ANSWER ALL QUESTIONS

8- 6C Consider two geothermal wells whose energy contents are estimated to be the same. Will the exergies of these wells necessarily be the same? Explain. 8-7C Consider two systems that are at the same pressure as the environment. The first system is at the same temperature as the environment, whereas the second system is at a lower temperature than the environment. How would you compare the exergies of these two systems? 8- 8C Consider an environment of zero absolute pressure (such as outer space). How will the actual work and the useful work compare in that environment? 8-9C What is the second-law efficiency? How does it differ from the first-law efficiency? 8-10C Does a power plant that has a higher thermal efficiency necessarily have a higher second-law efficiency than one with a lower thermal efficiency? Explain. 8-11C Does a refrigerator that has a higher COP necessarily have a higher second-law efficiency than one with a lower COP? Explain. 8-12C Can a process for which the reversible work is zero be reversible? Can it be irreversible? Explain. 471 CHAPTER 8 8-13C Consider a process during which no entropy is generated (Sgen = 0). Does the exergy destruction for this process have to be zero? 8-14 The electric power needs of a community are to be met by windmills with 20-m-diameter rotors. The windmills are to be located where the wind is blowing steadily at an average velocity of 6 m/s. Determine the minimum number of windmills that need to be installed if the required power output is 900 kW. 8-15E Saturated steam is generated in a boiler by converting a saturated liquid to a saturated vapor at 200 psia. This is done by transferring heat from the combustion gases, which are at 500F, to the water in the boiler tubes. Calculate the wasted work potential associated with this heat transfer process. How does increasing the temperature of the combustion gases affect the work potential of steam stream? Take T0 = 80F and P0 14.7 psia. Answer: 66.8 Btu/lbm W ater 2 0 0 psia - sat. liq. I 2 0 0 psia | sat. vap. FIGURE P8-15E 8-16 One method of meeting the extra electric power demand at peak periods is to pump some water from a large body of water (such as a lake) to a water reservoir at a higher elevation at times of low demand and to generate electricity at times of high demand by letting this water run down and rotate a turbine (i.e., convert the electric energy to potential energy and then back to electric energy). For an energy storage capacity of 5 X 106 kWh, determine the minimum amount of water that needs to be stored at an average elevation (relative to the ground level) of 75 m. Answer: 2.45 x 1010 kg A \ h = 75 m \ \ ' 1 V 8-17 How much of the 100 kJ of thermal energy at 800 K can be converted to useful work? Assume the environment to be at 25 C. 8-18 A heat engine that receives heat from a furnace at 1200C and rejects waste heat to a river at 20C has a thermal efficiency of 40 percent. Determine the second-law efficiency of this power plant. 8-19 Consider a thermal energy reservoir at 1500 K that can supply heat at a rate of 150,000 kJ/h. Determine the exergy of this supplied energy, assuming an environmental temperature of 25C. 8-20 A heat engine receives heat from a source at w 1100 K at a rate of 400 kJ/s, and it rejects the waste heat to a medium at 320 K. The measured power output of the heat engine is 120 kW, and the environment temperature is 25C. Determine (a) the reversible power, (b) the rate of irreversibility, and (c) the second-law efficiency of this heat engine. Answers-, (a) 284 kW, (b) 164 kW, (c) 42.3 percent 821 Reconsider Prob. 8-20. Using EES (or other) software, study the effect of reducing the temperature at which the waste heat is rejected on the reversible power, the rate of irreversibility, and the second-law efficiency as the rejection temperature is varied from 500 to 298 K, and plot the results. 8-22E A heat engine that rejects waste heat to a sink at 530 R has a thermal efficiency of 36 percent and a second-law efficiency of 60 percent. Determine the temperature of the source that supplies heat to this engine. Answer: 1325 R FIGURE P8-16 8-23 A house that is losing heat at a rate of 50,000 kJ/h when the outside temperature drops to 4C is to be heated by electric resistance heaters. If the house is to be maintained at 25C at all times, determine the reversible work input for this process and the irreversibility. Answers: 0.978 kW, 12.91 kW 472 EXERGY: A MEASURE OF WORK POTENTIAL 8-24E A freezer is maintained at 20F by removing heat from it at a rate of 75 Btu/min. The power input to the freezer is 0.70 hp, and the surrounding air is at 75F. Determine (a) the reversible power, (b) the irreversibility, and (c) the second-law efficiency of this freezer. Answers: (a) 0.20 hp, (b) 0.50 hp, (c) 28.9 percent 8-25 A geothermal power plant uses geothermal liquid water at 150C at a rate of 210 kg/s as the heat source, and produces 5.1 MW of net power in an environment at 25C. If 7.5 MW of exergy entering the plant with the geothermal water is destructed within the plant, determine (a) the exergy of the geothermal water entering the plant, (b) the second-law efficiency, and (c) the exergy of the heat rejected from the plant. 8-26 Show that the power produced by a wind turbine is proportional to the cube of the wind velocity and to the square of the blade span diameter. Exergy Analysis of Closed Systems 8-27C Can a system have a higher second-law efficiency than the first-law efficiency during a process? Give examples. 8-28 A mass of 8 kg of helium undergoes a process from an initial state of 3 rnVkg and 15C to a final state of 0.5 inVkg and 80C. Assuming the surroundings to be at 25C and 100 kPa, determine the increase in the useful work potential of the helium during this process. 8-29E Air is expanded in an adiabatic closed system from 150 psia and 100F to 15 psia with an isentropic expansion efficiency of 95 percent. What is the second-law efficiency of this expansion? Take T0 = 77F and P0 = 14.7 psia. 8-30E Which is a more valuable resource for work production in a closed system15 ft3 of air at 100 psia and 250F or 20 ft3 of helium at 60 psia and 200F? Take Tn = 77F and P0 = 14.7 psia. 8-31 Which has the capability to produce the most work in a closed system1 kg of steam at 800 kPa and 180C or 1 kg of R-134a at 800 kPa and 180C? Take T0 = 25C and PQ = 100 kPa. Answers-. 623 kJ, 5.0 kj 8-32 A piston-cylinder device contains 5 kg of refrigerant134a at 0.7 MPa and 60C. The refrigerant is now cooled at constant pressure until it exists as a liquid at 24C. If the surroundings are at 100 kPa and 24C, determine (a) the exergy of the refrigerant at the initial and the final states and (b) the exergy destroyed during this process. 8-33E A well-insulated rigid tank contains 6 lbm of saturated liquid-vapor mixture of water at 35 psia. Initially, threequarters of the mass is in the liquid phase. An electric resistance heater placed in the tank is turned on and kept on until all the liquid in the tank is vaporized. Assuming the surroundings to be at 75F and 14.7 psia, determine (a) the exergy destruction and (b) the second-law efficiency for this process. 8-34 A rigid tank is divided into two equal parts by a partition. One part of the tank contains 4 kg of compressed liquid water at 200 kPa and 80C and the other side is evacuated. Now the partition is removed, and the water expands to fill the entire tank. If the final pressure in the tank is 40 kPa, determine the exergy destroyed during this process. Assume the surroundings to be at 25C and 100 kPa. Answer: 10.3 kj 8-35 Reconsider Prob. 8-34. Using EES (or other) software, study the effect of final pressure in the tank on the exergy destroyed during the process. Plot the exergy destroyed as a function of the final pressure for final pressures between 45 and 5 kPa, and discuss the results. 8-36 An insulated piston-cylinder device contains 0.8 L of saturated liquid water at a constant pressure of 120 kPa. An electric resistance heater inside the cylinder is turned on, and electrical work is done on the water in the amount of 1400 kJ. Assuming the surroundings to be at 25C and 100 kPa, determine (a) the minimum work with which this process could be accomplished and (b) the exergy destroyed during this process. Answers-, (a) 278 kJ, (b) 1104 kJ Saturated liquid L H20 > W, P = 120 kPa < > FIGURE P8-36 8-37 Reconsider Prob. 8-36. Using EES (or other) re is software, investigate the effect of the amount of electrical work supplied to the device on the minimum work and the exergy destroyed as the electrical work is varied from 0 to 2000 kJ, and plot your results. 8-38 An insulated piston-cylinder device contains 0.05 m3 of saturated refrigerant-134a vapor at 0.8 MPa pressure. The refrigerant is now allowed to expand in a reversible manner 473 CHAPTER 8 until the pressure drops to 0.2 MPa. Determine the change in (he exergy of the refrigerant during this process and the reversible work. Assume the surroundings to be at 25C and 100 kPa. 8-39E Oxygen gas is compressed in a piston-cylinder device from an initial state of 12 ft3/lbm and 75F to a final state of 1.5 ft3/lbm and 525F. Determine the reversible work input and the increase in the exergy of the oxygen during this process. Assume the surroundings to be at 14.7 psia and 75F. Answers: 60.7 Btu/lbm, 60.7 Btu/lbm 8-40 A piston-cylinder device initially contains 2 L of air at 100 kPa and 25C. Air is now compressed to a final state of 600 kPa and 150C. The useful work input is 1.2 kJ. Assuming the surroundings are at 100 kPa and 25C, determine (a) the exergy of the air at the initial and the final states, (b) the minimum work that must be supplied to accomplish this compression process, and (c ) the second-law efficiency of this process. Answers: (a) 0, 0.171 kJ, (>) 0.171 kJ, (c) 14.3 percent * : Air = 2 L p i = lOOkPa = 25C FIGURE P 8 -4 0 8-41 A 1.2-m3 insulated rigid tank contains 2.13 kg of carbon dioxide at 100 kPa. Now paddle-wheel work is done on the system until the pressure in the tank rises to 120 kPa. Determine (a) the actual paddle-wheel work done during this process and (b) the minimum paddle-wheel work with which this process (between the same end states) could be accomplished. Take T0 = 298 K. Answers: (a) 87.0 kJ, (b) 7.74 kJ FIGURE P8-41 8-42 An insulated piston-cylinder device initially contains 20 L of air at 140 kPa and 27C. Air is now heated for 10 min by a 100-W resistance heater placed inside the cylinder. The pressure of air is maintained constant during this process, and the surroundings are at 27C and 100 kPa. Determine the exergy destroyed during this process. Answer: 19.9 kJ 8-43 An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains 3 kg of argon gas at 300 kPa and 70C, and the other side is evacuated. The partition is now removed, and the gas fills the entire tank. Assuming the surroundings to be at 25 C, determine the exergy destroyed during this process. Answer: 129 kJ 8-44E A 55-lbm copper block initially at 180F is dropped into an insulated tank that contains 1.2 ft3 of water at 75F. Determine (a) the final equilibrium temperature and (b) the work potential wasted during this process. Assume the surroundings to be at 75 F. 8-45 An iron block of unknown mass at 85C is dropped into an insulated tank that contains 100 L of water at 20C. At the same time, a paddle wheel driven by a 200-W motor is activated to stir the water. It is observed that thermal equilibrium is established after 20 min with a final temperature of 24C. Assuming the surroundings to be at 20C, determine (a) the mass of the iron block and (b) the exergy destroyed during this process. Answers: (a) 52.0 kg, (b) 375 kJ FIGURE P 8 -4 5 8-46 A 50-kg iron block and a 20-kg copper block, both initially at 80C, are dropped into a large lake at 15C. Thermal equilibrium is established after a while as a result of heat transfer between the blocks and the lake water. Assuming the surroundings to be at 20C, determine the amount of work that could have been produced if the entire process were executed in a reversible manner. 8-47E A 12-ft3 rigid tank contains refrigerant-134a at 40 psia and 55 percent quality. Heat is transferred now to the refrigerant from a source at 120F until the pressure rises to 60 psia. Assuming the surroundings to be at 75F, determine (a) the amount of heat transfer between the source and the refrigerant and (b) the exergy destroyed during this process. 474 EXERGY: A MEASURE OF WORK POTENTIAL 8-48 Chickens with an average mass of 1.6 kg and average specific heat of 3.54 kJ/kg-C are to be cooled by chilled water that enters a continuous-flow-type immersion chiller at 0.5C and leaves at 2.5C. Chickens are dropped into the chiller at a uniform temperature of 15C at a rate of 700 chickens per hour and are cooled to an average temperature of 3C before they are taken out. The chiller gains heat from the surroundings at a rate of 400 kJ/h. Determine (a) the rate of heat removal from the chicken, in kW, and (b) the rate of exergy destruction during this chilling process. Take T0 = 25C. 8-49 Carbon steel balls (p = 7833 kg/m3 and cp = 0.465 kJ/kg-C) 8 mm in diameter are annealed by heating them first to 900C in a furnace and then allowing them to cool slowly to 100C in ambient air at 35C. If 1200 balls are to be annealed per hour, determine (a) the rate of heat transfer from the balls to the air and (b) the rate of exergy destruction due to heat loss from the balls to the air. Answers: (a) 260 W, (b) 146 W 8-50 A piston-cylinder device initially contains 0.75 kg of refrigerant-134a at 120 kPa and 20C. Heat is now transferred to the refrigerant from a source at 150C, and the piston which is resting on a set of stops, starts moving when the pressure inside reaches 140 kPa. Heat transfer continues until the temperature reaches 90C. Assuming the surroundings to be at 25C and 100 kPa, determine (a) the work done, (b) the heat transfer, (c) the exergy destroyed, and (d) the second-law efficiency of this process. Answers: (a) 1.53 k j, (b) 44.2 kJ, (c) 8.94 kJ, (gO 31.6 percent FIGURE P8-50 8-51 A 0.04-m3 tank initially contains air at ambient conditions of 100 kPa and 22C. Now, a 15-liter tank containing liquid water at 85 C is placed into the tank without causing any air to escape. After some heat transfer from the water to the air and the surroundings, both the air and water are measured to be at 44C. Determine (a) the amount of heat lost to the surroundings and (b) the exergy destruction during this process. Exergy Analysis of Control Volumes 8-52 Refrigerant-134a enters an expansion valve at 1200 kPa as a saturated liquid and leaves at 200 kPa. Determine (a) the temperature of R-134a at the outlet of the expansion valve and (b) the entropy generation and the exergy destruction during this process. Take T0 = 25C. 8-53 Helium is expanded in a turbine from 1500 kPa and 300C to 100 kPa and 25 C. Determine the maximum work this turbine can produce, in kJ/kg. Does the maximum work require an adiabatic turbine? 8-54 f'M , Air is compressed steadily by an 8-kW compressor from 100 kPa and 17C to 600 kPa and 167C at a rate of 2.1 kg/min. Neglecting the changes in kinetic and potential energies, determine (a) the increase in the exergy of the air and (b) the rate of exergy destroyed during this process. Assume the surroundings to be at 17C. 600 kPa 167C t 100 kPa 17C FIGURE P8-54 8-55 Reconsider Prob. 8-54. Using EES (or other) softN H 1 ware, solve the problem and in addition determine the actual heat transfer, if any, and its direction, the minimum power input (the reversible power), and the compressor secondlaw efficiency. Then interpret the results when the outlet temperature is set to, say, 300C. Explain the values of heat transfer, exergy destroyed, and efficiency when the outlet temperature is set to 209.31 C and mass flow rate to 2.466 kg/min. 8-56 An adiabatic steam diffuser has steam entering at 500 kPa, 200C, and 30 m/s, and leaving as a saturated vapor at 200 kPa. Calculate the second-law efficiency of the diffuser. Take T0 25C. Answer: 88.4 percent 8-57 Air enters a nozzle steadily at 200 kPa and 65C with a velocity of 35 m/s and exits at 95 kPa and 240 m/s. The heat loss from the nozzle to the surrounding medium at 17C is estimated to be 3 kJ/kg. Determine (a) the exit temperature and (b) the exergy destroyed during this process. Answers: (a) 34.0C, (b) 36.9 kJ/kg 8-58 r ^ J Reconsider Prob. 8-57. Using EES (or other) software, study the effect of varying the nozzle exit velocity from 100 to 300 m/s on both the exit temperature and exergy destroyed, and plot the results. 8-59 Steam enters a diffuser at 10 kPa and 50C with a velocity of 300 m/s and exits as saturated vapor at 50C and 70 m/s. The exit area of the diffuser is 3 m2. Determine (a) the mass flow rate of the steam and (b) the wasted work potential during this process. Assume the surroundings to be at 25C. 8-60E Air is compressed steadily by a compressor from 14.7 psia and 60F to 100 psia and 480F at a rate of 22 lbm/min. Assuming the surroundings to be at 60F, determine the minimum power input to the compressor. Assume air to be an ideal gas with variable specific heats, and neglect the changes in kinetic and potential energies. 8-61 Steam enters an adiabatic turbine at 6 MPa, 600C, and 80 m/s and leaves at 50 kPa, 100C, and 140 m/s. If the power output of the turbine is 5 MW, determine (a) the reversible power output and (b) the second-law efficiency of the turbine. Assume the surroundings to be at 25C. Answers: (a) 5.81 MW. (b) 86.1 percent 80 m/s 6 MPa 600C I 50 kPa 100C 140 m/s FIGURE P8-61 475 CHAPTER 8 8-62 Steam is throttled from 6 MPa and 400C to a pressure of 2 MPa. Determine the decrease in exergy of the steam during this process. Assume the surroundings to be at 25C. Answer: 143 kJ/kg 8-63 Carbon dioxide enters a compressor at 100 kPa and 300 K at a rate of 0.2 kg/s and exits at 600 kPa and 450 K. Determine the power input to the compressor if the process involved no irreversibilities. Assume the surroundings to be at 25C. Answer: 25.5 kW 8-64 Combustion gases enter a gas turbine at 900C, 800 kPa, and 100 m/s and leave at 650C, 400 kPa, and 220 m/s. Taking cp = 1.15 kJ/kg C and k 1.3 for the combustion gases, determine (a) the exergy of the combustion gases at the turbine inlet and (b) the work output of the turbine under reversible conditions. Assume the surroundings to be at 25C and 100 kPa. Can this turbine be adiabatic? 8-65E Refrigerant-134a enters an adiabatic compressor as saturated vapor at 30 psia at a rate of 20 ft3/min and exits at 70 psia pressure. If the isentropic efficiency of the compressor is 80 percent, determine (a) the actual power input and (b) the second-law efficiency of the compressor. Assume the surroundings to be at 75F. Answers: (a) 2.85 hp, (b) 79.8 percent 8-66 Refrigerant-134a enters an adiabatic compressor at 26C as a saturated vapor at a rate of 0.45 m3/min and leaves at 800 kPa and 50C. Determine (a) the power input to the compressor, (b) the isentropic efficiency of the compressor, and (c ) the rate of exergy destruction and the second-law efficiency of the compressor. Take 7'(, = 27C. Answers: (a) 2.06 kW, (>) 82.4 percent, (c) 0.342 kW, 83.4 percent 800 kPa 50C t -26C 0.45 m3/min sat. vap. FIGURE P8-66 8-67 Refrigerant-134a is condensed in a refrigeration system by rejecting heat to ambient air at 25C. R-134a enters the condenser at 700 kPa and 50C at a rate of 0.05 kg/s and leaves at the same pressure as a saturated liquid. Determine (a) the rate of heat rejected in the condenser, (b) the 476 EXERGY: A MEASURE OF WORK POTENTIAL COP of this refrigeration cycle if the cooling load at these conditions is 6 kW, and (c ) the rate of exergy destruction in the condenser. Qh 25 C t 700 kPa sat. liq. R-134a ^ ^ ^ 700 kPa, 50C 0.05 kg/s Condenser FIGURE P8-67 8- 68E Refrigerant-22 absorbs heat from a cooled space at 50F as it flows through an evaporator of a refrigeration system. R-22 enters the evaporator at 10F at a rate of 0.08 lbm/s with a quality of 0.3 and leaves as a saturated vapor at the same pressure. Determine (a) the rate of cooling provided, in Btu/h, (b) the rate of exergy destruction in the evaporator, and (c) the second-law efficiency of the evaporator. Take T0 = 77F. The properties of R-22 at the inlet and exit of the evaporator are: /i, = 107.5 Btu/lbm, .s, = 0.2851 Btu/lbm-R, h2 = 172.1 Btu/lbm, s2 = 0.4225 Btu/lbm-R. which is at 100 kPa and 20C. The vapor is released until the last of the liquid inside the vessel disappears. 8-72E A 40-ft3 adiabatic container is initially evacuated. The supply line contains air that is maintained at 150 psia and 90F. The valve is opened until the pressure in the container is the same as the pressure in the supply line. Determine the work potential of the air in this container when it is filled. Take T0 = 80F. Evaporator FIGURE P8-68E 8-69 Air is compressed by a compressor from 101 kPa and 27C to 400 kPa and 220C at a rate of 0.15 kg/s. Neglecting the changes in kinetic and potential energies and assuming the surroundings to be at 25C, determine the reversible power input for this process. Answer: 24.5 kW 8-70 r g n Reconsider Prob. 8-69. Using EES (or other) software, investigate the effect of compressor exit pressure on reversible power. Vary the compressor exit pressure from 200 to 600 kPa while keeping the exit temperature at 220C. Plot the reversible power input for this process as a function of the compressor exit pressure. 8-71 How much exergy is lost in a rigid vessel filled with 1 kg of liquid R-134a, whose temperature remains constant at 20C, as R-134a vapor is released from the vessel? This vessel may exchange heat with the surrounding atmosphere, 8-73E What is the work potential of the air in the filled container of the previous problem if it is filled in such a way that the final pressure and temperature are both the same as in the supply line? The temperature of the surrounding environment is 80F. Note that the container cannot be adiabatic in this case, and it can exchange heat with the natural environment. Answer: 1110 Btu 8-74 Steam expands in a turbine steadily at a rate of 15,000 kg/h, entering at 8 MPa and 450C and leaving at 50 kPa as saturated vapor. Assuming the surroundings to be at 100 kPa and 25 C, determine (a) the power potential of the steam at the inlet conditions and (b) the power output of the turbine if there were no irreversibilities present. Answers: (a) 5515 kW, (>) 3902 kW 8-75E Air enters a compressor at ambient conditions of 15 psia and 60F with a low velocity and exits at 150 psia, 620F, and 350 ft/s. The compressor is cooled by the ambient air at 60F at a rate of 1500 Btu/min. The power input to the compressor is 400 hp. Determine (a) the mass flow rate of air and (b) the portion of the power input that is used just to overcome the irreversibilities. 8-76 Hot combustion gases enter the nozzle of a turbojet engine at 230 kPa, 627C, and 60 m/s and exit at 70 kPa and 450C. Assuming the nozzle to be adiabatic and the surroundings to be at 20C, determine (a) the exit velocity and (b) the decrease in the exergy of the gases. Take k = 1.3 and cp = 1.15 kJ/kg C for the combustion gases. 477 CHAPTER 8 FIGURE P8-76 8-77 Steam is usually accelerated in the nozzle of a turbine before it strikes the turbine blades. Steam enters an adiabatic nozzle at 7 MPa and 500C with a velocity of 70 m/s and exits at 5 MPa and 450C. Assuming the surroundings to be at 25C, determine (a) the exit velocity of the steam, (b) the isentropic efficiency, and (c) the exergy destroyed within the nozzle. 8-78 Ambient air at 100 kPa and 300 K is compressed isentropically in a steady-flow device to 1 MPa. Determine (a) the work input to the compressor, (b) the exergy of the air at the compressor exit, and (c) the exergy of compressed air after it is cooled to 300 K at 1 MPa pressure. 8-79 A 0.1 -ni5 rigid tank initially contains refrigerant-134a at 1.2 MPa and 100 percent quality. The tank is connected by a valve to a supply line that carries refrigerant-134a at 1.6 MPa and 30C. The valve is now opened, allowing the refrigerant to enter the tank, and it is closed when the tank contains only saturated liquid at 1.4 MPa. The refrigerant exchanges heat with its surroundings at 45C and 100 kPa during this process. Determine (a) the mass of the refrigerant that entered the tank and (b) the exergy destroyed during this process. 8-80 A 0.6 -m3 rigid tank is filled with saturated liquid water at 170C. A valve at the bottom of the tank is now opened, and one-half of the total mass is withdrawn from the tank in liquid form. Heat is transferred to water from a source of 210C so that the temperature in the tank remains constant. Determine (a) the amount of heat transfer and (b) the reversible work and exergy destruction for this process. Assume the surroundings to be at 25C and 100 kPa. Answers: (a) 2545 kJ, (b) 141.2 kJ, 141.2 kJ 8-81E An insulated 260-ft3 rigid tank contains air at 40 psia and 180F. A valve connected to the tank is opened, and air is allowed to escape until the pressure inside drops to 20 psia. The air temperature during this process is maintained constant by an electric resistance heater placed in the tank. Determine (a) the electrical work done during this process and (b) the exergy destruction. Assume the surroundings to be at 70F. Answers: (a) 962 Btu, (b) 782 Btu 8-82 A vertical piston-cylinder device initially contains 0.1 m3 of helium at 20C. The mass of the piston is such that it maintains a constant pressure of 300 kPa inside. A valve is now opened, and helium is allowed to escape until the volume inside the cylinder is decreased by one-half. Heat transfer takes place between the helium and its surroundings at 20C and 95 kPa so that the temperature of helium in the cylinder remains constant. Determine (a) the maximum work potential of the helium at the initial state and (b) the exergy destroyed during this process. 8-83 A 0.2 -m3 rigid tank initially contains saturated refrigerant- 134a vapor at 1 MPa. The tank is connected by a valve to a supply line that carries refrigerant-134a at 1.4 MPa and 60C. The valve is now opened, and the refrigerant is allowed to enter the tank. The valve is closed when one-half of the volume of the tank is filled with liquid and the rest with vapor at 1.2 MPa. The refrigerant exchanges heat during this process with the surroundings at 25C. Determine (a) the amount of heat transfer and (b) the exergy destruction associated with this process. 8-84 An insulated vertical piston-cylinder device initially contains 15 kg of water, 13 kg of which is in the vapor phase. The mass of the piston is such that it maintains a constant pressure of 300 kPa inside the cylinder. Now steam at 2 MPa and 400C is allowed to enter the cylinder from a supply line until all the liquid in the cylinder is vaporized. Assuming the surroundings to be at 25C and 100 kPa, determine (a) the amount of steam that has entered and (b) the exergy destroyed during this process. Answers: (a) 8.27 kg, (b) 2832 kJ 8-85 Consider a family of four, with each person taking a 6-minute shower every morning. The average flow rate through the shower head is 10 L/min. City water at 15C is heated to 55C in an electric water heater and tempered to 42C by cold water at the T-elbow of the shower before being routed to the shower head. Determine the amount of exergy destroyed by this family per year as a result of taking daily showers. Take T0 = 25C. 8-86 Liquid water at 200 kPa and 15C is heated in a chamber by mixing it with superheated steam at 200 kPa and 200C. Liquid water enters the mixing chamber at a rate of 4 kg/s, and the chamber is estimated to lose heat to the sur