -165.90 -165.44

1220.39 1220.38 1220.37 1220.36 1220.34 1220.33 1220.31

1052.22 1052.67 1053.11 1053.55 1053.99 1054.43 1054.87

-0.3448 -0.3438 -0.3428 -0.3418 -0.3407 -0.3397 -0.3387

2.7757 2.7694 2.7631 2.7568 2.7506 2.7444 2.7382

2.4309 2.4256 2.4203 2.4151 2.4098 2.4046 2.3995

-20 -19 -18 -17 -16 -15 -14

-44

Fundamentals ofTllermot/ynamics and Psycllrometries

-44 -43 -42 -41

AppendixB

8:2 Specific Volume, ft3IIb Temp. t, of

Absolute Pressure p

Sat. SolidILiq.

Entbalpy, BtulIb

Evap.

Sat. Vapor

Sat. SolidILiq. hi

Entropy, BtulIb·OF

Evap.

Sat. Vapor

Sat. SolidILiq.

Evap.

Sat. Vapor

hig

hg

si

Sig

Sg

Temp., of

1220.30 1220.28 1220.26 1220.24 1220.22 1220.20 1220.18 1220.16 1220.13 1220.11 1220.08 1220.05 1220.02

1055.32 1055.76 1056.20 1056.64 1057.08 1057.53 1057.97 1058.41 1058.85 1059.29 1059.73 1060.17 1060.62

-0.3377 -0.3366 -0.3356 -0.3346 -0.3335 -0.3325 -0.3315 -0.3305 -0.3294 -0.3284 -0.3274 -0.3264 -0.3253

2.7320 2.7259 2.7197 2.7136 2.7076 2.7015 2.6955 2.6895 2.6836 2.6776 2.6717 2.6658 2.6599

2.3943 2.3892 2.3841 2.3791 2.3740 2.3690 2.3640 2.3591 2.3541 2.3492 2.3443 2.3394 2.3346

-13 -12 -II -10 -9 -8 -7 -6 -5 -4 -3 -2 -I

1220.00 1061.06 1219.96 1061.50 1219.93 1061.94 12J9.90 1062.38 1219.87 1062.82 1219.83 1063.26 1219.80 1063.70 1219.76 1064.14 1219.72 1064.58 -1219.68 -1065.03

-0.3243 -0.3233 -0.3223 -0.3212 -0.3202 -0.3192 -0.3182 -0.3171 -0.3161 -0.3151

2.6541 2.6482 2.6424 2.6367 2.6309 2.6252 2.6194 2.6138 2.6081 -2.6024

2.3298 2.3249 2.3202 2.3154 2.3107 2.3060 2.3013 2.2966 2.2920 -2.2873

0 I 2 3 4 5 6 7 8 9

psi

in.Hg

vi

Vig

Vg

-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -I

0.009179 0.009702 0.010252 0.010830 0.011438 0.012077 0.012749 0.013456 0.014197 0.014977 0.015795 0.016654 0.017556

0.018689 0.019753 0.020873 0.022050 0.023288 0.024590 0.025958 0.027396 0.028906 0.030493 0.032159 0.033908 0.035744

0.01741 0.01741 0.01741 0.01741 0.01741 0.01741 0.01742 0.01742 0.01742 0.01742 0.01742 0.01742 0.01742

28983 27483 26067 24730 23467 22274 21147 20081 19074 18121 17220 16367 15561

28983 27483 26067 24730 23467 22274 21147 20081 19074 18121 17220 16367 15561

-164.98 -164.52 -164.06 -163.60 -163.14 -162.68 -162.21 -162.75 -161.28 -160.82 -160.35 -159.88 -159.41

0 I 2 3 4 5 6 7 8 9

0.018502 0.019495 0.020537 0.021629 0.022774 0.023975 0.025233 0.026552 0.027933 0.029379

0.037671 0.039693 0.041813 0.044037 0.046369 0.048813 0.051375 0.054059 0.056872 0.059817

0.01743 0.01743 0.01743 0.01743 0.01743 0.01743 0.01743 0.01744 0.01744 0.01744

14797 14073 13388 12740 12125 11543 10991 10468 9971 9500

14797 14073 13388 12740 12125 11543 10991 10468 9971 9500

-158.94 -158.47 -157.99 -157.52 -157.05 -156.57 -156.09 -155.62 -155.14 -154.66

10 II 12 13 14 15 16 17 18 19

0.030894 0.032480 0.034140 0.035878 0.037696 0.039597 0.041586 0.043666 0.045841 0.048113

0.062901 0.066131 0.069511 0.073047 0.076748 0.080621 0.084671 0.088905 0.093332 0.097960

0.01744 0.01744 0.01744 0.01745 0.01745 0.01745 0.01745 0.01745 0.01745 0.01745

9054 8630 8228 7846 7483 7139 6811 6501 6205 5924

9054 8630 8228 7846 7483 7139 6811 6501 6205 5924

-154.18 -153.70 -153.21 -152.73 -152.24 -151.76 -151.27 -150.78 -150.30 -149.81

1219.64 1219.60 1219.56 1219.52 1219.47 1219.43 1219.38 1219.33 1219.28 1219.23

1065.47 1065.91 1066.35 1066.79 1067.23 1067.67 1068.11 1068.55 1068.99 1069.43

-0.3141 -0.3130 -0.3120 -0.3110 -0.3100 -0.3089 -0.3079 -0.3069 -0.3059 -0.3049

2.5968 2.5912 2.5856 2.5801 2.5745 2.5690 2.5635 2.5580 2.5526 2.5471

2.2827 2.2782 2.2736 2.2691 2.2645 2.2600 2.2556 2.2511 2.2467 2.2423

10 II 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

0.050489 0.052970 0.055563 0.058271 0.061099 0.064051 0.067133 0.070349 0.073706 0.077207

0.102796 0.107849 0.113128 0.118641 0.124398 0.130408 0.136684 0.143233 0.150066 0.157195

0.01746 0.01746 0.01746 0.01746 0.01746 0.01746 0.01747 0.01747 0.01747 0.01747

5657 5404 5162 4932 4714 4506 4308 4119 3940 3769

5657 5404 5162 4932 4714 4506 4308 4119 3940 3769

-149.32 -148.82 -148.33 -147.84 -147.34 -146.85 -146.35 -145.85 -145.35 -144.85

1219.18 1219.13 1219.08 1219.02 1218.97 1218.91 1218.85 1218.80 1218.74 1218.68

1069.87 1070.31 1070.75 1071.19 1071.63 1072.07 1072.50 1072.94 1073.38 1073.82

-0.3038 -0.3028 -0.3018 -0.3008 -0.2997 -0.2987 -0.2977 -0.2967 -0.2956 -0.2946

2.5417 2.5363 2.5309 2.5256 2.5203 2.5149 2.5096 2.5044 2.4991 2.4939

2.2379 2.2335 2.2292 2.2248 2.2205 2.2162 2.2119 2.2077 2.2035 2.1992

20 21 22 23 24 25 26 27 28 29

30 31 32 32* 33 34 35 36 37 38 39

0.080860 0.084669 0.088640 0.08865 0.09229 0.09607 0.09998 0.10403 0.10822 0.11257 0.11707

0.164632 0.172387 0.180474 0.18049 0.18791 0.19559 0.20355 0.21180 0.22035 0.22919 0.23835

0.01747 0.01747 0.01747 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602

3606 3450 3302 3302.07 3178.15 3059.47 2945.66 2836.60 2732.13 2631.88 2535.86

3606 3450 3302 3302.09 3178.16 3059.49 2945.68 2836.61 2732.15 2631.89 2535.88

-144.35 -143.85 -143.35 -0.02 0.99 2.00 3.00 4.01 5.02 6.02 7.03

1218.61 1218.55 1218.49 1075.15 1074.59 1074.02 1073.45 1072.88 1072.32 1071.75 1071.18

1074.26 1074.70 1075.14 1075.14 1075.58 1076.01 1076.45 1076.89 1077.33 1077.77 1078.21

-0.2936 -0.2926 -0.2915 0.0000 0.0020 0.0041 0.0061 0.0081 0.0102 0.0122 0.0142

2.4886 2.4834 2.4783 2.1867 2.1811 2.1756 2.1700 2.1645 2.1590 2.1535 2.1481

2.1951 2.1909 2.1867 2.1867 2.1832 2.1796 2.1761 2.1726 2.1692 2.1657 2.1623

30 31 32 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49 50 51 52

0.12172 0.12654 0.13153 0.13669 0.14203 0.14755 0.15326 0.15917 0.16527 0.17158 0.17811 0.18484 0.19181

0.24783 0.25765 0.26780 0.27831 0.28918 0.30042 0.31205 0.32407 0.33650 0.34935 0.36263 0.37635 0.39053

0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01602 0.01603

2443.67 . 2355.22 2270.42 2189.02 2110.92 2035.91 1963.85 1894.71 1828.28 1764.44 1703.18 1644.25 1587.64

2443.69 2355.24 2270.43 2189.04 2110.94 2035.92 1963.87 1894.73 1828.30 1764.46 1703.20 1644.26 1587.65

8.03 9.04 10.04 11.04 12.05 13.05 14.05 15.06 16.06 17.06 18.06 19.06 20.07

1070.62 1070.05 1069.48 1068.92 1068.35 1067.79 1067.22 1066.66 1066.09 1065.53 1064.96 1064.40 1063.83

1078.65 1079.09 1079.52 1079.96 1080.40 1080.84 1081.28 1081.71 1082.15 1082.59 1083.03 1083.46 1083.90

0.0162 0.0182 0.0202 0.0222 0.0242 0.0262 0.0282 0.0302 0.0321 0.0341 0.0361 0.0381 0.0400

2.1426 2.1372 2.1318 2.1265 2.1211 2.1158 2.1105 2.1052 2.1000 2.0947 2.0895 2.0843 2.0791

2.1589 2.1554 2.1521 2.1487 2.1454 2.1420 2.1387 2.1354 2.1321 2.1288 2.1256 2.1224 2.1191

40 4J 42 43 44 45 46 47 48 49 50 51 52

*Extrapolated to represent metastable equilibrium with undercooled liquid.

AppendixB

Fundamentals ofTilermodynamics and Psycilrometrics

B: 3 Specific Volume, ft31lb Temp. t, of

Absolute Pressure p

Entropy, Btullb·oF

Enthalpy, Btullb

Sat. SolidILiq.

Evap.

Sat. Vapor

Sat. SolidILiq.

Evap.

Sat. Vapor

Sat. SolidILiq.

Evap.

Sat. Vapor

hi

hig

hg

si

Sig

Sg

Temp., of

psi

in.Hg

vi

Vig

Vg

53 54 55 56 57 58 59

0.19900 0.20643 0.21410 0.22202 0.23020 0.23864 0.24735

0.40516 0.42029 0.43591 0.45204 0.46869 0.48588 0.50362

0.01603 0.01603 0.01603 0.01603 0.01603 0.01603 0.01603

1533.22 1480.89 1430.61 1382.19 1335.65 1290.85 1247.76

1533.24 1480.91 1430.62 1382.21 1335.67 1290.87 1247.78

21.07 22.07 23.07 24.07 25.07 26.07 27.07

1063.27 1062.71 1062.14 1061.58 1061.01 1060.45 1059.89

1084.34 1084.77 1085.21 1085.65 1086.08 1086.52 1086.96

0.0420 0.0439 0.0459 0.0478 0.0497 0.0517 0.0536

2.0740 2.0689 2.0637 2.0586 2.0536 2.0485 2.0435

2. \159 2.1128 2.1096 2,1064 2.1033 2.0002 2.0971

53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

0.25635 0.26562 0.27519 0.28506 0.29524 0.30574 0.31656 0.32772 0.33921 0.35107

0.52192 0.54081 0.56029 0.58039 0.60\12 0.62249 0.64452 0.66724 0.69065 0.71478

0.01604 0.01604 0.01604 0.01604 0.01604 0.01604 0.01604 0.01605 0.01605 0.01605

1206.30 1166.38 1127.93 1090.94 1055.32 1020.98 987.95 956.11 925.44 895.86

1206.32 1166.40 1127.95 1090.96 1055.33 1021.00 987.97 956.12 925.45 895.87

28.07 29.07 30.07 31.07 32.07 33.07 34.07 35.07 36.07 37.07

1059.32 1058.76 1058.19 1057.63 1057.07 1056.50 1055.94 1055.37 1054.81 1054.24

1087.39 1087.83 1088.27 1088.70 1089.14 1089.57 1090.01 1090.44 1090.88 1091.31

0.0555 0.0575 0.0594 0.0613 0.0632 0.0651 0.0670 0.0689 0.0708 0.0727

2.0385 2.0334 2.0285 2.0235 2.0186 2.0136 2.0087 2.0039 1.9990 1.9941

2.0940 2.0909 2.0878 2.0848 2.0818 2.0787 2.0758 2.0728 2.0698 2.0668

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

0.36328 0.37586 0.38882 0.40217 0.41592 0.43008 0.44465 0.45966 0.47510 0.49100

0.73964 0.76526 0.79164 0.81883 0.84682 0.87564 0.90532 0.93587 0.96732 0.99968

0.01605 0.01605 0.01606 0.01606 0.01606 0.01606 0.01606 0.01607 0.01607 0.01607

867.34 839.87 813.37 787.85 763.19 739.42 716.51 694.38 673.05 652.44

867.36 839.88 813.39 787.87 763.21 739.44 726.53 794.40 673.06 652.46

38.07 39.07 40.07 41.07 42.06 43.06 44.06 45.06 46.06 47.06

1053.68 1053.11 1052.55 1051.98 1051.42 1050.85 1050.29 1049.72 1049.16 1048.59

1091.75 1092.18 1092.61 1093.05 1093.48 1093.92 1094.35 1094.78 1095.22 1095.65

0.0746 0.0765 0.0783 0.0802 0.0821 0.0840 0.0858 0.0877 0.0896 0.0914

1.9893 1.9845 1.9797 1.9749 1.9702 1.9654 1.9607 1.9560 1.9513 1.9466

2.0639 2.0610 2.0580 2.0552 2.0523 2.0494 2.0465 2.0437 2.0409 2.0380

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

0.50736 0.52419 0.54150 0.55931 0.57763 0.59647 0.61584 0.63575 0.65622 0.67726

1.03298 1.06725 1.10250 1.13877 1.17606 1.21442 1.25385 1.29440 1.33608 1.37892

0.01607 0.01608 0.01608 0.01608 0.01608 0.01609 0.01609 0.01609 0.01609 0.01610

632.54 613.35 594.82 576.90 559.63 542.93 526.80 511.21 496.14 481.60

632.56 613.37 594.84 576.92 559.65 542.94 526.81 511.22 496.15 481.61

48.06 49.06 50.05 51.05 52.05 53.05 54.05 55.05 56.05 57.04

1048.03 1047.46 1046.89 1046.33 1045.76 1045.19 1044.63 1044.06 1043.49 1042.92

1096.08 1096.51 1096.95 1097.38 1097.81 1098.24 1098.67 1099.11 1099.54 1099.97

0.0933 0.0951 0.0970 0.0988 0.1006 0.1025 0.1043 0.1061 0.1080 0.1098

1.9420 1.9373 1.9327 1.9281 1.9235 1.9189 1.9144 1.9098 1.9053 1.9008

2.0352 2.0324 2.0297 2.0269 2.0242 2.0214 2.0187 2.0160 2.0133 2.0106

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99

0.69889 0.72111 0.74394 0.76740 0.79150 0.81625 0.84166 0.86776 0.89456 0.92207

1.42295 1.46820 1.51468 1.56244 1.61151 1.66189 1.71364 1.76678 1.82134 1.87736

0.01610 0.01610 0.01611 0.01611 0.01611 0.01612 0.01612 0.01612 0.01612 0.01613

467.52 453.91 440.76 428.04 415.74 403.84 392.33 381.20 370.42 359.99

467.53 453.93 440.78 428.06 415.76 403.86 392.34 381.21 370.44 360.01

58.04 59.04 60.04 61.04 62.04 63.03 64.03 65.03 66.03 67.03

1042.36 1041.79 1041.22 1040.65 1040.08 1039.51 1038.95 1038.38 1037.81 1037.24

1100.40 1100.83 1101.26 1101.69 1102.12 1102.55 1102.98 1103.41 1103.84 1104.26

0.1 \16 0.1134 0.1152 0.1170 0.1188 0.1206 0.1224 0.1242 0.1260 0.1278

1.8963 1.8918 1.8874 1.8829 1.8785 1.8741 1.8697 1.8653 1.8610 1.8566

2.0079 2.0053 2.0026 2.0000 1.9973 1.9947 1.9921 1.9895 1.9870 1.9844

90 91 92 93 94 95 96 97 98 99

100 101 102 103 104 105 106 107 108 109

0.95031 0.97930 1.00904 1.03956 1.07088 1.10301 1.13597 1.16977 1.20444 1.23999

1.93485 1.99387 2.05443 2.11667 2.18034 2.24575 2.31285 2.38168 2.45226 2.52464

0.01613 0.01613 0.01614 0.01614 0.01614 0.01615 0.01615 0.01616 0.01616 0.01616

349.91 340.14 330.69 321.53 312.67 304.08 295.76 287.71 279.91 272.34

349.92 340.15 330.71 321.55 312.69 304.10 295.77 287.73 279.92 272.36

68.03 69.03 70.02 71.02 72.02 73.02 74.02 75.01 76.01 77.01

1036.67 1036.10 1035.53 1034.95 1034.38 1033.81 1033.24 1032.67 1032.10 1031.52

1104.69 1105.12 1105.55 1105.98 1106.40 1106.83 1107.26 1107.68 1108.11 1108.54

0.1296 0.1314 0.1332 0.1349 0.1367 0.1385 0.1402 0.1420 0.1438 0.1455

1.8523 1.8479 1.8436 1.8393 1.8351 1.8308 1.8266 1.8223 1.8181 1.8139

1.9819 1.9793 1.9768 1.9743 1.9718 1.9693 1.9668 1.9643 1.9619 1.9594

100 101 102 103 104 105 106 107 108 109

110 III 112 113 114 \15 116 117 118 119 120

1.27644 1.31381 1.35212 1.39138 1.43162 1.47286 1.51512 1.55842 1.60277 1.64820 1.69474

2.59885 2.67494 2.75293 2.83288 2.91481 2.99878 3.08481 3.17296 3.26327 3.35577 3.45052

0.01617 0.01617 0.01617 0.01618 0.01618 0.01619 0.01619 0.01619 0.01620 0.01620 0.01620

265.02 257.91 251.02 244.36 237.89 231.62 225.53 219.63 213.91 208.36 202.98

265.03 257.93 251.04 244.38 237.90 231.63 225.55 219.65 213.93 208.37 202.99

78.01 79.01 80.01 81.01 82.00 83.00 84.00 85.00 86.00 87.00 88.00

1030.95 1030.38 1029.80 1029.23 1028.66 1028.08 1027.51 1026.93 1026.36 1025.78 1025.20

1108.96 1109.39 1109.81 1110.24 \110.66 1111.09 1111.51 \111.93 1112.36 1112.78 1113.20

0.1473 0.1490 0.1508 0.1525 0.1543 0.1560 0.1577 0.1595 0.1612 0.1629 0.1647

1.8097 1.8055 1.8014 1.7972 1.7931 1.7890 1.7849 1.7808 1.7767 1.7726 1.7686

1.9570 1.9546 1.9521 1.9497 1.9474 1.9450 1.9426 1.9402 1.9379 1.9356 1.9332

\10 111 112 113 114 115 116 117 118 119 120

Fundamentals ofThermodynamics and Psychrometries

AppendixB

8:4 Specific Volume, ft31lb Temp. t, of

Absolute Pressure p

Entropy, Btullb·oF

Enthalpy, Btullb

Sat. SolidILiq.

Evap.

Sat. Vapor

Sat. SolidILiq.

Evap.

Sat. Vapor

Sat. SolidILiq.

Evap.

Sat. Vapor

si

Sig

Sg

Temp., of

psi

in.Hg

Vi

Vig

Vg

hi

h ig

hg

121 122 123 124 125 126 127 128 129

1.74240 1.79117 1.84117 1.89233 1.94470 1.99831 2.05318 2.10934 2.16680

3.54755 3.64691 3.74863 3.85282 3.95945 4.06860 4.18032 4.29465 4.41165

0.01621 0.01621 0.01622 0.01622 0.01623 0.01623 0.01623 0.01624 0.01624

197.76 192.69 187.78 182.98 178.34 173.85 169.47 165.23 161.11

197.76 192.69 187.78 182.99 178.36 173.86 169.49 165.25 161.12

89.00 90.00 90.99 91.99 92.99 93.99 94.99 95.99 96.99

1024.63 1024.05 1023.47 1022.90 1022.32 1021.74 1021.16 1020.58 1020.00

1113.62 1114.05 1114.47 1114.89 1115.31 1115.73 1I16.15 1116.57 II 16.99

0.1664 0.1681 0.1698 0.1715 0.1732 0.1749 0.1766 0.1783 0.1800

1.7645 1.7605 1.7565 1.7525 1.7485 1.7445 1.7406 1.7366 1.7327

1.9309 1.9286 1.9263 1.9240 1.9217 1.9195 1.9172 1.9150 1.9127

121 122 123 124 125 126 127 128 129

130 131 132 133 134 135 136 137 138 139

2.22560 2.28576 2.34730 2.41025 2.47463 2.54048 2.60782 2.67667 2.74707 2.81903

4.53136 4.65384 4.77914 4.90730 5.03839 5.17246 5.30956 5.44975 5.59308 5.73961

0.01625 0.01625 0.01626 0.01626 0.01627 0.01627 0.01627 0.01628 0.01628 0.01629

157.11 153.22 149.44 145.77 142.21 138.74 135.37 132.10 128.92 125.83

157.12 153.23 149.46 145.78 142.23 138.76 135.39 132.12 128.94 125.85

97.99 98.99 99.99 100.99 101.99 102.99 103.98 104.98 105.98 106.98

1019.42 1018.84 1018.26 1017.68 1017.10 1016.52 1015.93 1015.35 1014.77 1014.18

1117.41 II 17.83 II 18.25 1118.67 1119.08 1119.50 11I9.92 1120.34 1120.75 1121.17

0.1817 0.1834 0.1851 0.1868 0.1885 0.1902 0.1919 0.1935 0.1952 0.1969

1.7288 1.7249 1.7210 1.7171 1.7132 1.7093 1.7055 1.7017 1.6978 1.6940

1.9105 1.9083 1.9061 1.9039 1.9017 1.8995 1.8974 1.8952 1.8930 1.8909

130 131 132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149

2.89260 2.96780 3.04465 3.12320 3.20345 3.28546 3.36924 3.45483 3.54226 3.63156

5.88939 6.04250 6.19897 6.35888 6.52229 6.68926 6.85984 7.03410 7.21211 7.39393

0.01629 0.01630 0.01630 0.01631 0.01631 0.01632 0.01632 0.01633 0.01633 0.01634

122.82 119.90 117.05 114.29 111.60 108.99 106.44 103.96 101.55 99.21

122.84 II 9.92 II 7.07 114.31 II 1.62 109.00 106.45 103.98 101.57 99.22

107.98 108.98 109.98 110.98 111.98 112.98 113.98 114.98 115.98 116.98

1013.60 1013.01 1012.43 1011.84 1011.26 1010.67 1010.09 1009.50 1008.91 1008.32

1121.58 1122.00 1122.41 1122.83 1123.24 1123.66 1124.07 1124.48 1124.89 1125.31

0.1985 0.2002 0.2019 0.2035 0.2052 0.2068 0.2085 0.2101 0.2118 0.2134

1.6902 1.6864 1.6827 1.6789 1.6752 1.6714 1.6677 1.6640 1.6603 1.6566

1.8888 1.8867 1.8845 1.8824 1.8803 1.8783 1.8762 1.8741 1.8721 1.8700

140 141 142 143 144 145 146 147 148 149

150 151 152 153 154 155 156 157 158 159

3.72277 3.81591 3.91101 4.00812 4.10727 4.20848 4.31180 4.41725 4.52488 4.63472

7.57962 7.76925 7.96289 8.16061 8.36247 8.56854 8.77890 8.99360 9.21274 9.43637

0.01634 0.01635 0.01635 0.01636 0.01636 0.01637 0.01637 0.01638 0.01638 0.01639

96.93 94.70 92.54 90.44 88.39 86.40 84.45 82.56 80.72 78.92

96.94 94.72 92.56 90.46 88.41 86.41 84.47 82.58 80.73 78.94

117.98 118.99 119.99 120.99 121.99 122.99 123.99 124.99 125.99 126.99

1007.73 1007.14 1006.55 1005.96 1005.37 1004.78 1004.19 1003.60 1003.00 1002.41

1125.72 1126.13 1126.54 1126.95 1127.36 1127.77 1128.18 1128.59 1128.99 1129.40

0.2151 0.2167 0.2184 0.2200 0.2216 0.2233 0.2249 0.2265 0.2281 0.2297

1.6529 1.6492 1.6455 1.6419 1.6383 1.6346 1.6310 1.6274 1.6238 1.6202

1.8680 1.8659 1.8639 1.8619 1.8599 1.8579 1.8559 1.8539 1.8519 1.8500

150 151 152 153 154 155 156 157 158 159

160 161 162 163 164 165 166 167 168 169

4.7468 4.8612 4.9778 5.0969 5.2183 5.3422 5.4685 5.5974 5.7287 5.8627

9.6646 9.8974 10.1350 10.3774 10.6246 10.8768 11.1340 11.3963 11.6638 11.9366

0.01639 0.01640 0.01640 0.01641 0.01642 0.01642 0.01643 0.01643 0.01644 0.01644

77.175 75.471 73.812 72.196 70.619 69.084 67.587 66.130 64.707 63.320

77.192 75.488 73.829 72.213 70.636 69.101 67.604 66.146 64.723 63.336

127.99 128.99 130.00 131.00 132.00 133.00 134.00 135.00 136.01 137.01

1001.82 1001.22 1000.63 1000.03 999.43 998.84 998.24 997.64 997.04 996.44

1129.81 1130.22 1130.62 1131.03 1131.43 1131.84 1132.24 1132.64 1133.05 1133.45

0.2314 0.2330 0.2346 0.2362 0.2378 0.2394 0.2410 0.2426 0.2442 0.2458

1.6167 1.6131 1.6095 1.6060 1.6025 1.5989 1.5954 1.5919 1.5884 1.5850

1.8480 1.8461 1.8441 1.8422 1.8403 1.8383 1.8364 1.8345 1.8326 1.8308

160 161 162 163 164 165 166 167 168 169

170 171 172 173 174 175 176 177 178 179

5.9993 6.1386 6.2806 6.4253 6.5729 6.7232 6.8765 7.0327 7.1918 7.3539

12.2148 12.4983 12.7874 13.0821 13.3825 13.6886 14.0006 14.3186 14.6426 14.9727

0.01645 0.01646 0.01646 0.01647 0.01647 0.01648 0.01648 0.01649 0.01650 0.01650

61.969 60.649 59.363 58.112 56.887 55.694 54.532 53.397 52.290 51.210

61.986 60.666 59.380 58.128 56.904 55.711 54.549 53.414 52.307 51.226

138.01 139.01 140.oI 141.02 142.02 143.02 144.02 145.03 146.03 147.03

995.84 995.24 994.64 994.04 993.44 992.83 992.23 991.63 991.02 990.42

1133.85 1134.25 1134.66 1135.06 1135.46 1135.86 1136.26 1136.65 1137.05 1137.45

0.2474 0.2490 0.2506 0.2521 0.2537 0.2553 0.2569 0.2585 0.2600 0.2616

1.5815 1.5780 1.5746 1.5711 1.5677 1.5643 1.5609 1.5575 1.5541 1.5507

1.8289 1.8270 1.8251 1.8233 1.8214 1.8196 1.8178 1.8159 1.8141 1.8123

170 171 172 173 174 175 176 177 178 179

180 181 182 183 184 185 186 187 188 189

7.5191 7.6874 7.8589 8.0335 8.2114 8.3926 8.5770 8.7649 8.9562 9.1510

15.3091 15.6518 16.0008 16.3564 16.7185 17.0874 17.4630 17.8455 18.2350 18.6316

0.01651 0.01651 0.01652 0.01653 0.01653 0.01654 0.01654 0.01655 0.01656 0.01656

50.155 49.126 48.122 47.142 46.185 45.251 44.339 43.448 42.579 41.730

50.171 49.143 48.138 47.158 46.202 45.267 44.356 43.465 42.595 41.746

148.04 149.04 150.04 151.05 152.05 153.05 154.06 155.06 156.07 157.07

989.81 989.20 988.60 987.99 987.38 986.77 986.16 985.55 984.94 984.32

1137.85 1138.24 1138.64 1139.03 1139.43 1139.82 1140.22 1140.61 1141.00 1141.39

0.2632 0.2647 0.2663 0.2679 0.2694 0.2710 0.2725 0.2741 0.2756 0.2772

1.5473 1.5440 1.5406 1.5373 1.5339 1.5306 1.5273 1.5240 1.5207 1.5174

1.8105 1.8087 1.8069 1.8051 1.8034 1.8016 1.7998 1.7981 1.7963 1.7946

180 181 182 183 184 185 186 187 188 189

AppendixB

Fundamentals ofTilermodynamics and Psycllrometrics

B: 5 Specific Volume, ft 311b Temp. t, of

Absolute Pressure p psi

in.Hg

Entropy, Btullb·oF

Enthalpy, Btullb

Sat. SolidILiq.

Evap.

Sat. Vapor

Sat. SolidILiq.

Evap.

Sat. Vapor

vi

Vig

Vg

hi

h ig

hg

Sat. SolidILiq.

Evap.

Sat. Vapor

si

Sig

Sg

Temp., of

190 191 192 193 194 195 196 197 198 199

9.3493 9.5512 9.7567 9.9659 10.1788 10.3955 10.6160 10.8404 11.0687 11.3010

19.0353 19.4464 19.8648 20.2907 20.7242 21.1653 21.6143 22.0712 22.5361 23.0091

0.01657 0.01658 0.01658 0.01659 0.01659 0.01660 0.01661 0.01661 0.01662 0.01663

40.901 40.092 39.301 38.528 37.774 37.035 36.314 35.611 34.923 34.251

40.918 40.108 39.317 38.544 37.790 37.052 36.331 35.628 34.940 34.268

158.07 159.08 160.08 161.09 162.09 163.10 164.10 165.11 166.11 167.12

983.71 983.10 982.48 981.87 981.25 980.63 980.02 979.40 978.78 978.16

1141.78 1142.18 1142.57 1142.95 1143.34 1143.73 1144.12 1144.51 1144.89 1145.28

0.2787 0.2803 0.2818 0.2834 0.2849 0.2864 0.2880 0.2895 0.2910 0.2926

1.5141 1.5109 1.5076 1.5043 1.5011 1.4979 1.4946 1.4914 1.4882 1.4850

1.7929 1.7911 1.7894 1.7877 1.7860 1.7843 1.7826 1.7809 1.7792 1.7776

190 191 192 193 194 195 196 197 198 199

200 201 202 203 204 205 206 207 208 209

11.5374 11.7779 12.0225 12.2713 12.5244 12.7819 13.0436 13.3099 13.5806 13.8558

23.4904 23.9800 24.4780 24.9847 25.5000 26.0241 26.5571 27.0991 27.6503 28.2108

0.01663 0.01664 0.01665 0.01665 0.01666 0.01667 0.01667 0.01668 0.01669 0.01669

33.594 32.951 32.324 31.710 31.110 30.523 29.949 29.388 28.839 28.303

33.610 32.968 32.340 31.726 31.127 30.540 29.965 29.404 28.856 28.319

168.13 169.13 170.14 171.14 172.15 173.16 174.16 175.17 176.18 177.18

977.54 976.92 976.29 975.67 975.05 974.42 973.80 973.17 972.54 971.92

1145.66 1146.05 1146.43 1146.81 1147.20 1147.58 1147.96 1148.34 1148.72 1149.10

0.2941 0.2956 0.2971 0.2986 0.3002 0.3017 0.3032 0.3047 0.3062 0.3077

1.4818 1.4786 1.4755 1.4723 1.4691 1.4660 1.4628 1.4597 1.4566 1.4535

1.7759 1.7742 1.7726 1.7709 1.7693 1.7677 1.7660 1.7644 1.7628 1.7612

200 201 202 203 204 205 206 207 208 209

210 212 214 216 218 220 222 224 226 228

14.1357 14.7096 15.3025 15.9152 16.5479 17.2013 17.8759 18.5721 19.2905 20.0316

28.7806 29.9489 31.1563 32.4036 33.6919 35.0218 36.3956 37.8131 39.2758 40.7848

0.01670 0.01671 0.01673 0.01674 0.01676 0.01677 0.01679 0.01680 0.01682 0.01683

27.778 26.763 25.790 24.861 23.970 23.118 22.299 21.516 20.765 20.045

27.795 26.780 25.807 24.878 . 23.987 23.134 22.316 21.533 20.782 20.062

178.19 180.20 182.22 184.24 186.25 188.27 190.29 192.31 194.33 196.35

971.29 970.03 968.76 967.50 966.23 964.95 963.67 962.39 961.11 959.82

1149.48 1150.23 1150.98 1151.73 1152.48 1153.22 1153.96 1154.70 1155.43 1156.16

0.3092 0.3122 0.3152 0.3182 0.3212 0.3241 0.3271 0.3301 0.3330 0.3359

1.4503 1.4442 1.4380 1.4319 1.4258 1.4197 1.4136 1.4076 1.4016 1.3957

1.7596 1.7564 1.7532 1.7501 1.7469 1.7438 1.7407 1.7377 1.7347 1.7316

210 212 214 216 218 220 222 224 226 228

230 232 234 236 238 240 242 244 246 248

20.7961 21.5843 22.3970 23.2345 24.0977 24.9869 25.9028 26.8461 27.8172 28.8169

42.3412 43.9461 45.6006 47.3060 49.0633 50.8738 52.7386 54.6591 56.6364 58.6717

0.01684 0.01686 0.01688 0.01689 0.01691 0.01692 0.01694 0.01695 0.01697 0.01698

19.355 18.692 18.056 17.446 16.860 16.298 15.757 15.238 14.739 14.259

19.372 18.709 18.073 17.463 16.877 16.314 15.774 15.255 14.756 14.276

198.37 200.39 202.41 204.44 206.46 208.49 210.51 212.54 214.57 216.60

958.52 957.22 955.92 954.62 953.31 952.00 950.68 949.35 948.03 946.70

1156.89 1157.62 1158.34 1159.06 1159.77 1160.48 1161.19 1161.90 1162.60 1163.29

0.3389 0.3418 0.3447 0.3476 0.3505 0.3534 0.3563 0.3592 0.3621 0.3649

1.3898 1.3839 1.3780 1.3722 1.3664 1.3606 1.3548 1.3491 1.3434 1.3377

1.7287 1.7257 1.7227 1.7198 1.7169 1.7140 1.7111 1.7083 1.7055 1.7026

230 232 234 236 238 240 242 244 246 248

250 252 254 256 258 260 262 264 266 268

29.8457 30.9043 31.9934 33.1135 34.2653 35.4496 36.6669 37.9180 39.2035 40.5241

60.7664 62.9218 65.1391 67.4197 69.7649 72.1760 74.6545 77.2017 79.8190 82.5078

0.01700 0.01702 0.01703 0.01705 0.01707 0.01708 0.01710 0.01712 0.01714 0.01715

13.798 13.355 12.928 12.526 12.123 11.742 11.376 11.024 10.684 10.357

13.815 13.372 12.945 12.147 12.140 11.759 11.393 11.041 10.701 10.374

218.63 220.66 222.69 226.73 226.76 228.79 230.83 232.87 234.90 236.94

945.36 944.02 942.68 939.99 939.97 938.61 937.25 935.88 934.50 933.12

1163.99 1164.68 1165.37 1166.72 1166.73 1167.40 1168.08 1168.74 1169.41 1170.Q7

0.3678 0.3706 0.3735 0.3764 0.3792 0.3820 0.3848 0.3876 0.3904 0.3932

1.3321 1.3264 1.3208 1.3153 1.3097 1.3042 1.2987 1.2932 1.2877 1.2823

1.6998 1.6971 1.6943 1.6691 1.6889 1.6862 1.6835 1.6808 1.6781 1.6755

250 252 254 256 258 260 262 264 266 268

270 272 274 276 278 280 282 284 286 288

41.8806 43.2736 44.7040 46.1723 47.6794 49.2260 50.8128 52.4406 54.1103 55.8225

85.2697 88.1059 91.0181 94.0076 97.0761 100.2250 103.4558 106.7701 110.1695 113.6556

0.01717 0.01719 0.01721 0.01722 0.01724 0.01726 0.01728 0.01730 0.01731 0.01733

10.042 9.737 9.445 9.162 8.890 8.627 8.373 8.128 7.892 7.664

10.059 9.755 9.462 9.179 8.907 8.644 8.390 8.146 7.910 7.681

238.98 241.03 243.07 245.11 247.16 249.20 251.25 253.30 255.35 257.40

931.74 930.35 928.95 927.55 926.15 924.74 923.32 921.90 920.47 919.03

1170.72 1171.38 1172.02 1172.67 1173.31 1173.94 1174.57 1175.20 1175.82 1176.44

0.3960 0.3988 0.4016 0.4044 0.4071 0.4099 0.4127 0.4154 0.4182 0.4209

1.2769 1.2715 1.2661 1.2608 1.2554 1.2501 1.2448 1.2396 1.2343 1.2291

1.6729 1.6703 1.6677 1.6651 1.6626 1.6600 1.6575 1.6550 1.6525 1.6500

270 272 274 276 278 280 282 284 286 288

290 292 294 296 298 300

57.5780 59.3777 61.2224 63.1128 65.0498 67.0341

117.2299 120.8941 124.6498 128.4987 132.4425 136.4827

0.01735 0.01737 0.01739 0.01741 0.01743 0.01745

7.444 7.231 7.026 6.827 6.635 6.450

7.461 7.248 7.043 6.844 6.652 6.467

259.45 261.51 263.56 265.62 267.68 269.74

917.59 916.15 914.69 913.24 911.77 910.30

1177.05 1177.66 1178.26 1178.86 1179.45 1180.04

0.4236 0.4264 0.4291 0.4318 0.4345 0.4372

1.2239 1.2187 1.2136 1.2084 1.2033 1.1982

1.6476 1.6451 1.6427 1.6402 1.6378 1.6354

290 292 294 296 298 300

Fundamentals ofThermodynamics and Psychrometrics

AppendixB

c:

1

Appendix C-l: R-22 Properties of Saturated Liquid and Saturated Vapor Density, Volume, Enthalpy, Entropy, Specific Heat cp ' Velocity of Viscosity, Thermal Cond, Surface •• 1 Btullb Sound, fils _ _ _ Ib.,lft·oF Btulh·ft·oF Temp,· Pressure, Iblft3 .,lIb _ _Btullb·OF _ _ _ _ _ _Btullb·oF _ _ _ _ cplc, -:-:-_ __ "'-__- - _ _ _ _ _ _ Tension, Temp,. of psia Liquid Vapor Liquid Vapor Liquid Vapor Liquid Vapor Vapor Liquid Vapor Liquid Vapor Liquid Vapor dyne/cm OF -250.00 -240.00 -230.00 -220.00 -210.00

0.002 0.004

107.37 -63.169 106.41 -56.462 105.48 -51.569 104.58 16805. -47.705 103.70 6982.6 -44.426

76.604 77.629 78.669 79.724 80.796

-0.21914 -0.18786 -0.16605 -0.14958 -0.13616

0.44952 0.42332 0.40101 0.38211 0.36538

0.1018 0.1033 0.1048 0.1064 0.1080

1.2914 1.2860 1.2807 1.2754 1.2703

395. 403. 411. 419. 427.

-250.00 -240.00 36.75 -230.00 35.70 -220.00 34.67 -210.00

-200.00 -190.00 -180.00 -170.00 -160.00

0.010 0.022 0.044 0.084 0.151

102.81 101.92 101.03 100.12 99.22

3151.5 1527.4 787.79 429.22 245.51

-41.474 -38.706 -36.038 -33.424 -30.839

81.882 82.984 84.100 85.230 86.373

-0.12457 -0.11411 -0.10439 -0.09521 -0.08644

0.35048 0.33715 0.32518 0.31441 0.30470

0.1096 0.1113 0.1130 0.1147 0.1165

1.2653 1.2604 1.2558 1.2515 1.2474

435. 442. 449. 456. 463.

33.63 32.61 31.59 30.58 29.57

-200.00 -190.00 -180.00 -170.00 -160.00

-150.00 -140.00 -130.00 -120.00 -110.00

0.262 0.435 0.6% 1.080 1.626

98.30 97.38 %.46 95.53 94.60

146.65 91.059 58.544 38.833 26.494

-28.269 -25.708 -23.150 -20.594 -18.D38

87.528 88.692 89.864 91.040 92.218

-0.07800 -0.06986 -0.06198 -0.05435 -0.04694

0.29594 0.28801 0.28082 0.27430 0.2555 0.26838 0.2555

0.1183 0.1201 0.1221 0.1241 0.1262

1.2437 1.2403 1.2374 1.2349 3483. 1.2329 3384.

470. 476. 482. 488. 494.

0.0765

28.57 27.57 26.59 25.61 24.64

-150.00 -140.00 -130.00 -120.00 -110.00

-100.00 -90.00 -80.00 -70.00 -60.00

2.384 3.413 4.778 6.555 8.830

93.66 92.71 91.75 90.79 89.81

18.540 -15.481 13.275 -12.921 9.7044 -10.355 7.2285 -7.783 5.4766 -5.201

93.397 94.572 95.741 %.901 98.049

-0.03973 -0.03271 -0.02587 -0.01919 -0.01266

0.26298 0.25807 0.25357 0.24945 0.24567

0.2557 0.2561 0.2567 0.2574 0.2584

0.1285 0.1308 0.1334 0.1361 0.1389

1.2315 1.2307 1.2305 1.2310 1.2323

3290. 3198. 3110. 3023. 2937.

500. 505. 510. 514. 519.

0.0749 0.0734 0.0718 0.0703 0.0688

0.00292 0.00315 0.00338 0.00360

23.67 -100.00 22.71 -90.00 21.76 -80.00 20.82 -70.00 19.89 -60.00

-50.00 -45.00 -41.44b -40.00 -35.00 -30.00

11.6% 13.383 14.6% 15.255 17.329 19.617

88.83 88.33 87.97 87.82 87.32 86.81

4.2138 -2.608 99.182 -0.00627 0.24220 0.25% 3.7160 -1.306 99.742 -0.00312 0.24056 0.2604 3.4048 -0.377 100.138 -0.00090 0.23944 0.2609 3.2880 0.000 100.296 0.00000 0.23899 0.2611 2.9185 1.310 100.847 0.00309 0.23748 0.2620 2.5984 2.624 101.391 0.00616 0.23602 0.2629

0.1420 0.1436 0.1448 0.1453 0.1471 0.1489

1.2344 1.2358 1.2369 1.2374 1.2393 1.2414

2852. 2810. 2780. 2768. 2725. 2683.

522. 524. 525. 526. 527. 529.

0.0673 0.0665 0.0660 0.0658 0.0651 0.0643

0.00382 0.00393 0.00401 0.00404 0.00414 0.00425

18.% 18.50 18.18 18.05 17.59 17.14

-50.00 -45.00 -41.44 -40.00 -35.00 -30.00

-25.00 22.136 -20.00 24.899 -15.00 27.924 -10.00 31.226 -5.00 34.821

86.29 85.77 85.25 84.72 84.18

2.3202 2.0774 1.8650 1.6784 1.5142

3.944 5.268 6.598 7.934 9.276

101.928 102.461 102.986 103.503 104.013

0.00920 0.01222 0.01521 0.01818 0.02113

0.23462 0.2638 0.1507 1.2437 0.23327 0.2648 0.1527 1.2463 0.23197 0.2659 0.1547 1.2493 0.23071 0.2671 0.1567 1.2525 0.22949 0.2684 0.1589 1.2560

2641. 2599. 2557. 2515. 2473.

530. 531. 532. 533. 534.

0.0636 0.0629 0.0622 0.0614 0.0607

0.00435 0.00445 0.00456 0.00466 0.00476

16.69 16.24 15.79

-25.00 -20.00 -15.00 -10.00 -5.00

0.00 5.00 10.00 15.00 20.00

38.726 42.960 47.538 52.480 57.803

83.64 83.09 82.54 81.98 81.41

1.3691 1.2406 1.1265 1.0250 0.9343

10.624 11.979 13.342 14.712 16.090

104.515 105.009 105.493 105.%8 106.434

0.02406 0.02697 0.02987 0.03275 0.03561

0.22832 0.22718 0.22607 0.22500 0.22395

0.2697 0.2710 0.2725 0.2740 0.2756

0.1611 0.1634 0.1658 0.1683 0.1709

1.2599 1.2641 1.2687 1.2737 1.2792

2431. 2389. 2346. 2304. 2262.

535. 535. 535. 536. 536.

0.615 0.597 0.580 0.563 0.546

0.0268 0.0271 0.0274 0.0276 0.0279

0.0600 0.0593 0.0586 0.0579 0.0572

0.00486 0.004% 0.00506 0.00516 0.00526

0.00 5.00 10.00 15.00 20.00

25.00 30.00 35.00 40.00 45.00

63.526 69.667 76.245 83.280 90.791

80.84 80.26 79.67 79.07 78.46

0.8532 0.7804 0.7150 0.6561 0.6029

17.476 18.871 20.275 21.688 23.111

106.891 107.336 107.769 108.191 108.600

0.03846 0.04129 0.04411 0.04692 0.04972

0.22294 0.22195 0.22098 0.22004 0.21912

0.2773 0.2791 0.2809 0.2829 0.2849

0.1737 0.1765 0.1794 0.1825 0.1857

1.2851 1.2915 1.2984 1.3059 1.3141

2219. 2177. 2134. 2091. 2048.

536. 536. 535. 535. 534.

0.530 0.515 0.499 0.484 0.470

0.0282 0.0284 0.0287 0.0290 0.0292

0.0566 0.0559 0.0552 0.0545 0.0538

0.00536 0.00546 0.00555 0.00565 0.00575

25.00 30.00 35.00 40.00 45.00

50.00 98.799 55.00 107.32 60.00 116.38 65.00 126.00

77.84 77.22 76.58 75.93

0.5548 0.5111 0.4715 0.4355

24.544 108.997 25.988 109.379 27.443 109.748 28.909 110.103

0.05251 0.05529 0.05806 0.06082

0.21821 0.21732 0.21644 0.21557

0.2870 0.2893 0.2916 0.2941

0.1891 0.1927 0.1964 0.2003

1.3229 1.3324 1.3428 1.3540

2005. 1%2. 1919. 1876.

533. 532. 531. 530.

0.456 0.442 0.429 0.416

0.0295 0.0298 0.0301 0.0303

0.0532 0.0525 0.0518 0.0512

0.00584 0.00594 0.00604 0.00613

50.00 55.00 60.00 65.00

70.00 75.00 80.00 85.00 90.00 95.00

136.19 146.98 158.40 170.45 183.17 1%.57

75.27 74.60 73.92 73.22 72.51 71.79

0.4026 0.3726 0.3451 0.3199 0.2%8 0.2756

30.387 31.877 33.381 34.898 36.430 37.977

110.441 110.761 111.066 111.350 111.616 111.859

0.06358 0.06633 0.06907 0.07182 0.07456 0.07730

0.21472 0.2%7 0.2045 0.21387 0.2994 0.2089 0.21302 0.3024 0.2135 0.21218 0.3055 0.2185 0.21134 0.3088 0.2238 0.21050 0.3123 0.2295

1.3663 1.37% 1.3941 1.4100 1.4275 1.4467

1832. 1788. 1744. 1700. 1655. 1611.

528. 527. 525. 523. 520. 518.

0.404 0.392 0.380 0.369 0.358 0.348

0.0505 0.0499 0.0492 0.0486 0.0479 0.0473

0.00623 0.00632 0.00642 0.00652 0.00661 0.00671

70.00 75.00 80.00 85.00 90.00 95.00

100.00 105.00 110.00 115.00 120.00

210.69 225.53 241.14 257.52 274.71

71.05 70.29 69.51 68.71 67.89

0.2560 0.2379 0.2212 0.2058 0.1914

39.538 41.119 42.717 44.334 45.972

112.081 112.278 112.448 112.591 112.704

0.08003 0.08277 0.08552 0.08827 0.09103

0.20%5 0.20879 0.20793 0.20705 0.20615

0.3162 0.3203 0.3248 0.3298 0.3353

0.2356 0.2422 0.2495 0.2573 0.2660

1.4678 1.4912 1.5173 1.5464 1.5791

1566. 1520. 1474. 1428. 1382.

515. 512. 509. 506. 502.

0.338

0.0466 0.0460 0.0454 0.0447 0.0441

0.00680 0.00690 0.00699 0.00709 0.00719

100.00 105.00 110.00 115.00 120.00

125.00 130.00 135.00 140.00 145.00

292.73 311.61 331.38 352.07 373.71

67.05 66.17 65.27 64.33 63.35

0.1781 0.1657 0.1542 0.1434 0.1332

47.633 49.319 51.032 52775 54.553

112.783 112.825 112.826 112.784 112.692

0.09379 0.09657 0.09937 0.10220 0.10504

0.20522 0.20427 0.20329 0.20227 0.20119

0.3413 0.3482 0.3559 0.3648 0.3752

0.2756 0.2864 0.2985 0.3123 0.3282

1.6160 1.6581 1.7063 1.7621 1.8275

1334. 1287. 1238. 1189. 1139.

498. 494. 489. 485. 479.

125.00 130.00 135.00 140.00 145.00

150.00 160.00 170.00 180.00 190.00

3%.32 444.65 497.35 554.82 617.53

62.33 60.12 57.59 54.57 50.62

0.1237 0.1063 0.0907 0.0763 0.0625

56.370 60.145 64.175 68.597 73.742

112.541 112.035 111.165 109.753 107.398

0.10793 0.11383 0.12001 0.12668 0.13432

0.20006 0.19757 0.19464 0.19102 0.18613

0.3873 0.4198 0.4711 0.5657 0.7952

0.3468 0.3957 0.4716 0.6073 0.9222

1.9050 1088. 2.1126 983. 2.4409 873. 3.0349 752. 4.4150 616.

474. 462. 448. 433. 415.

150.00 160.00 170.00 180.00 190.00

200.00 686.11 205.06c 723.74

44.44 32.70

0.0478 80.558 0.0306 91.052

102.809 91.052

0.14432 0.17805 0.15989 0.15989

o.

o.

"temperatures are on the ITS-90 scale

b = boiling point

Fundamentals ofThermodynamics and Psychrometries

0.00

200.00 205.06

c =critical point

AppendixC

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c:

3

Appendix C-3: R-134a Properties of Saturated Liquid and Saturated Vapor Temp,. Pressure, OF

psia

Density, Volume, Enthalpy, Entropy, Specific Heat cp' Velocity or Viscosity, Thennal Cond, Surface o Ib/rt 3 rt 311b _ _B_t_uII_b_ _ _ _B_t_uII_b_o_F_ _ _ _B_tull_b_oo_F_ c/c, _S_o_un_d_,rtI_s_ _ _I_b",..If_t_oO_F_ _ _ _ B_tu/h_o_ft_oo_F_ Tension, Temp,. Liquid

Vapor Liquid

Vapor

Liquid

dyne/cm

OF

32.989 31.902 29.093 26.238

80.235 80.783 82.190 83.618

0.09154 0.27880 0.08801 0.27588 0.07908 0.26903 0.07029 0.26294

0.2740 0.1397 1.1628 0.2776 0.1409 1.1615 0.2837 0.1438 1.1583 0.2870 0.1467 1.1554

3723. 3670. 3552. 3448.

416. 418. 424. 430.

5.289 4.913 4.117 3.497

0.0160 0.0163 0.0168 0.0173

28.15 27.76 26.78 25.81

-153.94 -150.00 -140.00 -130.00

23359 20.467 17.569 14.665 11.755

85.066 86.531 88.011 89.504 91.005

0.06169 0.05330 0.04513 0.03717 0.02940

0.25752 0.25270 0.24842 0.24462 0.24125

0.2886 0.2895 0.2900 0.2906 0.2913

1.1528 1.1507 1.1489 1.1475 1.1466

3352. 3261. 3173. 3087. 3001.

436. 441. 446. 451. 456.

3.006 2.613 2.292 2.028 1.808

0.0179 0.0184 0.0190 0.0195 0.0200

0.0721 0.0706

24.86 23.92 22.99 22.08 21.17

-120.00 -110.00 -100.00 -90.00 -80.00

16.680 10.297 14.138 8.837 12.045 7.374 10.310 5.907 8.8656 4.437

91.759 92.514 93.270 94.026 94.783

0.02559 0.02182 0.01809 0.01440 0.01075

0.23972 0.23827 0.23691 0.23563 0.23443

0.2917 0.1641 1.1463 0.2922 0.1658 1.1462 0.2928 0.1676 1.1461 0.2935 0.1694 1.1462 0.2943 0.1712 1.1465

2959. 2916. 2874. 2832. 2790.

458. 460. 462. 464. 466.

1.712 1.623 1.542 1.466 1.396

0.0203 0.0206 0.0209 0.0212 0.0214

0.0699 0.0691 0.0684 0.0677 0.00405 0.0669 0.00423

20.73 20.28 19.84 19.40 18.96

-75.00 -70.00 -{;5.00 -{;D.OO -55.00

2.963 1.484 0.000 1.489 2.984

95.539 96.295 97.050 97.804 98.556

0.00713 0.00355 0.00000 0.00352 0.00701

0.23331 0.23225 0.23125 0.23032 0.22945

0.2951 0.2960 0.2970 0.2981 0.2992

0.1731 0.1750 0.1769 0.1789 0.1810

1.1468 1.1473 1.1479 1.1487 1.1497

2747. 2705. 2663. 2621. 2579.

468. 470. 471. 473. 474.

1.331 1.271 1.215 1.163 1.113

0.0217 0.0220 0.0223 0.0225 0.0228

0.0662 0.00440 0.0654 0.00457 0.0647 0.00473 0.0639 0.00489 0.0632 0.00505

18.52 18.09 17.66 17.23 16.81

-50.00 -45.00 -40.00 -35.00 -30.00

86.82 86.32 85.81 85.80 85.29 84.77

3.9014 4.484 3.4452 5.991 3.0519 7.505 3.0462 7.529 2.7116 9.026 2.4161 10.554

99.306 100.054 100.799 100.811 101.542 102.280

0.01048 0.01392 0.01733 0.01739 0.02073 0.02409

0.22863 0.22786 0.22714 0.22713 0.22647 0.22584

0.3004 0.3017 0.3031 0.3031 0.3045 0.3060

0.1831 0.1852 0.1874 0.1874 0.1897 0.1920

1.1508 1.1521 1.\535 1.\535 1.\552 1.\570

2536. 2494. 2452. 2451. 2410. 2367.

476. 477. 478. 478. 479. 480.

1.068 1.024 0.984 0.983 0.946 0.910

0.0231 0.0234 0.0237 0.0237 0.0240 0.0243

0.0625 0.0617 0.0610 0.0610 0.0602 0.0595

0.00521 0.00536 0.00550 0.00551

0.00565 0.00579

16.38 15.96 15.54 15.54 15.13 14.71

-25.00 -20.00 -15.00 -14.92 -10.00 -5.00

21.162 23.767 26.617 29.726 33.110

84.25 83.72 83.18 82.64 82.10

2.1587 1.9337 1.7365 1.5630 1.4101

103.015 103.745 104.471 105.192 105.907

0.02744 0.03077 0.03408 0.03737 0.04065

0.22525 0.22470 0.22418 0.22370 0.22325

0.3075 0.3091 0.3108 0.3126 0.3144

0.1943 0.1968 0.1993 0.2018 0.2045

1.1590 1.\613 1.\ 637 1.1664 1.1694

2325. 2283. 2240. 2198. 2155.

481. 481. 482. 482. 482.

0.876 0.843 0.813 0.784 0.756

0.0245 0.0248 0.0251 0.0254 0.0257

0.0588 0.00593 0.0580 0.00607 0.0573 0.00621 0.0565 0.00635 0.0558 0.00649

14.30 13.89 13.48 13.08 12.67

0.00 5.00 10.00 15.00 20.00

25.00 30.00 35.00 40.00 45.00

36.785 40.768 45.075 49.724 54.732

81.55 80.99 80.42 79.85 79.26

1.0484 23.085 108.016 0.9534 24.694 108.705 0.8685 26.314 109.386

0.04391 0.22283 0.04715 0.22244 0.05038 0.22207 0.05359 0.22172 0.05679 0.22140

0.3162 0.3182 0.3202 0.3223 0.3244

0.2072 0.2100 0.2129 0.2159 0.2190

1.1726 1.1761 1.\799 1.1841 1.1886

2113. 2070. 2027. 1985. 1942.

482. 482. 482. 482. 481.

0.730 0.705 0.681 0.658 0.636

0.0260 0.0263 0.0267 0.0270 0.0273

0.0550 0.00662 0.0543 0.00676 0.0536 0.00690 0.0528 0.00704 0.0521 0.00718

12.27 11.87 11.48 11.08 10.69

25.00 30:00 35:00 40.00 45.00

50.00 55.00 60.00 65.00 70.00

60.116 65.895 72.087 78.712 85.787

78.67 78.07 77.46 76.84 76.21

0.7925 0.7243 0.6630 0.6077 0.5577

27.944 29.586 31.239 32.905 34.583

110.058 11 0.722 111.376 112.019 112.652

0.05998 0.06316 0.06633 0.06949 0.07264

0.22110 0.22081 0.22054 0.22028 0.22003

0.3267 0.2222 1.\935 0.3290 0.2255 1.1988 0.3314 0.2289 1.2046 0.3339 0.2325 1.2109 0.3366 0.2363 1.2178

1899. 1856. 1813. 1770. 1726.

481. 480. 479. 477. 476.

0.615 0.595 0.576 0.557 0.539

0.0276 0.0280 0.0283 0.0286 0.0290

0.0513 0.00732 0.0506 0.00746 0.0499 0.00761 0.0491 0.00776 0.0484 0.00791

10.30 9.91 9.53 9.15 8.77

50.00 55.00 60.00 65.00 70.00

75.00 80.00 85.00 90.00 95.00

93.333 101.37 109.92 1\9.00 128.63

75.57 74.91 74.25 73.57 72.87

0.5125 0.4715 0.4343 0.4004 0.3694

36.274 37.978 39.697 41.430 43.179

113.272 113.880 114.475 115.055 115.619

0.07578 0.07892 0.08205 0.08518 0.08830

0.21979 0.21957 0.21934 0.21912 0.21890

0.3393 0.3422 0.3453 0.3485 0.3519

1683. 1640. 1596. 1552. 1509.

474. 472. 470. 468. 466.

0.522 0.505 0.489 0.473 0.458

0.0294 0.0297 0.0301 0.0305 0.0309

0.0476 0.00806 0.0469 0.00822 0.0462 0.00838 0.0454 0.00855 0.0447 0.00872

8.39 8.02 7.65 7.28 6.91

75.00 80.00 85.00 90.00 95.00

100.00 105.00 110.00 1\5.00 120.00

138.83 149.63 161.05 173.11 185.84

72.16 71.43 70.68 69.91 69.12

0.3411 0.3153 0.2915 0.2697 0.2497

44.943 46.725 48.524 50.343 52.181

116.166 116.694 117.203 117.690 118.153

0.09142 0.21868 0.09454 0.21845 0.09766 0.21822 0.10078 0.21797 0.10391 0.21772

0.3555 0.2633 1.2748 1465. 0.3594 0.2689 1.2880 1421. 0.3635 0.2748 1.3026 1376. 0.3680 0.2812 1.3189 1332. 0.3728 0.2881 1.3372 1288.

463. 460. 457. 454. 450.

0.443 0.428 0.414 0.400 0.387

0.0313 0.0318 0.0322 0.0327 0.0332

0.0439 0.0432 0.0425 0.0417 0.04 10

0.00890 0.00908 0.00926 0.00946 0.00965

6.55 5.84 5.49 5.15

100.00 105.00 110.00 115.00 120.00

125.00 130.00 135.00 140.00 145.00

199.25 213.38 228.25 243.88 260.31

68.31 67.47 66.60 65.70 64.77

0.2312 0.2141 0.1983 0.1836 0.1700

54.040 55.923 57.830 59.764 61.727

118.591 119.000 119.377 119.720 120.024

0.10704 0.11018 0.11333 0.11650 0.11968

0.3781 0.3839 0.3903 0.3974 0.4053

1243. 1198. 1153. 110S. 1062.

446. 442. 437. 432. 427.

0.374 0.361 0.348 0.335 0.323

0.0338 0.0343 '0.0349 0.0356 0.0363

0.0403 0.0395 0.0388 0.0380 0.0373

0.00986 0.01007 0.01029 0.01052 0.01075

4.80 4.47 4.\3 3.81 3.48

125.00 130.00 135.00 140.00 145.00

150.00 155.00 160.00 165.00 170.00

277.57 295.69 314.69 334.62 355.51

63.80 62.78 61.72 60.60 59.42

0.1574 0.1455 0.1345 0.1241 0.1144

63.722 65.752 67.823 69.939 72.106

120.284 120.495 120.650 120.739 120.753

0.12288 0.21566 0.12611 0.21517 0.12938 0.21463 0.13268 0.21400 0.13603 0.21329

0.4144 0.3486 1.5143 1017. 0.4247 0.3640 1.5630 97 I. 0.4368 0.3821 1.6213 924. 0.4511 0.4036 1.6921 877. 0.4683 0.4299 1.7798 829.

421. 416. 409. 403. 396.

0.311 0.298 0.286 0.274 0.262

0.0370 0.0378 0.0387 0.0397 0.0407

0.0366 0.0358 0.0351 0.0343 0.0336

om I 00 0.01125 om151 0.01178 0.01206

3.17 2.86 2.55 2.26 1.97

150.00 155.00 160.00 165.00 170.00

175.00 180.00 185.00 190.00 195.00

377.40 400.34 424.37 449.55 475.95

58.16 56.80 55.33 53.70 51.86

0.1052 0.0965 0.0881 0.0801 0.0723

74.335 76.636 79.027 81.534 84.196

120.677 120.493 120.175 119.684 118.963

0.13945 0.14295 0.14655 0.15029 0.15423

0.21247 0.21151 0.21037 0.2090 I 0.20733

0.4896 0.4627 1.8908 0.5168 0.5048 20354 0.5527 0.5612 2.2309 0.6031 0.6406 2.5087 0.6794 0.7612 29338

781. 731. 680. 627. 572.

388. 380. 372. 363. 353.

0.249 0.237 0.224 0.211 0.197

0.0420 0.0434 0.0450 0.0469 0.0493

0.0329 0.0321 0.0314

0.01235 0.01265 0.01296

1.69 1.41 1.15 0.90 0.67

175.00 180.00 185.00 190.00 195.00

200.00 205.00 210.00 213.85c

503.64 532.72 563.34 588.27

49.70 47.00 43.03 32.04

0.0646 87.088 0.0566 90.368 0.0474 94.548 0.0312103.775

117.906 116.289 113.411 103.775

0.15847 0.16326 0.16933 0.18128

0.20519 0.20226 0.19750 0.18128

0.8100 0.9673 3.6640 1.0906 1.4042 5.2174

514. 450. 378. O.

343. 331. 316.

0.182 0.164 0.142

0.0523 0.0566 0.0639

0.45 0.25 0.09 0.00

200.00 205.00 210.00 213.85

-153.94a -150.00 -140.00 -130.00

0.057 0.072 0.130 0.222

99.34 98.95 97.98 97.01

564.85 449.29 259.15 155.69

-120.00 -110.00 -100.00 -90.00 -80.00

0.367 0.586 0.906 1.363 1.997

96.05 95.09 94.13 93.17 92.21

97.027 62.509 41.496 28.303 19.783

-75.00 -70.00 -{;5.00 -{;D.OO -55.00

2.396 2.859 3.393 4.006 4.707

91.73 91.25 90.77 90.28 89.80

-50.00 -45.00 -40.00 -35.00 -30.00

5.505 6.409 7.429 8.577 9.862

89.31 88.82 88.32 87.83 87.33

7.6569 6.6405 5.7819 5.0533 4.4325

-25.00 -20.00 -15.00 -14.92b -10.00 -5.00

11.297 12.895 14.667 14.696 16.626 18.787

0.00 5.00 10.00 15.00 20.00

12.090 13.634 15.187 16.748 18.318

1.2749 19.897 106.617 \.1550 21.486 107.320

"temperatures are OR the ITS-90 scale

Vapor

0.21744 0.21715 0.21683 0.21648 0.21609

Liquid

a =triple point

Fundamentals ofThermodynamics and Psychrometries

Vapor Vapor Liquid Vapor

0.1497 0.1527 0.1559 0.1591 0.1624

0.2402 0.2444 0.2487 0.2533 0.2582

0.2957 0.3040 0.3133 0.3236 0.3353

1.2252 1.2334 1.2424 1.2522 1.2630

1.3577 1.3810 1.4075 1.4379 1.4731

Liquid Vapor

O. b = boiling point

Liquid

Vapor

6.20

c =critical point

AppendixC

20

60

100

140

180

220

260

IJ I

3000 2000

1000~

1000

~

g

~

-

as 'u; c.

-

~ I

..

200 ~

200

~

100

100

w a:

40

::l

en en w

a:

D.

20

20 10

~

~

= ~ ~ = ......

=-~ ..... ~ C ..... ~

(JQ

~

4

9

4

~

11

2

2 1

260

ENTHALPY

(Btu/Ibm)

~

I-l ~ ~ ~

D: 1

Appendix D-l: Thermodynamic Properties of Moist Air at 14.696 psia Condensed Water Temp. Humidity Ratio, I, OF Ib,.JIbda Ws

Enthalpy, Btullb dry air

Volume, air

ft 31lb dry

va

va g

hga

Entropy, Btul(Ib dry air) • OF Sg a Saga Sa

Vapor Enthalpy, Entropy, Press., Btullb Btullb· OF in.Hg pg" h., S.,

Temp., OF

9.553 9.579 9.604 9.629 9.655 9.680 9.705 9.731 9.756 9.782

ha -19.221 -18.980 -18.740 -18.500 -18.259 -18.019 -17.778 -17.538 -17.298 -17.057

ha/ 0.005 0.005 0.006 0.007 0.007 0.007 0.008 0.009 0.010 0.010

-19.215 -18.975 -18.734 -18.493 -18.252 -18.0ll -17.770 -17.529 -17.288 -17.047

-