exergy analysis in thermodynamics

Section-1: Exergy Balance Equation(Recapitulation) 6-1-1

A crane lifts a 1000-kg load vertically up at a speed of 0.5 m/s. Assuming no destruction of exergy, determine (a) the rate at which exergy is transferred into the system (load), and (b) the rate of change of exergy of the system. [Manual Solution]

Answers: (a) 4.905 kW, (b) 4.905 kW Anim. 6-1-1 (click) 6-1-2

A closed system operating at steady state receives 5000 kW of heat from a source at 1500 K, produces 2000 kW of useful power and rejects the remaining heat into the atmosphere. Determine the rate at which exergy (a) enters and (b) leaves the system. Assume the atmospheric temperature to be 300 K. [Manual Solution] Answers: (a) 4 MW, (b) 2 MW 6-1-3

Heat is transferred from a TER at 1500 K to a TER (thermal energy reservoir) at 400 K at a rate of 10 kW. If the atmospheric temperature is 300 K, determine the rates at which exergy (a) leaves the TER at higher temperature, and (b) enters the TER at lower temperature. (c) How do you explain the discontinuity in the result? [Manual Solution] Answers: (a) 8 kW, (b) 2.5 kW Anim. 6-1-3 (click) 6-1-4

Heat is transferred from a TER at 1500 K to a TER at 500 K at a rate of 5 kW. Determine the rate at which exergy (a) leaves the hightemperature TER, (b) enters the low-temperature TER, and (c) destroyed in the thermodynamic universe. Assume the atmospheric temperature to be 300 K. [Manual Solution] Answers: (a) 4 kW, (b) 2 kW, (c) 2 kW 6-1-5

A closed system receives heat at a rate of 2 kW from a source at 1000 K, electrical power at a rate of 2 kW, and shaft power at a rate of 2 kW. Determine the net rate of (a) energy transfer and (b) exergy transfer into the system. (c) What is the maximum possible rate of exergy rise in the system? [Manual Solution] Answers: (a) 8 kW, (b) 5.4 kW, (c) 13.4 kW Anim. 6-1-5 (click)

6-1-6

Three kilogram of water undergo a process from an initial state where the water is saturated vapor at 140oC, the velocity is 40 m/s, and the elevation is 5 m to a final state where the water is saturated liquid at 15oC, the velocity is 25 m/s, and the elevation is 2 m. Determine the exergy at (a) the initial state, (b) the final state, (b) and the change in exergy. Take T0= 25oC, p0=1 atm. [Manual Solution] [TEST Solution] Answers: (a) 1623 kJ, (b) 3.15 kJ, (b) 1619 kJ 6-1-7

An insulated tank contains 20 kg of liquid water at 100 kPa and 25oC. An internal electric heater is turned on, which consumes 10 kW of electric power. Determine the rate of increase of (a) temperature and (b) exergy of the water in the tank. (c) How do you explain the fact that the rate of exergy increase is much less than the rate of exergy transfer? [Manual Solution] [TEST Solution] Answers: (a) 0.12 K, (b) 2 J Anim. 6-1-7 (click) A rigid tank contains 20 kg of liquid water at 100 kPa and 25oC. Heat at a rate of 10 kW is transferred into the tank from a source at 1000 K. Determine (a) the rate of exergy transfer from the heating source, and the rate of increase of (b) temperature and (c) exergy of the water in the tank. Assume the atmospheric temperature to be 300 K. [Manual Solution*] [TEST Solution] Answers: (a) 7 kW, (b) 0.12 K/s, (c) 2 W Anim. 6-1-8 (click) 6-1-8

A cylinder of an internal combustion engine contains 3000 cm3 of gaseous products at a pressure of 10 bars and a temperature of 800oC just before the exhaust valve opens. Determine (a) the specific exergy of the gas, and (b) the exergy stored in the cylinder. Model the combustion products as air, a perfect gas. Take T0= 25oC, p0=1 atm. (c) What-if scenario: How would the answer change if the ideal gas model was used for air? [Manual Solution] [TEST Solution] Answers: (a) 313.64 kJ/kg, (b) 3.06 kJ, (c) 3.38 kJ 6-1-9

A 1 m3 tank contains air. (a) Plot how the total stored energy and total stored exergy of air in the tank changes as the pressure is increased from 10 kPa to 10 MPa with temperature held constant at 25 deg-C. (Assume atmospheric conditions to be 100 kPa, 25 deg-C ). (b) Repeat the plot for the specific stored energy and specific stored exergy. (c) Plot how the stored energy and stored exergy of air in the tank changes as the temperature is increased from -100 deg-C to 1000 deg-C with pressure held constant at 100 kPa. (d) Repeat the plot for the specific stored energy and specific stored exergy. [Manual Solution*] [TEST Solution] 6-1-10 [TEST]

Image of an Internal Combustion engine

Answers: (a) 5130 kJ, (b) 7310 kJ, (c) 7429 kJ A granite rock (density 2700 kg/m3, specific heat 1.017 kJ/kg.K) with m = 5000 kg, heats up to T = 45oC during daytime due to solar heating. Assuming the surroundings to be at 20oC. Determine (a) the maximum amount of useful work that could be extracted from the rock. What-if scenario: How would the answer change if (b) the rock temperature increased by 5 oC or (c) the ambient temperature decreased by 5°C? [Manual Solution] [TEST Solution] Answers: (a) 5130 kJ, (b) 7310 kJ, (c) 7429 kJ 6-1-11

Steam at 1 MPa, 500oC flows through a 10-cm-diameter pipe with a velocity of 25 m/s. Determine the rate of (a) exergy transported by the flow. Use the PC model and assume atmospheric conditions to be 100 kPa, 25°C. (b) What-if scenario: How would the answer change if air (use PG model) instead of steam was flowing through the pipe? [Manual Solution*] [TEST Solution] Answers: (a) 648.2 kW, (b) 344.1 kW 6-1-12

Figure 6-1-12

6-1-13

A 20-cm-diameter pipe carries water at 500 kPa, 25°C and 30 m/s. (a) Determine the flow rate of exergy through the pipe. Assume atmospheric conditions to be 100 kPa, 25°C, and use the SL model for water. (b) What-if scenario: How would the answer change if the kinetic energy was neglected? [Manual Solution*] [TEST Solution]

Section-2: Exergy Analysis of Closed Systems

• Closed Steady Systems 6-2-1

A house is electrically heated with resistance heater that draws 15 kW of electric power. It maintains the house at a temperature of 20oC while the outside is 5oC. Assuming steady state, determine (a) the reversible power, and (b) the rate of irreversibility. [Manual Solution] Answers: (a) 0.77 kW (b)14.2 kW

Figure 6-2-1

6-2-2 [mEE]

Heat is conducted steadily through a 5-m x 10-m x 10cm brick wall of a house. On a certain day, the temperature inside is maintained at 25°C when the temperature outside is -5°C. The temperature of the inner and outer surface of the wall are measured to be 20°C and 0°C respectively. If the rate of heat transfer is 1 kW, determine the rate of exergy destruction (a) in the wall and (b) its universe. [Manual Solution] Answers: (a) 0.067 kW, (b) 0.101 kW Anim. 6-2-2 (click)

6-2-3 [mEE]

A refrigerator has a second-law efficiency of 45%, and heat is removed from it at a rate of 200 kJ/min. If the refrigerator is maintained at 2oC, while the surrounding air is at 27oC, determine the power input to the refrigerator [Manual Solution] [TEST Solution] Answers: (a) 0.303 kW

Anim. 6-2-3 (click)

6-2-4

An air-conditioning system is required to transfer heat from a house at a rate of 800 kJ/min to maintain its temperature at 20oC while the outside temperature is 40°C. If the COP of the system is 3.7, determine (a) the power required for air conditioning the house, and (b) the rate of exergy destruction in the universe. [Manual Solution] [TEST Solution] Answers: (a) 3.6 kW (b) 2.69 kW

6-2-5

A heat engine receives heat from a source at 2000 K at a rate of 500 kW, and rejects the waste heat to the atmosphere at 300 K. The net output from the engine is 300 kW. Determine (a) the reversible power output, (b) the rate of exergy input into the engine, (c) the rate of exergy destruction in the universe, and (d) the exergetic (second-law) efficiency. [Manual Solution] [TEST Solution] Answers: (a) 425.0 kW (b) 425.0 kW, (c) 125 kW, (d) 70.59% Anim. 6-2-5 (click)

6-2-6

A heat engine produces 40 kW of power while consuming 40

kW of heat from a source at 1200 K, 50 kW of heat from a source at 1500 K, and rejecting the waste heat to the atmosphere at 300 K. Determine (a) the reversible power, and (b) the rate of exergy destruction in the engine's universe. [Manual Solution] Answers: (a) 70 kW (b) 30 kW

• Closed Processes (Sec. 2 Continued) An insulated rigid tank contains 1.5 kg of helium at 30oC and 500 kPa. A paddle wheel with a power rating of 0.1 kW is operated within the tank for 30 minutes. Determine (a) the minimum work with which this process could be accomplished, and (b) the exergy destroyed in the universe during the process. Assume the surroundings to be at 100 kPa, 25oC. [Manual Solution] [TEST Solution] Answers: (a) -13.33 kJ, (b) 166.66 kJ 6-2-7

Anim. 6-2-7 (click)

6-2-8

An insulated rigid tank contains 1.0 kg of air at 130 kPa and 20 C. A paddle wheel inside the tank is now rotated by an external power source until the temperature in the tank rises to 54oC. If the surrounding air is at 20oC. Determine (a) the exergy destroyed and (b) the reversible work. Use the IG model for air. (c) What-if scenario: How would the answer in part (a) change if the initial pressure was 180 kPa instead? [Manual Solution] [TEST Solution] Answers: (a) 23.1 kJ, (b) -1.31 kJ, (c) 12.6 kJ o

6-2-9

A steam radiator (used for space heating) has a volume of 20 L and is filled up with steam at 200 kPa and 250oC. Now the inlet and exit ports are closed. As the radiator cools down to a room temperature of 20oC. Determine (a) the heat transfer, (b) reversible work. (c) Whatif scenario: How would the answer in part (b) change if the steam pressure in the radiator was 400 kPa instead? [Manual Solution] [TEST Solution] Answers: (a) -43.4 kJ, (b) 7.35 kJ, (c) 19.07 kJ Anim. 6-2-9 (click)

A piston cylinder device initially contains 10 ft3 of helium gas at 25 psia and 40oF. The gas is now compressed in a polytropic process (pV1.3 = constant) to 70 psia. Determine (a) the minimum work with which this process could be accomplished, (b) 2nd law efficiency. Assume the surroundings to be at 14.7 psia, 70oF. [Manual Solution] [TEST Solution] Answers: (a) -19,526.3 ft .lbf, (b) 94.8% 6-2-10

6-2-11

A piston-cylinder device contains 0.1 kg of steam at 1.4 MPa and 290oC. Steam now expands to a final state of 220 kPa and 150oC, doing boundary work. Heat losses from the system to the surroundings are estimated to be 4 kJ during this process. Assume the surroundings to be at 25oC and 100 kPa, determine (a) the exergy change of steam, and (b) the exergy destroyed during the process. (c) [Manual Solution] [TEST Solution] Answers: (a) -21.8 kJ, (b) 13.5 kJ

Water initially a saturated liquid at 95oC is contained in a piston-cylinder assembly. The water undergoes a process to the corresponding saturated vapor state, during which the piston moves freely in the cylinder. The change in state is brought about adiabatically by the stirring action of paddle wheel. Determine on a unit of mass basis the (a) change in stored exergy, (b) the exergy transfer accompanying work, (b) the exergy transfer accompanying heat, (c) and the exergy destruction, each in kJ/kg. Let T0 = 20oC, p0 = 1 bar. [Manual Solution] [TEST Solution] Answers: (a) -2303.5 kJ/kg, (b) 0 kJ/kg, (c) 1807.5 kJ/kg 6-2-12

6-2-13

An insulated piston cylinder device contains 20 L of O2 at 300 kPa and 100oC. It is now heated for 1 min by a 200W resistance heater placed inside the cylinder. The pressure of O2 is maintained constant during the process. Determine (a) the change in stored exergy, and (b) irreversibility during the process. Assume the surroundings to be at 100 kPa, 25oC. (c) What-if scenario: How would the answer in part (b) change if the volume was 50 L instead? [Manual Solution] [TEST Solution]

Anim. 6-2-10 (click)

Answers: (a) 2.13 kJ, (b) 7.57 kJ, (c) 8.57 kJ

Anim. 6-2-13 (click)

6-2-14

A piston-cylinder device initially contains 20 g of saturated water vapor at 300 kPa. A resistance heater is operated within the cylinder with a current of 0.4 A from a 240 V source until the volume doubles. At the same time a heat loss of 4 kJ occurs. Determine (a) the final temperature, (b) duration of the process and (c) second-law efficiency. Assume the surrounding temperature and pressure to be 20oC and 100 kPa respectively. (d) What-if scenario: How would the answer in (c) change if the heat loss was negligible during the process? [Manual Solution] [TEST Solution] Answers: (a) 516.14oC, (b) 207 sec, (c) 31%, (d) 40.2%

6-2-15

A piston-cylinder device contains 0.1 kg of steam at 900 kPa and 320oC. Steam now expands to a final state of 180 kPa and 135oC, doing work. Heat losses from the system to the surroundings are estimated to be 4 kJ during this process. Assuming the surroundings to be at 25oC and 100 kPa, determine (a) the exergy of the steam at the initial and final states, (b) the exergy change of steam, (c) the exergy destroyed, and (d) the exergetic (second-law) efficiency. [Manual Solution] [TEST Solution] Answers: (a) 70.1 kJ, 49.8 kJ, (b) -20.3 kJ (c) 4.25 (d) 79%

6-2-16

Two insulated tanks are connected, both containing H2O. Tank-A is at 200 kPa, v = 0.4 m3/kg, V = 1 m3 and tank B contains 3.5 kg at 0.5 MPa, 400oC. The valve is now opened and the two come to a uniform state. Determine (a) the final pressure, (b) temperature, and (c) irreversibility of the process. Assume the surroundings to be at 100 kPa, 25oC. [Manual Solution] [TEST Solution] Answers: (a) 305.9 kPa, (b) 134.2oC, (c) 253.6 kJ

A 0.5 m3 rigid tank containing hydrogen at 40oC and 200 kPa is connected to another 1 m3 rigid tank containing hydrogen at 20oC 6-2-17

Anim. 6-2-16 (click)

and 600 kPa. The valve is opened and the system is allowed to reach thermal equilibrium with the surroundings at 15oC. Determine the irreversibility in this process. Assume variable c_p. [Manual Solution*] [TEST Solution] Answer: 71.4 kJ

6-2-18

A tank whose volume is unknown is divided into two parts by a partition. One side contains 0.02 m3 of saturated liquid R-12 at 0.7 MPa, while the other side is evacuated. The partition is now removed, and R-12 fills up the entire volume. If the final state is 200 kPa, quality 90%. Determine (a) the volume of the tank, (b) heat transfer and (c) the irreversible work. The atmospheric temperature is 30oC. [Manual Solution] [TEST Solution] Answers: (a) 1.95 m3, (b) 2328.5 kJ, (c) 909 kJ

Anim. 6-2-18 (click)

6-2-19

An insulated rigid tank has two compartments, one 10 times larger than the other, divided by a partition. At the beginning the smaller side contains 4 kg of H2O at 200 kPa and 90oC and the other side is evacuated. The partition is removed and the water expands to a new equilibrium condition. Determine the irreversibility during the process. Assume the surrounding conditions to be 100 kPa and 25oC. (b) What-if scenario: How would the answer change if the larger chamber was 100 times larger? [Manual Solution] [TEST Solution] Answers: (a) 2.152 kJ, (b) 17.57 kJ

A 40 kg aluminum block at 90oC is dropped into an insulated tank that contains 0.5 m3 of liquid water at 20oC. Determine the irreversibility in the resulting process if the surrounding temperature is 27oC. [Manual Solution] [TEST Solution] Answer: 270 kJ 6-2-20

A 4 kg iron block initially at 300oC is dropped into an insulated tank that contains 80 kg of water at 25oC. Assuming the water that vaporizes during this process condenses back in the tank and 6-2-21

Anim. 6-2-20 (click)

the surroundings are at 20oC and 100 kPa. Determine (a) the final equilibrium temperature, (b) the exergy of the combined system at initial and final states, and (c) the wasted work potential during this process. [Manual Solution] [TEST Solution] Answer: (a) 26.45 oC, (b) 164.6 kJ, 24.6 kJ, (c) 138 kJ

Section-3: Open Systems

6-3-1

A 5 kW pump is raising water to an elevation of 25 m from the free surface of a lake. The temperature of water increases by 0.1oC. Neglecting the KE, determine (a) the mass flow rate, (b) the minimum power required, and (c) the exergetic (second-law) efficiency of the system. Assume the ambient temperature to be 20oC. (d) [Manual Solution] [TEST Solution] Answers: (a) 7.534 kg/s, (b) -1.85 kW, (c) 37% Anim. 6-3-1 (click) 6-3-2

Measurements during steady state operation indicate that warm air exits a hand held hair dryer at a temperature of 90oC with a velocity of 10 m/s through an area of 20 cm3. Air enters the dryer at a temperature of 25oC and pressure 100 kPa with a velocity of 3 m/s. No significant change in pressure is observed. Also, no significant heat transfer between the dryer and its surroundings occurs. Determine (a) the external power, and (b) the exergetic efficiency. Let T0= 25o, p0= 1 atm. Use the PG model. [Manual Solution] [TEST Solution] Answers: (a) -1.25 kW, (b) 9.6%

A feedwater heater has 5 kg/s water at 5 MPa, 40oC flowing through it, being heated from two sources. One source adds 900 kW from a 100oC reservoir and the other source adds heat from a 200oC reservoir such that the water exit condition is 5 MPa, 180oC. Determine the exergetic efficiency of the device. Let T0= 25o, p0= 1 atm [Manual Solution*] [TEST Solution] 6-3-3

Answers: (a) 67.4% Argon gas enters an adiabatic compressor at 100 kPa and 25oC with a velocity of 20 m/s and exits at 1 MPa, 550oC and 100 m/s. The 6-3-4

Figure 6-3-3

inlet area of the compressor is 75 cm2. Assuming the surroundings to be at 100 kPa and 25oC, determine (a) the reversible power, (b) irreversibility for this device, and (c) the exergetic efficiency. (d) What-if scenario: How would the answers change if the compressor lost 5 kW of heat to the atmosphere due to poor insulation? [Manual Solution] [TEST Solution] Answers: (a) -63.6 kW, (b) 3.544 kW, (c) 94.7%, (d) -63.6 kW, 8.55 kW, 88.1% Refrigerant-134a is to be compressed from 0.2 MPa and -5oC to 1 MPa and 50oC steadily by an adiabatic compressor. Taking the environment conditions to be 20oC and 95 kPa, Determine (a) the exergy change of the refrigerant (b) and the minimum work input that needs to be supplied to the compressor per unit mass of the refrigerant [Manual Solution] [TEST Solution] Answers: (a) 33.9 kJ/kg, (b) 33.9 kJ/kg 6-3-5

6-3-6

Refrigerant-134a enters an adiabatic compressor as saturated vapor at 120 kPa at a rate of 1 m3/min and exits at 1 MPa. The compressor has an adiabatic efficiency of 85%. Assuming the surrounding conditions to be 100 kPa and 25oC. Determine (a) the actual power and (b) the second-law efficiency of the compressor. (c) What-if scenario: How would the conclusion in (a) change if the compressor had an adiabatic efficiency of 70%? [Manual Solution] [TEST Solution] Answers: (a) -5.36 kW, (b) 86.25 %, (c) -6.51 kW 6-3-7

Consider an air compressor that receives ambient air at 100 kPa, 25oC.It compresses the air to a pressure of 2 MPa, where it exits at a temperature of 800 K. Since the air and compressor housing are hotter than the ambient it loses 80 kJ per kilogram air flowing through the compressor. Determine (a) the reversible work, (b) and the irreversibility in the process. Use the IG model for air. [Manual Solution] [TEST Solution] Answers: (a) -476 kJ/kg, (b) 130 kJ/kg Carbon dioxide (CO2) enters a nozzle at 35 psia, 1400oF and 250 ft/s and exits at 12 psia and 1200oF. Assuming the nozzle to be adiabatic and the surroundings to be at 14.7 psia and 65oF. Determine (a) the exit velocity and (b) the availability drop between the inlet and the exit. (c) What-if scenario: How would the conclusion in (a) change if carbon dioxide entered the nozzle at 500 ft/s? [Manual Solution] 6-3-8

Anim. 6-3-6 (click)

[TEST Solution] Answers: (a) 1731 ft/s, (b) 470 Btu/min, (c) 1784 ft/s

Anim. 6-3-8 (click)

6-3-9

Steam enters a turbine with a pressure of 3 MPa, a temperature of 400 oC, and a velocity of 140 m/s. Steam exits as saturated vapor at 100oC with a velocity of 105 m/s. At steady state, the turbine develops work at a rate of 500 kJ per kg of steam flowing through the turbine. Heat transfer between the turbine and its surroundings occurs at an average outer surface temperature of 450 K. Determine the irreversibility per unit mass of steam flowing through the turbine in kJ/kg. Neglect PE. [Manual Solution] [TEST Solution] Answers: 188.3 kJ/kg 6-3-10

An insulated steam turbine, receives 25 kg of steam per second at 4 MPa, 400oC. At the point in turbine where the pressure is 0.5 MPa, steam is bled off for processing equipment at a rate of 10 kg/s. The temperature of this steam is 230oC. The balance of steam leaves the turbine at 30 kPa, 95% quality. Determine (a)the specific flow exergy at each port, and (b) the exergetic efficiency of the turbine. [Manual Solution] [TEST Solution] Answers: (a) 1200 kJ/kg, 781 kJ/kg, 298.3 kJ/kg, (b) 76 % 6-3-11

Steam enters an adiabatic turbine steadily at 6 MPa and 600 C, 50 m/s, and exits at 50 kPa, 100oC and 150 m/s. The turbine produces 5 MW. If the ambient condition is 100 kPa, 20oC. Determine (a) the maximum possible power output, (b) the second-law efficiency, and (c) the irreversibility. (d) What-if scenario: How would the conclusion in (c) change if the ambient temperature was 40oC? [Manual Solution] [TEST Solution] Answers: (a) 5.79 MW, (b) 86.35 %, (c) 790 kW, (d) 844 kW o

6-3-12

Steam enters a turbine steadily at 2 MPa, a temperature of 400 C at a rate of 6 kg/s and exits at 0.3 MPa and 150oC. The steam is losing heat to the surrounding air at 100 kPa and 25oC at a rate of 200 kW. Determine (a) actual power output, (b) the maximum possible power output, (c) the second law efficiency, and (d) the exergy destroyed. [Manual Solution] [TEST Solution] o

Answers: (a) 2343.37 kW, (b) 2706.1 kW, (C) 86%, (d) 362.8 kw

Anim. 6-3-11 (click)

Steam enters an adiabatic turbine steadily at 8 MPa, 500 oC, 50 m/s, and exits at 30 kPa and 150 m/s. The mass flow rate is 1 kg/s, the adiabatic efficiency is 90%, and the ambient temperature is 300 K. Determine (a) the second law efficiency of the turbine. (b) What-if scenario: How would the conclusion change if the adiabatic efficiency was 85%? [Manual Solution] [TEST Solution] Answers: (a) 91 %, (b) 86.5 % 6-3-13

6-3-14 [TEST]

A steam turbine has the inlet conditions of 5 MPa, 500 deg-C and an exit pressure of 12 kPa. Assuming the atmospheric conditions to be 100 kPa, 25 deg-C, plot how the exergetic efficiency of the turbine changes as the isentropic efficiency decreases from 100% to 75%. [Manual Solution] [TEST Solution] Answers: 6-3-15

Refrigerant-12 is throttled by a valve from the saturated liquid state at 800 kPa to a pressure of 150 kPa at a flow rate of 0.5 kg/s. Assuming the surrounding conditions to be 100 kPa and 25oC. Determine (a) the rate of exergy destruction, and (b) the reversible power. [Manual Solution] [TEST Solution] Answers: (a) 2.98 kW, (b) 2.98 kW

Anim. 6-3-15 (click)

Superheated water vapor enters a valve at 3445 kPa, 260oC and exits at a pressure of 551 kPa. Determine (a) the specific flow exergy at the inlet and exit, and (b) the rate of exergy destruction in the valve per unit of mass flow. Let T0= 25o, p0= 1 atm [Manual Solution] [TEST Solution] Answers: (a) 1018 kJ/kg, 781 kJ/kg, (b) 236.1 kJ/kg 6-3-16

6-3-17

Water at 140 kPa and 280 K enters a mixing chamber at a rate of 2 kg/s, where it is mixed steadily with steam entering at 140 kPa and 400 K. The mixture leaves the chamber at 140 kPa and 320 K, and heat is being lost to the surrounding air at 20oC at a rate of 3 kW. Determine (a) the reversible work, (b) and the rate of exergy destruction. [Manual Solution] [TEST Solution] Answers: (a) 69.65 kW (b) 69.65 kW Liquid water at 100 kPa, 10oC, 1 kg/s is heated by mixing it with an unknown amount of steam at 100 kPa and 200oC in an adiabatic mixing chamber. The surrounding atmosphere is at 100 kPa, 25°C. If the mixture leaves at 100 kPa and 50oC, determine (a) the 6-3-18

Anim. 6-3-17 (click)

mass flow rate of steam. Also determine the rate of transport exergy (b) into and (c) out of the chamber. [Manual Solution] [TEST Solution] Answers: (a) 0.063 kg/s, (b) 35.8 kW, (c) 4.38 kW 6-3-19

Steam enters a closed feedwater heater at 1.1 MPa and 200 C and leaves as saturated liquid at the same pressure. Feedwater enters the heater at 2.5 MPa and 50oC and leaves 12oC below the exit temperature of steam. Neglecting any heat losses, determine (a) the mass flow rate ratio, and (b) the exergetic efficiency of the heat exchanger. Assume surroundings to be at 100 kPa, 25oC. [Manual Solution] [TEST Solution] Answers: (a) 0.254 kg/s, (b) 62.8% o

Anim. 6-3-19 (click)

• Open Processes (Sec. 3 Continued) A 0.5 m3 tank initially contains saturated liquid water at 200 C. A valve in the bottom of the tank is opened and half the liquid is drained. Heat is transferred from a source at 300oC to maintain constant temperature inside the tank. Determine (a) the heat transfer and (b) the reversible work. Assume the surroundings to be at 25oC and 100 kPa. [Manual Solution*] [TEST Solution] Answers: (a) 3843 kJ, (b) 422 kJ 6-3-20 o

A 100 m3 rigid tank initially contains atmospheric air at 100 kPa and 300 K and is to be used as a storage vessel for compressed air at 2 MPA and 300K. Compressed air is to be supplied by a compressor that takes in atmospheric air at 100 kPa and 300 K. Determine the reversible work. Use the PG model for air. [Manual Solution*] [TEST Solution] Answers: (a) 409.146 MJ 6-3-21

A 0.2 m3 tank initially contains R-12 at 1 MPa and x = 1. The tank is charged to 1.2 MPa, x = 0 from a supply line that carries R-12 at 1.5 MPa and 30oC. Determine (a) the heat transfer and (b) the wasted work potential associated with the process. Assume the surrounding temperature to be 50oC? [Manual Solution*] [TEST Solution] Answers: (a) 2803 kJ, (b) 387.2 kJ Anim. 6-3-22 (click) 6-3-22

Copyright 1998-2013: Subrata Bhattacharjee

EXAMPLE E6-1

A tank contains one kg of superheated steam at 10 MPa. Calculate the (a) energy, and (b) exergy stored in the tank. Evaluate the rate of transport of (c) energy and (d) exergy if steam at the same state flows through a pipe. [Manual Solution] [TEST Solution] Answers: (a) 3046kJ, (b) 1087 kJ, (c) 3374 kW, (d) 1411 kW

EXAMPLE E6-2

A thin wall separates two large chambers, the left chamber containing boiling water at 200oC and the right chamber containing a boiling refrigerant at 0oC . The heat transfer through the wall at steady state is measured at 20 kW. Assuming each wall surface to be at the respective chamber temperature and the atmospheric temperature to be 10oC , determine (a) the rate at which exergy enters the wall through the left face, (b) the rate at which exergy leaves the wall through the right face, (c) the rate of exergy destruction in the wall and its immediate surroundings, and (d) the reversible work. [Manual Solution] Answers: (a) 8.034 kW, (b) -0.733 kW, (c) 8.767 kW, (d) 8.767 kW Anim. E6-2 (click)

EXAMPLE E6-3

A heat engine operates with between a reservoir at 1500 K and the atmosphere at 298 K while producing a net power of 30 kW at a thermal efficiency of 40%. Determine (a) the rate of exergy destruction, (b) the exergetic efficiency, and (c) the reversible power. [Manual Solution]

Answers: (a) 30.1 kW, (b) 49.18%, (c) 60.1 kW Anim. E6-3 (click)

EXAMPLE E6-4

An electric water heater supplies hot water at 150 kPa, 70oC at a flow rate of 10 L/min as shown in the accompanying diagram. The water temperature at the inlet is 15oC . Due to poor insulation, heat is lost to the atmosphere at a rate of 2 kW to the surrounding atmosphere at 100 KPa, 25oC . Using the SL (solid/liquid) model for water and neglecting kinetic and potential energy effects, determine (a) the electrical power consumption, (b) the energetic efficiency, (c) the exergetic efficiency, (d) the rate of exergy destruction, and (e) the reversible power. Assume no pressure loss in the system [Manual Solution] [TEST Solution] Answers: (a) (b) (c) 5.04%, (d) 38.17 kW, (e) 2.027 kW Anim. E6-4 (click)

EXAMPLE E6-5

A steam turbine operates steadily with a mass flow rate of 5 kg/s. The steam enters the turbine at 500 kPa, 400oC and leaves at a pressure of 7.5 kPa and a quality of 0.95. Neglecting the changes in ke and pe as well as any heat loss from the turbine to the surroundings which is at 100 kPa and 25oC , determine (a) the reversible work output, (b) the exergetic efficiency. If the cost of exergy is valued at $0.10 per kWh, (c) determine the daily cost of exergy destruction in the turbine's universe. What-if-Scenario: (d) How would the exergetic efficiency change if the turbine were isentropic? [Manual Solution] [TEST Solution] Answers: (a) 4197.7 kW, (b) 97.35 %, (c) $266.9,(d) 100% Anim. E6-5 (click)

EXAMPLE E6-6

R-134a enters the throttling valve of a refrigeration system at 1.5 MPa and 50oC . The valve is set to create an exit pressure of 150 kPa. Determine the rate of exergy destruction per unit mass of the refrigerant. Assume the atmospheric temperature to be 25oC. [Manual Solution] [TEST Solution] Answers: (a) 13.9 kJ/kg Anim. E6-6 (click)

Superheated ammonia at 200 kPa, -10oC enters an adiabatic mixing chamber with a flow rate of 2 kg/s where it mixes with a flow of saturated mixture of ammonia at a quality of 20%. The desuperheated ammonia exits as saturated vapor. Assuming pressure to remain constant, and neglecting change in ke and pe, determine (a) the rate of exergy destruction, and (b) the reversible power. [Manual Solution] [TEST Solution] Answers: (a) 2 kW, (b) 2 kW, Anim. E6-7 (click) EXAMPLE E6-7

EXAMPLE E6-8

Three different options are being considered to raise the temperature of 1000 L of water stored in an insulated tank from 15oC to 70oC . (i) Use electrical resistance heating, (ii) heat transfer from a source at 1500oC , and (iii) heat transfer from a source at 100oC . Based on an exergy analysis, evaluate the best option. Assume atmospheric conditions to be 100 kPa, 25oC . [Manual Solution] [TEST Solution] Answers: Third option

Figure

E6-8

Figure

E6-9

EXAMPLE E6-9

A rubber ball of mass m is dropped from a height h on a rigid floor. It bounces back and forth and finally comes to rest on the floor. What is the entropy generation in the universe due to this irreversible phenomenon? Assume the atmospheric temperature to be To [Manual Solution] Answers: mgh/(1000To) kJ/K

A 40 kg aluminum block at 100oC is dropped into an insulated tank that contains an unknown mass of liquid water at 20oC . After thermal equilibrium is established the temperature is measured as 22oC . Determine (a) the change of stored exergy in the combined system, and (b) the exergy destroyed in this process. [Manual Solution] [TEST Solution] EXAMPLE E6-10

Answers: (a) -329.1 kJ, (b) 329.1 kJ

Anim.

E6-10 (click)

A 1 m3 evacuated, insulated rigid tank is being filled from a supply line carrying steam at 100 kPa and 400oC . Determine the (a) initial exergy and (b) final exergy stored in the tank. Also evaluate (c) the exergy destroyed during the process. Use the PG model for steam and assume the atmospheric conditions to be 100 kPa and 25oC . [Manual Solution] [TEST Solution] EXAMPLE E6-11

Answers: (a) 100 kJ, (b) 121.5 kJ, (c) 38.3 kJ

Anim.

E6-11 (click)