08 Specific Heat Capacity

45

Specific Heat Capacity PRE-LAB ASSIGNMENTS :

To be assigned by your lab instructor.

STUDENT LEARNING  OUTCOMES: • • • • • • •

The First Law of Thermodynamics Thermal energy as a function of temperature The units of energy Sign conventions in heat flow Heat capacity Specific heat capacity Factors in experimental error 

EXPERIMENTAL  GOALS:

You will will measur measuree the specific specific heat capacity capacity of a known known metal. metal. Then Then you you will will measur measuree the specific heat capacity of an unknown to identify the metal.

INTRODUCTION : Heat Capacity

 large large part part of chemis chemistry try is studyi studying ng and underst understandi anding ng the physic physical al and chemic chemical al changes that matter matter undergoes. undergoes. The driving driving force for most chemical and physical physical changes is energy energy! often in the form of thermal energy energy "heat#. "heat#. Temper Temperature ature and heat are not the same $uanti $uantity ty.. The temper temperatu ature re of an ob%ect is an indica indicator tor of the amount amount of therma thermall energy energy it &possesses'! but heat is a measure of the transfer of energy to or from an ob%ect. (e know that the more a substance substance is heated! the more its temperature temperature will rise. This relations relationship hip is a direct direct  proportionality that may be expressed as q ∝ ∆T  ! where $ is the heat absorbed or released by the  system and  system and )T is its temperature change ")T *T final + Tinitial#. This proportionality proportionality may be also be written as an e$uality! q ∆T 

=

constant

or

q

=

constant ⋅ ∆T 

,-

The constant of proportionality is the heat capacity ! C ! and is defined as the $uantity of heat re$uired re$uired to change an ob%ect/s ob%ect/s temperature temperature by one unit of temperatur temperaturee "usually "usually - o0 or - 1#. Hence we can rewrite 2$uation - as q

=

C  ⋅ ∆T 

,3

4=

6t follows that heat capacity has units related to  J  o

C 

energy temperatur e

 and is commonly expressed as

 "also written as 7890 or 7 90 :-#.

The heat capacity of a system is dependent on a few factors. The heat capacity is dependent on the amount   of a sample present as shown in Figure -! and is thus an extensive  property; a larger amount of sample re$uires more heat than a smaller amount of the same substance to raise the substance/s temperature by one unit. 6n addition to the amount of  substance present! the kind   of substance has a direct bearing on its heat capacity. The same amounts of different substances usually have different heat capacities! and heat capacity is often used for samples of a fixed si Titanium @.A33 Silver @.35A Eotassium @.JAJ Strontium @.5@ luminum @.>4J 0opper @.5>A Magnesium -.@3 Ninc @.5>> Sodium -.35

4> SAMPLE CALCULATION

OF THE CALIBRATION OF A CALORIMETER :

(ater with a mass of A@.@ g at >@.- o0 was added to A@.@ g of water at 3J.3 o0. Gpon mixing! the final temperature attained was A-.4 o0. (hat is the heat capacity of the calorimeter! C cal O "ote; This example calculates the heat capacity of the calorimeter! whereas in the laboratory you will need to calculate the specific heat of the metal. The calculations are similar! but the distinction needs to be recogni 78gDo0#D"A-.4 o0 + >@.- o0# * :A>4@ 7 Heat gained by cool water; $gained * "A@.@ g#D"=.-> 78gDo0#D"A-.4 o0 + 3J.3 o0# * A-@ 7 Heat absorbed by calorimeter; $cal * :":A>4@ 7  A-@ 7# * J5@ 7 Heat capacity of calorimeter; C cal 

=

J5@ 7

(A-.4



0 − 3J.3 0) 

=

34 78o0

PROCEDURE : A$ Mea%!"e the

C s .f

a 01.21 Sa3p(e$

-. ?btain two nested coffee:cups. Nero the balance and weigh the empty! dry cups to the nearest milligram. dd approximately A@ mL of water to the cups and determine the mass of  water by difference. ssemble the coffee:cup calorimeter as shown in Figure 5. First! insert the thermometer into the split stopper! and slide the stopper toward the top of the thermometer. ext! slide the thermometer into the center hole of the calorimeter lid. Elace the ring stand clamp on the stopper! and ad%ust the clamp on the ring stand to where it will hold the thermometer bulb about - cm from the bottom of the cup. Finally! insert the stirrer  in the second hole of the lid with the loop encircling the bulb of the thermometer. (ait approximately A minutes before recording the temperature of the water to the nearest @.- o0. 3. Measure the mass of a weighing boat! add approximately 5@ g of a known sample of metal! and obtain the mass of the metal by difference. "The metals used should be large pieces of  metalP metal shot and foil don/t work very well.# Transfer the sample into an appropriately si. Gse the same procedure for determining the specific heat of a known sample to determine the specific heat of an unknown sample. Ce sure to indicate which unknown you have.

-@@ LAB R EPORT Specific Heat Capacity

 ame

VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV

Eartner VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV

Wate VVVVVVVVV

Ieport Krade VVVVVV 

Section VVVVVVVVV

A$ Specific Heat .f a 01.21 Meta($

-. Mass of the coffee:cups

VVVVVVVVVVVV  

Mass of the cups  water

VVVVVVVVVVVV  

Mass of the water

VVVVVVVVVVVV  

Temperature of cool water

VVVVVVVVVVVV 

3. 6dentity of metal sample

VVVVVVVVVVVV  

Mass of metal sample

VVVVVVVVVVVV  

Temperature of boiling water

VVVVVVVVVVVV 

5. Time vs. temperature data + first run; Time "sec#

Temperature "90#

Time "sec#

Temperature "90#

Time "sec#

@

-@A

3-@

-A

-3@

33A

5@

-5A

3=@

=A

-A@

3AA

@

-A

3J@

JA

->@

3>A

4@

-4A

5@@

Maximum System Temperature "Tf #

Temperature "90#

VVVVVVVVVVVV  

=. 0alculate the specific heat of the known and percent error . Show workQ C  s =  VVVVVVVVVV 78gDo0

U error * VVVVVVVVVVVV 

-@-

A. Mass of the coffee:cups

VVVVVVVVVVVV  

Mass of the cups  water

VVVVVVVVVVVV  

Mass of the water

VVVVVVVVVVVV  

Temperature of cool water

VVVVVVVVVVVV 

. 6dentity of metal sample

VVVVVVVVVVVV  

Mass of metal sample

VVVVVVVVVVVV  

Temperature of boiling water

VVVVVVVVVVVV 

J. Time vs. temperature data + second run; Time "sec#

Temperature "90#

Time "sec#

Temperature "90#

Time "sec#

@

-@A

3-@

-A

-3@

33A

5@

-5A

3=@

=A

-A@

3AA

@

-A

3J@

JA

->@

3>A

4@

-4A

5@@

Maximum System Temperature "Tf #

Temperature "90#

VVVVVVVVVVVV  

>. 0alculate the specific heat of the known and percent error . Show workQ C  s =  VVVVVVVVVV 78gDo0

U error * VVVVVVVVVVVV 

4. verage specific heat of the known and percent error . C  s =  VVVVVVVVVV 78gDo0

U error * VVVVVVVVVVVV 

-@3 B$ Specific Heat .f a1 U141.21 Meta($

-. Gnknown umber

VVVVVVVVVVVV  

Mass of the coffee:cups

VVVVVVVVVVVV  

Mass of the cups  water

VVVVVVVVVVVV  

Mass of the cool water

VVVVVVVVVVVV  

Temperature of water

VVVVVVVVVVVV  

3. Mass of unknown

VVVVVVVVVVVV  

Temperature of boiling water

VVVVVVVVVVVV 

5. Time vs. temperature data; Time "sec#

Temperature "90#

Time "sec#

Temperature "90#

Time "sec#

@

-@A

3-@

-A

-3@

33A

5@

-5A

3=@

=A

-A@

3AA

@

-A

3J@

JA

->@

3>A

4@

-4A

5@@

Maximum System Temperature "Tf #

Temperature "90#

VVVVVVVVVVVV  

=. 0alculate the specific heat of the unknown and identify it. Show workQ C  s =  VVVVVVVVVV 78gDo0

6dentity * VVVVVVVVVVVV 

-@5