Solved: The inner and outer surfaces of a 5-m 3 6-m brick

Problem 145P Steam enters a turbine steadily at 4 MPa and 400°C and exits at 0.2 MPa and 150°C in an environment at 25°C. The decrease in the exergy of the steam as it flows through the turbine is (a) 58 kJ/kg ________________ (b) 445 kJ/kg ________________ (c) 458 kJ/kg ________________ (d) 518 kJ/kg (e) 597 kJ/kg

Problem 1P What final state will maximize the work output of a device?

Problem 2P Is the exergy of a system different in different environments?

Problem 3P How does useful work differ from actual work? For what kind of systems are these two identical?

Problem 4P Consider a process that involves no irreversibilities. Will the actual useful work for that process be equal to the reversible work?

Problem 5P Consider two geothermal wells whose energy consents are estimated to be the same. Will the exergies of these wells necessarily be the same? Explain.

Problem 10P Can a process for which the reversible work is zero be reversible? Can it be irreversible? Explain.

Problem 8P 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.

Problem 11P Consider a process , during which no entropy is generated (Sgen = 0). Does the exergy destruction for this process have to be zero?

Problem 7P What is the second-law efficiency? How does it differ from the first-law efficiency?

Problem 6P 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?

Problem 15P How much of the 100 kJ of thermal energy at 650 K can be converted to useful work? Assume the environment to be at 25°C.

Problem 12P The electric power needs of a community are to be met by windmills with 40-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 1500 kW.

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 \(5 \times 10^{6} \mathrm{kWh}\), determine the minimum amount of water that needs to be stored at an average elevation (relative to the ground level) of 75 m. Equation Transcription: Text Transcription: 5 x 106 kWh

Problem 16P A heat engine that receives heat from a furnace at 1200°C and rejects waste heat to a river at 20°C has a thermal efficiency of 40 percent. Determine the second-law efficiency of this power plant.

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 \(500^{\circ} \mathrm{F}\), 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 \(T_{0}=80^{\circ} \mathrm{C} \text { and } P_{0}=14.7 \mathrm{psia}\) Equation Transcription: Text Transcription: 500°F T0=80°C and P0=14.7 psia ________________

A heat engine receives heat from a source at at a rate of \(400 \mathrm{~kJ} / \mathrm{s}\), and it rejects the waste heat to a medium at . The measured power output of the heat engine is , and the environment temperature is \(25^{\circ} \mathrm{C}\). Determine () the reversible power, () the rate of irreversibility, and the second-law efficiency of this heat engine. Equation Transcription: Text Transcription: 400 kJ/s 25°C

Reconsider Prob. 8-18. 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 , and plot the results.

A heat engine that rejects waste heat to a sink at has a thermal efficiency of 25 percent and a second-law efficiency of 50 percent. Determine the temperature of the source that supplies heat to this engine.

Problem 17P 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 25°C.

Problem 21P A house that is losing heat at a rate of 50,000 kJ/h when the outside temperature drops to 4°C is to be heated by electric resistance heaters. If the house is to be maintained at 25°C at all times, determine the reversible work input for this process and the irreversibility.

Problem 23P 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.

Problem 25P A mass of 8 kg of helium undergoes a process from an initial state of 3 m3/kg and 15°C to a final state of 0.5 m3/kg and 80°C. Assuming the surroundings to be at 25°C and 100 kPa, determine the increase in the useful work potential of the helium during this process.

Problem 22P A freezer is maintained at 20°F 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 75°F. Determine (a) the reversible power, (b) the irreversibility, and (c) the second-law efficiency of this freezer.

Problem 26P Air is expanded in an adiabatic closed system from 180 psia and 140°F to 20 psia with an isentropic expansion efficiency of 95 percent. What is the second-law efficiency of this expansion? Take T0 = 77°F and P0 = 14.7 psia.

Problem 27P Which is a more valuable resource for work production in a closed system—15 ft3 of air at 100 psia and 250°F or 20 ft3 of helium at 60 psia and 200°F? Take T0= 77°F and P0 = 14.7 psia.

Which has the capability to produce the most work in a closed system of steam at 80 \(\mathrm{kPa} \text { and } 180^{\circ} \mathrm{C}\) or of R-134a at \(80 \mathrm{kPa} \text { and } 180^{\circ} \mathrm{C}\) ? Take \(T_{0}=25^{\circ} \mathrm{C} \text { and } P_{0}=100 \mathrm{kPa}\). Answers: Equation Transcription: Text Transcription: 80kPa and 180°C 80kPa and 180°C T0=25°C and P0=100kPa

An insulated piston–cylinder device contains 0.8 L of saturated liquid water at a constant pressure of \(120 \mathrm{kPa}\). An electric resistance heater inside the cylinder is turned on, and electrical work is done on the water in the amount of \(1400 \mathrm{~kJ}\). Assuming the surroundings to be at \(25^{\circ} \mathrm{C}\) and \(100 \mathrm{kPa}\), determine () the minimum work with which this process could be accomplished and () the exergy destroyed during this process Equation Transcription: Text Transcription: 120 kPa 1400 kJ 25°C 100 kPa

Problem 32P A well-insulated rigid tank contains 6 Ibm of saturated liquid–vapor mixture of water at 35 psia. Initially, three-quarters 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. Assurning the surroundings to be at 75°F and 14.7 psia, determine (a) the exergy destruction and (b) the second-law efficiency for this process.

Problem 29P A piston-cylinder device contains 8 kg of refrigerant-134a at 0.7 MPa and 60°C. The refrigerant is now cooled at constant pressure until it exists as a liquid at 20°C. If the surroundings are at 100 kPa and 20°C, determine (a) the exergy of the refrigerant at the initial and the final states and (b) the exergy destroyed during this process.

The radiator of a steam heating system has a volume of and is filled with superheated water vapor at \(200 \mathrm{kPa} \text { and } 200^{\circ} \mathrm{C}\). At this moment both the inlet and the exit valves to the radiator are closed. After a while it is observed that the temperature of the steam drops to as a result of heat transfer to the room air, which is at \(21^{\circ} \mathrm{C}\). Assuming the surroundings to be at \(0^{\circ} \mathrm{C}\) determine the amount of heat transfer to the room and the maximum amount of heat that can be supplied to the room if this heat from the radiator is supplied to a heat engine that is driving a heat pump! Assume the heat engine operates between the radiator and the surroundings. Equation Transcription: Text Transcription: 200 kPa and 200°C 21°C 0°C

Reconsider Prob. 8–33. Using EES (or other) 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 \(2000 \mathrm{~kJ}\), and plot your results. Equation Transcription: Text Transcription: 2000 kJ

Problem 35P An insulated piston-cylinder device contains 0.03 m3 of saturated refrigerant-134a vapor at 0.6 MPa pressure. The refrigerant is now allowed to expand in a reversible manner until the pressure drops to 0.16 MPa. Determine the change in the exergy of the refrigerant during this process and the reversible work. Assume the surroundings to be at 25°C and 100 kPa.

Problem 36P Oxygen gas is compressed in a piston-cylinder device from an initial state of 12 ft3/lbm and 75°F to a final state of 1.5 ft3/lbm and 525°F. 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 75°F.

Problem 39P An insulated piston-cylinder device initially contains 20 L of air at 140 kPa and 27°C. 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 27°C and 100 kPa. Determine the exergy destroyed during this process.

Problem 40P 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 70°C, 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.

Problem 41P A 70-lbm copper block initially at 220°F is dropped into an insulated tank that contains 1.2 ft3 of water at 65°F. Determine (a) the final equilibrium temperature and (b) the work potential wasted during this process. Assume the surroundings to be at 65°F.

A piston-cylinder device initially contains of air at \(100 \mathrm{kP} \text { a and } 25^{\circ} \mathrm{C}\). Air is now compressed to a final state of \(600 \mathrm{kP} \text { a and } 150^{\circ} \mathrm{C}\). The useful work input is \(1.2 \mathrm{~kJ}\). Assuming the surroundings are at \(100 \mathrm{kP} \text { a and } 25^{\circ} \mathrm{C}\), determine the exergy of the air at the initial and the final states, () the minimum work that must be supplied to accomplish this compression process, and the second-law efficiency of this process. Equation Transcription: Text Transcription: 100kPa and 25°C 600kPa and 150°C 1.2 kJ 100kPa and 25°C

A \(0.8-m^{3}\) insulated rigid tank contains \(1.54 \mathrm{~kg}\) of carbon dioxide at . Now paddle-wheel work is done on the system until the pressure in the tank rises to . Determine (a) the actual paddle-wheel work done during this process and the minimum paddle-wheel work with which this process (between the same end states) could be accomplished. Take \(T_{0}=298 \mathrm{~K}\) Equation Transcription: Text Transcription: 0.8-m3 1.54 kg T0=298 K

An iron block of unknown mass at \(85^{\circ} \mathrm{C}\) is dropped into an insulated tank that contains of water at \(20^{\circ} \mathrm{C}\). 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 \(24^{\circ} \mathrm{C}\). Assuming the surroundings to be at \(20^{\circ} \mathrm{C}\), determine (a) the mass of the iron block and the exergy destroyed during this process. Answers: (a) , (b) Equation Transcription: Text Transcription: 85°C 20°C 24°C 20°C

Problem 43P A 12-ft3 rigid tank contains refrigerant-134a at 30 psia and 55 percent quality. Heat is transferred now to the refrigerant from a source at 120°F until the pressure rises to 50 psia. Assuming the surroundings to be at 75°F, determine (a) the amount of heat transfer between the source and the refrigerant and (b) the exergy destroyed during this process.

Problem 44P Stainless steel ball bearings (? = 8085 kg/m3 and cp = 0.480 kJ/kg·°C) having a diameter of 1.2 cm are to be quenched in water at a rate of 1400 per minute. The balls leave the oven at a uniform temperature of 900°C and are exposed to air at 30°C for a while before they are dropped into the water. If the temperature of the balls drops to 850°C prior to quenching, 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.

An ordinary egg can be approximated as a 5.5-cmdiameter sphere. The egg is initially at a uniform temperature of \(8^{\circ} \mathrm{C}\) and is dropped into boiling water at \(97^{\circ} \mathrm{C}\). Taking the properties of egg to be \(\rho=1020 \mathrm{~kg} / \mathrm{m}^{3} \text { and } c_{p}=3.32 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\), determine how much heat is transferred to the egg by the time the average temperature of the egg rises to \(70^{\circ} \mathrm{C}\) and the amount of exergy destruction associated with this heat transfer process. Take \(T_{0}=25^{\circ} \mathrm{C}\) Equation Transcription: Text Transcription: 8°C 97°C \rho =1020 kg/m3 and cp=3.32 kJ/kg°C 70°C T0=25°C

Problem 46P Chickens with an average mass of 1.6 kg and average specific heat of 3.54 U/kg °C are to be cooled by chilled water that enters a continuous-flow-type immersion chiller at 0.5°C and leaves at 2.5°C. Chickens are dropped into the chiller at a uniform temperature of 15°C at a rate of 700 chickens per hour and are cooled to an average temperature of 3°C 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 =25°C.

A piston-cylinder device initially contains of refrigerant- at \(100 \mathrm{kPa} \text { and } 20^{\circ} \mathrm{C}\). Heat is now transferred to the refrigerant from a source at \(150^{\circ} \mathrm{C}\), and the piston which is resting on a set of stops, starts moving when the pressure inside reaches . Heat transfer continues until the temperature reaches \(80^{\circ} \mathrm{C}\). Assuming the surroundings to be at \(25^{\circ} \mathrm{C} \text { and } 100 \mathrm{kPa}\), determine the work done, the heat transfer, the exergy destroyed, and the second-law efficiency of this process. Equation Transcription: Text Transcription: 100kPa and 20°C 150°C 80°C 25°C and 100 kPa

Problem 48P Refrigerant-134a at 1 MPa and 100°C is throttled to a pressure of 0.8 MPa. Determine the reversible work and exergy destroyed during this throttling process. Assume the surroundings to be at 30°C.

Problem 50P Helium is expanded in a turbine from 1500 kPa and 300°C 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?

Reconsider Prob. 8-51. Using EES (or other) software, 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 second-law efficiency. Then interpret the results when the outlet temperature is set to, say, \(300^{\circ} \mathrm{C}\). Explain the values of heat transfer, exergy destroyed, and efficiency when the outlet temperature is set to \(209.31^{\circ} \mathrm{C}\) and mass flow rate to \(2.466 \mathrm{~kg} / \mathrm{min}\) Equation Transcription: Text Transcription: 300°C 209.31°C 2.466 kg/min

Air is compressed steadily by an 8-kW compressor from 100 kPa and \(17^{\circ} \mathrm{C}\) to 600 kPa and \(167^{\circ} \mathrm{C}\) at a rate of \(2.1 \mathrm{~kg} / \mathrm{min}\). Neglecting the changes in kinetic and potential energies, determine () the increase in the exergy of the air and () the rate of exergy destroyed during this process. Assume the surroundings to be at \(17^{\circ} \mathrm{C}\) Equation Transcription: Text Transcription: 17°C 167°C 2.1 kg/min 17°C

Problem 53P Air enters a nozzle steadily at 200 kPa and 65 °C 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 17°C is estimated to be 3 kJ/kg. Determine (a) the exit temperature and (b) the exergy destroyed during this process.

Problem 55P Steam enters a diffuser at 10 kPa and 60°C with a velocity of 375 m/s and exits as saturated vapor at 50°C 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 25°C.

Reconsider Prob. 8–53. 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. Equation Transcription: Text Transcription: 100 to 300 m/s

Problem 56P Air is compressed steadily by a compressor from 14.7 psia and 60°F to 100 psia and 480°F at a rate of 22 lbm/min. Assuming the surroundings to be at 60°F, 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.

Problem 57P Argon gas enters an adiabatic compressor at 120 kPa and 30°C with a velocity of 20 m/s and exits at 1.2 MPa, 530°C, and 80 m/s. The inlet area of the compressor is 130 cm2. Assuming the surroundings to be at 25°C, determine the reversible power input and exergy destroyed.

Problem 59P Steam is throttled from 7 MPa and 500°C to a pressure of 1 MPa. Determine the decrease in exergy of the steam during this process. Assume the surroundings to be at 25°C.

Problem 60P 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 25°C.

Steam enters an adiabatic turbine at \(6 M P a, 600^{\circ} C \text { and } 80 \mathrm{~m} / \mathrm{s}\) and leaves at \(50 \mathrm{kP} a, 100^{\circ} \mathrm{C} \text { and } 140 \mathrm{~m} / \mathrm{s}\). If the power output of the turbine is 5 MW, determine () the reversible power output and () the second-law efficiency of the turbine. Assume the surroundings to be at \(25^{\circ} \mathrm{C}\) Equation Transcription: Text Transcription: 6 MPa, 600°C and 80 m/s 50 kPa, 100°C and 140 m/s 25°C

Problem 61P Combustion gases enter a gas turbine at 900°C, 800 kPa, and 100 m/s and leave at 650°C, 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 25°C and 100 kPa. Can this turbine be adiabatic?

Refrigerant-134a enters an adiabatic compressor at \(-30^{\circ} \mathrm{C}\) as a saturated vapor at a rate of \(0.45 \mathrm{~m}^{3} / \mathrm{min}\) and leaves at and \(55^{\circ} \mathrm{C}\). Determine the power input to the compressor, (b) the isentropic efficiency of the compressor, and the rate of exergy destruction and the second-law efficiency of the compressor. Take \(T_{0}=27^{\circ} \mathrm{C}\) Equation Transcription: Text Transcription: -30°C 0.45 m3/min 55°C T0=27°C

Refrigerant-134a is condensed in a refrigeration system by rejecting heat to ambient air at \(25^{\circ} \mathrm{C}\) R-134a enters the condenser at 700 kPa and \(50^{\circ} \mathrm{C}\) at a rate of \(0.05 \mathrm{~kg} / \mathrm{s}\) and leaves at the same pressure as a saturated liquid. Determine () the rate of heat rejected in the condenser, () the 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. Equation Transcription: Text Transcription: 25°C 50°C 0.05 kg/s

Problem 64P Air enters the evaporator section of a window air conditioner at 100 kPa and 27°C with a volume flow rate of 6 m3/min. Refrigerant-134a at 120 kPa with a quality of 0.3 enters the evaporator at a rate of 2 kg/min and leaves as saturated vapor at the same pressure. Determine the exit temperature of the air and the exergy destruction for this process, assuming (a) the outer surfaces of the air conditioner are insulated and (b) heat is transferred to the evaporator of the air conditioner from the surrounding medium at 32°C at a rate of 30 kJ/min.

Problem 66P How much exergy is lost in a rigid vessel filled with 1 kg of liquid R-134a, whose temperature remains constant at 24°C, as R-134a vapor is released from the vessel? This vessel may exchange heat with the surrounding atmosphere, which is at 100 kPa and 24°C. The vapor is released until the last of the liquid inside the vessel disappears.

Refrigerant-22 absorbs heat from a cooled space at \(50^{\circ} \mathrm{F}\) as it flows through an evaporator of a refrigeration system. R-22 enters the evaporator at \(10^{\circ} \mathrm{F}\) at a rate of \(0.08 \mathrm{lbm} / \mathrm{s}\) with a quality of and leaves as a saturated vapor at the same pressure. Determine the rate of cooling provided, in the rate of exergy destruction in the evaporator, and the second-law efficiency of the evaporator. Take \(T_{0}=77^{\circ} \mathrm{F}\) The properties of R-22 at the inlet and exit of the evaporator are: \(h_{1}=107.5 \mathrm{Btu} / \mathrm{lbm}, s_{1}=0.2851 \mathrm{Btu} / \mathrm{lbm} \cdot R, h_{2}=172.1 \mathrm{Btu} / \mathrm{lbm}, s_{2}=0.4225 \mathrm{Btu} / \mathrm{lbm} \cdot R\) Equation Transcription: Text Transcription: 50°F 10°F 0.08lbm/s T0=77°F h1=107.5Btu/lbm, s1=0.2851Btu/lbmR,h2=172.1Btu/lbm, s2=0.4225Btu/lbmR

A \(40-f t^{3}\) adiabatic container is initially evacuated. The supply line contains air that is maintained at 150 psia and \(90^{\circ} \mathrm{F}\). 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 \(T_{0}=80^{\circ} \mathrm{F}\). Equation Transcription: Text Transcription: 40-ft3 90°F T0=80°F

Problem 68P 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 80°F. Note that the container cannot be adiabatic in this case, and it can exchange heat with the natural environment.

Problem 69P Steam expands in a turbine steadily at a rate of18,000kg/h, entering at 7 MPa and 600°C 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.

Hot combustion gases enter the nozzle of a turbojet engine at \(230 \mathrm{kPa}, 627^{\circ} \mathrm{C} \text { and } 60 \mathrm{~m} / \mathrm{s}\) and exit at and \(450^{\circ} \mathrm{C}\). Assuming the nozzle to be adiabatic and the surroundings to be at \(20^{\circ} \mathrm{C}\), determine the exit velocity and () the decrease in the exergy of the gases. Take \(k=1.3 \mathrm{and} c_{p}=1.15 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\) for the combustion gases. Equation Transcription: Text Transcription: 230 kPa, 627°C and 60 m/s 450°C 20°C k=1.3 and cp=1.15 kJ/kg°C

Problem 72P 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 500°C with a velocity of 70 m/s and exits at 5 MPa and 450°C. Assuming the surroundings to be at 25°C, determine (a) the exit velocity of the steam, (b) the isentropic efficiency, and (c) the exergy destroyed within the nozzle.

Problem 73P Ambient air at 100 kPa and 300 K is compressed isentropically in a steady-flow device to 0.8 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 0.8 MPa pressure.

Problem 70P Air enters a compressor at ambient conditions of 15 psia and 60°F with a low velocity and exits at 150 psia, 620°F, and 350 ft/s. The compressor is cooled by the ambient air at 60°F at a rate of 1500 Btu/min. The power input to the compressor is 400 hp. rJetermine (a) the mass flow rate of air and (b) the portion of the power input that is used just to overcome the irreversibilities.

Problem 76P An insulated 260-ft3 rigid tank contains air at 40 psia and 180°F. 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 70°F.

Problem 74P A 0.6-m3 rigid tank is filled with saturated liquid water at 170°C. A valve at the bottom of the tank is now opened, and one-half of the total mass is withdrawn from the fcink in liquid form. Heat is transferred to water from a source of 210°C 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 25°C and 100 kPa.

Problem 75P A 0.1-m3 rigid tank contains saturated refrigerant-134a at 800 kPa. Initially, 30 percent of the volume is occupied by liquid and the rest by vapor. A valve at the bottom of the tank is opened, and liquid is withdrawn from the tank. Heat is transferred to the refrigerant from a source at 60°C so that the pressure inside the tank remains constant. The valve is closed when no liquid is left in the tank and vapor starts to come out. Assuming the surroundings to be at 25°C, determine (a) the final mass in the tank and (b) the reversible work associated with this process.

Cold water \(\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) leading to a shower enters a well-insulated, thin-walled, double-pipe, counterflow heat exchanger at \(15^{\circ} \mathrm{C}\) at a rate of \(0.25 \mathrm{~kg} / \mathrm{s}\) and is heated to \(45^{\circ} \mathrm{C}\) by hot water \(\left(c_{p}=4.19 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) that enters at \(100^{\circ} \mathrm{C}\) at a rate of \(3 \mathrm{~kg} / \mathrm{s}\) Determine the rate of heat transfer and the rate of exergy destruction in the heat exchanger. Take \(T_{0}=25^{\circ} \mathrm{C}\) Equation Transcription: Text Transcription: (cp=4.18 kJ/kg°C) 15°C 0.25 kg/s 45°C (cp=4.19 kJ/kg°C) 100°C 3 kg/s T0=25°C

Outdoor air \(\left(c_{p}=1.005 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) is to be preheated by hot exhaust gases in a cross-flow heat exchanger before it enters the furnace. Air enters the heat exchanger at \(101 \mathrm{kPa} \text { and } 30^{\circ} \mathrm{C}\) at a rate of \(0.5 \mathrm{~m}^{3} / \mathrm{s}\). The combustion gases \(\left(c_{p}=1.10 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) enter at \(350^{\circ} \mathrm{C}\) at a rate of \(0.85 \mathrm{~kg} / \mathrm{s}\) and leave at \(260^{\circ} \mathrm{C}\) Determine the rate of heat transfer to the air and the rate of exergy destruction in the heat exchanger. Equation Transcription: Text Transcription: (cp=1.005 kJ/kg°C) 101kPa and 30°C 0.5 m3/s (cp=1.10kJ/kg°C) 350°C 0.85 kg/s 260°C

Problem 78P 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 400°C 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 25°C and 100 kPa, determine (a) the amount of steam that has entered and (b) the exergy destroyed during this process.

A vertical piston-cylinder device initially contains \(0.12 \mathrm{~m}^{3}\) of helium at \(20^{\circ} \mathrm{C}\) The mass of the piston is such that it maintains a constant pressure of inside. 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 \(20^{\circ} \mathrm{C} \text { and } 95 \mathrm{kPa}\) so that the temperature of helium in the cylinder remains constant. Determine the maximum work potential of the helium at the initial state and the exergy destroyed during this process. Equation Transcription: Text Transcription: 0.12 m3 20°C 20°C and 95 kPa

Problem 79P 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 15°C is heated to 55°C in an electric water heater and tempered to 42°C 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 =25°C.

Problem 82P Steam is to be condensed on the shell side of a heat exchanger at 120°F. Cooling water enters the tubes at 60°F at a rate of 115.3 lbm/s and leaves at 73°F. Assuming the heat exchanger to be well insulated, determine (a) the rate of heat transfer in the heat exchanger and (b) the rate of exergy destruction in the heat exchanger. Take T0 = 77°F.

Problem 83P Air enters a compressor at ambient 'conditions of 100 kPa and 20°C at a rate of 4.5 m3/s with a low velocity, and exits at 900 kPa, 60°C, and 80 m/s. The compressor is cooled by cooling water that experiences a temperature rise of 10°C. The isothermal efficiency of the compressor is 70 percent. Determine (a) the actual and reversible power inputs, (b) the second-law efficiency, and (c) the mass flow rate of the cooling water.

Problem 84P A hot-water stream at 160°F enters an adiabatic mixing chamber with a mass flow rate of 4 lbm/s, where it is mixed with a stream of cold water at 70°F. If the mixture leaves the chamber at 110°F, determine (a) the mass flow rate of the cold water and (b) the exergy destroyed during this adiabatic mixing process. Assume all the streams are at a pressure of 50 psia and the surroundings are at 75°F.

Liquid water at \(20^{\circ} \mathrm{C}\) is heated in a chamber by mixing it with saturated steam. Liquid water enters the chamber at the steam pressure at a rate of \(4.6 \mathrm{~kg} / \mathrm{s}\) and the saturated steam enters at a rate of \(0.19 \mathrm{~kg} / \mathrm{s}\). The mixture leaves the mixing chamber as a liquid at \(45^{\circ} \mathrm{C}\). If the surroundings are at \(20^{\circ} \mathrm{C}\), determine the temperature of saturated steam entering the chamber, the exergy destruction during this mixing process, and the second-law efficiency of the mixing chamber. Equation Transcription: Text Transcription: 20°C 4.6 kg/s 0.19 kg/s 45°C 20°C

Problem 86P A refrigerator has a second-law efficiency of 28 percent, and heat is removed from the refrigerated space at a rate of 800 Btu/min. If the space is maintained at 25°F while the surrounding air temperature is 90°F, determine the power input to the refrigerator.

Problem 87P Refrigerant-134a is expanded adiabatically in an expansion valve from 700 kPa and 25°C to 160 kPa. For environment conditions of 100 kPa and 20°C, determine (a) the work potential of R-134a at the inlet, (b) the exergy destruction during the process, and (c) the second-law efficiency.

Problem 89P Steam is condensed in a closed system at a constant pressure of 75 kPa from a saturated vapor to a saturated liquid by rejecting heat to a thermal energy reservoir at 37°C. Determine the second-law efficiency of this process. Take T0 = 25°C and P0= l00kPa.

Refrigerant-134a is converted from a saturated liquid to a saturated vapor in a closed system using a reversible constant pressure process by transferring heat from a heat reservoir at \(6^{\circ} \mathrm{C}\) From second-law point of view, is it more effective to do this phase change at or ? Take \(T_{0}=25^{\circ} \mathrm{C} \text { and } P_{0}=100 \mathrm{kPa}\). Equation Transcription: Text Transcription: 6°C T0=25°C and P0=100kPa

Problem 88P Steam enters an adiabatic nozzle at 3.5 MPa and 300°C with a low velocity and leaves at 1.6 MPa and 250°C at a rate of 0.4 kg/s. If the ambient state is 100 kPa and 18°C, determine (a) the exit velocity, (b) the rate of exergy destruction, and (c) the second-law efficiency.

Problem 91P An adiabatic heat exchanger is to cool ethylene glycol (c = 2.56 kJ/kg·°C) flowing at a rate of 2 kg/s from 80 to 40°C by water (cp = 4.18 kJ/kg·°C) that enters at 20°C and leaves at 55°C. Determine (a) the rate of heat transfer and (b) the rate of exergy destruction in the heat exchanger.

Problem 94P A crater lake has a base area of 20,000 m2, and the water it contains is 12 m deep. The ground surrounding the crater is nearly flat and is 140 m below the base of the lake. Determine the maximum amount of electrical work, in kWh, that can be generated by feeding this water to a hydroelectric power plant.

The inner and outer surfaces of a \(5-m \times 6-m\) brick wall of thickness \(30 \mathrm{~cm}\) are maintained at temperatures of \(20^{\circ} \mathrm{C} \text { and } 5^{\circ} \mathrm{C}\), respectively, and the rate of heat transfer through the wall is . Determine the rate of exergy destruction associated with this process. Take \(T_{0}=0^{\circ} \mathrm{C}\). Equation Transcription: Text Transcription: 5-m x 6 -m 30 cm 20°C and 5°C T0=0°C

Hot exhaust gases leaving an internal combustion engine at \(400^{\circ} \mathrm{C}$ and $150 \mathrm{kPa}\) at a rate of \(0.8 \mathrm{~kg} / \mathrm{s}\) is to be used to produce saturated steam at \(200^{\circ}\) in an insulated heat exchanger. Water enters the heat exchanger at the ambient temperature of \(20^{\circ} \mathrm{C}\), and the exhaust gases leave the heat exchanger at \(350^{\circ} \mathrm{C}\). Determine the rate of steam production, the rate of exergy destruction in the heat exchanger, and the second-law efficiency of the heat exchanger. Equation Transcription: Text Transcription: 400°C and 150 kPa 0.8 kg/s 200°C 20°C 350°C

A well-insulated, thin-walled, counter-flow heat exchanger is to be used to cool oil \(\left(c_{p}=2.20 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) from \(150 \mathrm{to} 40^{\circ} \mathrm{C}\) at a rate of \(2 \mathrm{~kg} / \mathrm{s}\) by water \(\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)\) that enters at \(22^{\circ} \mathrm{C}\) at a rate of \(1.5 \mathrm{~kg} / \mathrm{s}\) The diameter of the tube is , and its length is . Determine the rate of heat transfer and the rate of exergy destruction in the heat exchanger. Equation Transcription: Text Transcription: (cp=2.20 kJ/kg°C) 150 to 40°C 2 kg/s (cp=4.18 kJ/kg°C) 22°C 1.5 kg/s

Problem 96P A 1000-W iron is left on the ironing board with its base exposed to the air at 20°C. If the temperature of the base of the iron is 150°C, determine the rate of exergy destruction for this process due to heat transfer, in steady operation.

A \(30-\mathrm{cm}-\text { long }\), 1500-W electric resistance heating element whose diameter is is immersed in of water initially at \(20^{\circ} \mathrm{C}\). Assuming the water container is well insulated, determine how long it will take for this heater to raise the water temperature to \(80^{\circ} \mathrm{C}\). Also, determine the minimum work input required and exergy destruction for this process, in kJ. Take \(T_{0}=20^{\circ} \mathrm{C}\). Equation Transcription: Text Transcription: 30 -cm-long 20°C 80°C T0=20°C

Problem 98P An adiabatic steam nozzle has steam entering at 300 kPa, 150°C, and 45 m/s, and leaving as a saturated vapor at 150 kPa. Calculate the actual and maximum outlet velocity. Take T0 = 25°C.

Problem 99P A steam turbine is equipped to bleed 6 percent of the inlet steam for feedwater heating. It is operated with 500 psia and 600°F steam at the inlet, a bleed pressure of 100 psia, and an exhaust pressure of 5 psia. The turbine efficiency between the inlet and bleed point is 97 percent, and the efficiency between the bleed point and exhaust is 95 percent. Calculate this turbine's second-law efficiency. Take T0 =77°F.

To control an isentropic steam turbine, a throttle valve is placed in the steam line leading to the turbine inlet. Steam at \(6 M P a \text { and } 600^{\circ} \mathrm{C}\) is supplied to the throttle inlet, and the turbine exhaust pressure is set at . What is the effect on the stream exergy at the turbine inlet when the throttle valve is partially closed such that the pressure at the turbine inlet is . Compare the second-law efficiency of this system when the valve is partially open to when it is fully open. Take \(T_{0}=25^{\circ} \mathrm{C}\). Equation Transcription: Text Transcription: 6MPa and 600°C T0=25°C

Two rigid tanks are connected by a valve. Tank is insulated and contains \(0.2 \mathrm{~m}^{3}\) of steam at and 80 percent quality. Tank is uninsulated and contains of steam at and \(250^{\circ} \mathrm{C}\). The valve is now opened, and steam flows from tank to tank until the pressure in tank drops to . During this process of heat is transferred from tank to the surroundings at \(0^{\circ} \mathrm{C}\) Assuming the steam remaining inside tank to have undergone a reversible adiabatic process, determine the final temperature in each tank and the work potential wasted during this process. Equation Transcription: Text Transcription: 0.2 m3 250°C 0°C

Problem 102P A piston-cylinder device initially contains 8 ft3 of helium gas at 40 psia and 70°F. Helium is now compressed in a polytropic process (P Vn = constant) to 140 psia and 320°F. Assuming the surroundings to be at 14.7 psia and 70°F, determine (a) the actual useful work consumed and (b) the minimum useful work input needed for this process.

Steam enters a two-stage adiabatic turbine at \(8 M P a \text { and } 500^{\circ} C\). It expands in the first stage to a state of \(2 M P a \text { and } 350^{\circ} \mathrm{C}\). Steam is then reheated at constant pressure to a temperature of \(500^{\circ} \mathrm{C}\) before it is routed to the second stage, where it exits at and a quality of 97 percent. The work output of the turbine is . Assuming the surroundings to be at \(25^{\circ} \mathrm{C}\), determine the reversible power output and the rate of exergy destruction within this turbine. Equation Transcription: Text Transcription: 8MPa and 500°C 2MPa and 350°C 500°C 25°C

Problem 103P Steam at 7 MPa and 400°C enters a two-stage adia-batic turbine at a rate of 15 kg/s. Ten percent of the steam is extracted at the end of the first stage at a pressure of 1.8 MPa for other use. The remainder of the steam is further expanded in the second stage and leaves the turbine at 10 kPa. If the turbine has an isentropic efficiency of 88 percent, determine the wasted power potential during this process as a result of irreversibilities. Assume the surroundings to be at 25°C.

A well-insulated \(4-m x 4-m x 5-m \) room initially at \(10^{\circ} \mathrm{C}\) is heated by the radiator of a steam heating system. The radiator has a volume of and is filled with superheated vapor at \(200 k P \text { a and } 200^{\circ} \mathrm{C}\). At this moment both the inlet and the exit valves to the radiator are closed. A fan is used to distribute the air in the room. The pressure of the steam is observed to drop to after as a result of heat transfer to the room. Assuming constant specific heats for air at room temperature, determine ( ) the average temperature of room air in the entropy change of the steam, the entropy change of the air in the room, and the exergy destruction for this process, in Assume the air pressure in the room remains constant at at all times, and take \(T_{0}=10^{\circ} \mathrm{C}\). Equation Transcription: Text Transcription: 4 - m x 4 - m x 5 - m 10°C 200kPa and 200°C T0=10°C

Reconsider Prob. 8–109. Using EES (or other) software, investigate the effect of the state of the steam at the inlet of the feedwater heater on the ratio of mass flow rates and the reversible power. Vary the extracted steam pressure between \(200 \text { and } 2000 \mathrm{kPa}\). Plot both the ratio of the mass flow rates of the extracted steam and the feedwater heater and the reversible work for this process per unit mass of feedwater as functions of the extraction pressure. Equation Transcription: Text Transcription: 200 and 2000 kPa

Problem 108P Argon gas enters an adiabatic turbine at 1300°F and 200 psia at a rate of 40 lbm/min and exhausts at 20 psia. If the power output of the turbine is 105 hp, determine (a) the isentropic efficiency and (b) the second-law efficiency of the turbine. Assume the surroundings to be at 77°F.

Consider a well-insulated horizontal rigid cylinder that is divided into two compartments by a piston that is free to move but does not allow either gas to leak into the other side. Initially, one side of the piston contains \(1 m^{3} of N_{2}\) gas at \(500 \mathrm{kPa} and 80^{\circ} \mathrm{C}\) while the other side contains \(1 \mathrm{~m}^{3} of \mathrm{He}\) gas at \(500 \mathrm{kP} a and 25^{\circ} \mathrm{C}\). Now thermal equilibrium is established in the cylinder as a result of heat transfer through the piston. Using constant specific heats at room temperature, determine (a) the final equilibrium temperature in the cylinder and the wasted work potential during this process. What would your answer be if the piston were not free to move? Take \(T_{0}=25^{\circ} \mathrm{C}\) Equation Transcription: Text Transcription: 1m3 of N2 500kPa and 80°C 1m3 of He 500kPa and 25°C T0=25°C

Problem 107P Repeat Prob. 8–115 by assuming the piston is made of 5 kg of copper initially at the average temperature of the two gases on both sides.

In large steam power plants, the feedwater is & frequently heated in closed feedwater heaters, which are basically heat exchangers, by steam extracted from the turbine at some stage. Steam enters the feedwater heater at \(1.6 \mathrm{MP} \text { a and } 250^{\circ} \mathrm{C}\) and leaves as saturated liquid at the same pressure. Feedwater enters the heater at \(4 M P \text { a and } 30^{\circ} \mathrm{C}\) and leaves \(10^{\circ} \mathrm{C}\) below the exit temperature of the steam. Neglecting any heat losses from the outer surfaces of the heater, determine (a) the ratio of the mass flow rates of the extracted steam and the feedwater heater and the reversible work for this process per unit mass of the feedwater. Assume the surroundings to be at \(25^{\circ} \mathrm{C}\) Equation Transcription: Text Transcription: 1.6MPa and 250°C 4MPa and 30°C 10°C 25°C

Problem 112P One method of passive solar heating is to stack gallons of liquid water inside the buildings and expose them to the sun. The solar energy stored in the water during the day is released at night to the room air, providing some heating. Consider a house that is maintained at 22°C and whose heating is assisted by a 350-L water storage system. If the water is heated to 45°C during the day, determine the amount of heating this water will provide to the house at night. Assuming an outside temperature of 5°C, determine the exergy destruction associated with this process.

Problem 113P A passive solar house that is losing heat to the outdoors at 5°C at an average rate of 50,000 kJ/h is maintained at 22°C at all times during a winter night for 10 h. The house is to be heated by 50 glass containers, each containing 20 L of water that is heated to 80°C during the day by absorbing solar energy. A thermostat-controlled 15-kW back-up electric resistance heater turns on whenever necessary to keep the house at 22°C. Determine (a) how long the electric heating system was on that night, (b) the exergy destruction, and (c) the minimum work input required for that night, in kJ.

Problem 111P In order to cool 1 ton of water at 20°C in an insulated tank, a person pours 80 kg of ice at ?5°C into the water. Determine (a) the final equilibrium temperature in the tank and (b) the exergy destroyed during this process. The melting temperature and the heat of fusion of ice at atmospheric pressure are 0°C and 333.J kJ/kg, respectively. Take T0 =20°C.

Consider a 20-L evacuated rigid bottle that is surrounded by the atmosphere at \(100 \mathrm{kP} \text { a and } 25^{\circ} \mathrm{C}\). A valve at the neck of the bottle is now opened and the atmospheric air is allowed to flow into the bottle. The air trapped in the bottle eventually reaches thermal equilibrium with the atmosphere as a result of heat transfer through the wall of the bottle. The valve remains open during the process so that the trapped air also reaches mechanical equilibrium with the atmosphere. Determine the net heat transfer through the wall of the bottle and the exergy destroyed during this filling process. Equation Transcription: Text Transcription: 100kPa and 25°C

A constant-volume tank contains \(30 \mathrm{~kg}\) of nitrogen at \(900 \mathrm{~K}\), and a constant-pressure device contains \(15 \mathrm{~kg}\) of argon at \(300 \mathrm{~K}\). A heat engine placed between the tank and device extracts heat from the high-temperature tank, produces work, and rejects heat to the low-temperature device. Determine the maximum work that can be produced by the heat engine and the final temperatures of the nitrogen and argon. Assume constant specific heats at room temperature. Equation Transcription: Text Transcription: 30 kg 900 K 15 kg 300 K

Problem 116P Two constant-pressure devices, each filled with 30 kg of air, have temperatures of 900 K and 300 K. A heat engine placed between the two devices extracts heat from the high-temperature device, produces work, and rejects heat to the low-temperature device. Determine the maximum work that can be produced by the heat engine and the final temperatures of the devices. Assume constant specific heats at room temperature.

A frictionless piston-cylinder device, shown in Fig. P8-115, initially contains \(0.01 \mathrm{~m}^{3}\) of argon gas at 400 K and 350 kPa. Heat is now transferred to the argon from a furnace at 1200 K, and the argon expands isothermally until its volume is doubled. No heat transfer takes place between the argon and the surrounding atmospheric air, which is at 300 K and 100 kPa. Determine (a) the useful work output, (b) the exergy destroyed, and (c) the maximum work that can be produced during this process. Equation Transcription: Text Transcription: 0.01 m3

Problem 118P A 100-L well-insulated rigid tank is initially tilled with nitrogen at 1000 kPa and 20°G. Now a valve is opened and one-half of nitrogen’s mass is allowed to escape. Determine the change in the exergy content of the tank.

What would your answer to Prob. 8–119 be if heat were supplied to the pressure cooker from a heat source at \(180^{\circ} \mathrm{C}\) instead of the electrical heating unit? Equation Transcription: Text Transcription: 180°C

Problem 124P A constant-volume tank has a temperature of 600 K and a constant-pressure device has a temperature of 280 K. Both the tank and device are filled with 40 kg of air. A heat engine placed between the tank and device receives heat from the high-temperature tank, produces work, and rejects heat to ; the low-temperature device. Determine the maximum work pat can be produced by the heat engine and the final temperatures of the tank and device. Assume constant specific heats lat room temperature.

Problem 123P The air stored in the tank of the previous problem is f now released through the isentropic turbine until the tank contents are at 100 kPa and 20°C. The pressure is always 100 kPa at the turbine outlet, and all heat exchanges are with the I surrounding air, which is at 20°C. How does the total work I produced by the turbine compare to the change in the work potential of the air in the storage tank?

The compressed-air storage tank shown in Fig. P8–122 has a volume of \(500,000 \mathrm{~m}^{3}\), and it initially contains air at 100 kPa and \(20^{\circ} \mathrm{C}\). The isentropic compressor proceeds to compress air that enters the compressor at 100 kPa and \(20^{\circ} \mathrm{C}\) until the tank is filled at 600 kPa and \(20^{\circ} \mathrm{C}\). All heat exchanges are with the surrounding air at \(20^{\circ} \mathrm{C}\). Calculate the change in the work potential of the air stored in the tank. How does this compare to the work required to compress the air as the tank was being filled? Equation Transcription: Text Transcription: 500, 000 m^3 20°C 20°C 20°C 20°C

Problem 121P Steam is to be condensed in the condenser of a steam power plant at a temperature of 50°C with cooling water from a nearby lake that enters the tubes of the condenser at 12°C at a rate of 240 kg/s and leaves at 20°C. Assuming the condenser to be perfectly insulated, determine (a) the rate of condensation of the steam and (b) the rate of exergy destruction in the condenser.

In a production facility, -in-thick, 1 -ft -ft square brass plates \(\left(\rho=532.5 \mathrm{lbm} / \mathrm{ft}^{3} \text { and } c_{p}=0.091 \mathrm{Btu} / \mathrm{lbm} \cdot{ }^{\circ} \mathrm{F}\right)\) that are initially at a uniform temperature of \(75^{\circ} \mathrm{F}\) are heated by passing them through an oven at \(1300^{\circ} \mathrm{F}\) at a rate of 175 per minute. If the plates remain in the oven until their average temperature rises to \(1000^{\circ} \mathrm{F}\), determine the rate of heat transfer to the plates in the furnace and the rate of exergy destruction associated with this heat transfer process. Equation Transcription: Text Transcription: (\rho=532.5 lbm/ft3 and cp=0.091 Btu/lbm°F) 75°F 1300°F 1000°F

A 4-L pressure cooker has an operating pressure of . Initially, one-half of the volume is filled with liquid water and the other half by water vapor. The cooker is now placed on top of a electrical heating unit that is kept on for 20 min. Assuming the surroundings to be at \(25^{\circ} \mathrm{C} \text { and } 100 \mathrm{kP} \text { a }\), determine the amount of water that remained in the cooker and the exergy destruction associated with the entire process, including the conversion of electric energy to heat energy. Equation Transcription: Text Transcription: 25°C and 100kPa

Refrigerant-134a enters an adiabatic compressor at superheated by \(2.3^{\circ} \mathrm{C}\), and leaves at . If the compressor has a second-law efficiency of 85 percent, determine the actual work input, the isentropic efficiency, and the exergy destruction. Take the environment temperature to be \(25^{\circ} \mathrm{C}\). Answers: (a) , (c) Equation Transcription: Text Transcription: 2.3°C 25°C

Combustion gases enter a gas turbine at \(627^{\circ} \mathrm{C} and 1.2 \mathrm{MPa}\) at a rate of \(2.5 \mathrm{~kg} / \mathrm{s}\) and leave at \(527^{\circ} \mathrm{C} and 500 \mathrm{kPa}\). It is estimated that heat is lost from the turbine at a rate of . Using air properties for the combustion gases and assuming the surroundings to be at \(25^{\circ} \mathrm{C}\) and , determine the actual and reversible power outputs of the turbine, the exergy destroyed within the turbine, and the second-law efficiency of the turbine. Equation Transcription: Text Transcription: 627°C and 1.2MPa 2.5 kg/s 527°C and 500kPa 25°C

Problem 126P In a dairy plant, milk at 4°C is pasteurized continuously at 72°C at a rate of 12 L/s for 24 h/day and 365 days/yr. The milk is heated to the pasteurizing temperature by hot water heated in a natural gas-fired boiler having an efficiency of 82 percent. The pasteurized milk is then cooled by cold water at 18°C before it is finally refrigerated back to 4°C. To save energy and money, the plant installs a regenerator that has an effectiveness of 82 percent. If the cost of natural gas is $1.30/therm (1 therm = 105,500 kJ), determine how much energy and money the regenerator will save this company per year and the annual reduction in exergy destruction.

Argon gas expands from \(3.5 \mathrm{MPa} \text { and } 100^{\circ} \mathrm{C}\) to in an adiabatic expansion valve. For environment conditions of and \(25^{\circ} \mathrm{C}\) determine the exergy of argon at the inlet, the exergy destruction during the process, and the second-law efficiency. Equation Transcription: Text Transcription: 3.5 MPa and 100°C 25°C

Problem 129P Water enters a pump at 100 kPa and 30°C at a rate of 1.35 kg/s, and leaves at 4 MPa. If the pump has an isentropic efficiency of 70 percent, determine (a) the actual power input, (b) the rate of factional heating, (c) the exergy destruction, and (d) the second-law efficiency for an environment temperature of 20°C.

Problem 131P Nitrogen gas enters a diffuser at 100 kPa and 110°C with a velocity of 205 m/s, and leaves at 110 kPa and 45 m/s. It is estimated that 2.5 kJ/kg of heat is lost from the diffuser to the surroundings at 100 kPa and 27°C. The exit area of the diffuser is 0.04 m2. Accounting for the variation of the specific heats with temperature, determine (a) the exit temperature, (b) the rate of exergy destruction, and (c) the second-law efficiency of the diffuser.

Problem 132P Obtain a relation for the second-law efficiency of a heat engine that receives heat QH from a source at temperature TH and rejects heat QL to a sink at TL, which is higher than T0 (the temperature of the surroundings), while producing work in the amount of W.

Writing the first- and second-law relations and simplifying, obtain the reversible work relation for a steady-flow system that exchanges heat with the surrounding medium at \(T_{0}\) a rate of \(Q_{0}\) as well as a thermal reservoir at \(T_{R}\) at a rate of \(Q_{R\). (Hint: Eliminate \(Q_{0}\) between the two equations.) Equation Transcription: Text Transcription: T0 Q0 TR QR Q0

Problem 135P Writing the first- and second-law relations and simplifying, obtain the reversible work relation for a uniform-flow system that exchanges heat with the surrounding medium at T0 in the amount of Q0as well as a heat reservoir at TR in the amount of QR.(Hint: Eliminate Q0 between the two equations.)

Problem 133P Writing the first- and second-law relations and simplifying, obtain the reversible work relation for a closed system that exchanges heat with the surrounding medium at T0 in the amount of Q0 as well as a heat reservoir at TR in the amount of QR.(Hint: Eliminate Q0 between the two equations.)

Problem 139P A water reservoir contains 100 tons of water at an average elevation of 60 m. The maximum amount of electric power that can be generated from this water is (a) 8 kWh ________________ (b) 16 kWh ________________ (c) 1630 kWh ________________ (d) 16,300 kWh ________________ (c) 58,800 kWh

Problem 136P Heat is lost through a plane wall steadily at a rate of 800 W. If the inner and outer surface temperatures of the wall are 20°C and 5°C, respectively, and the environment temperture is 0°C, the rate of exergy destruction within the wall is (a)40W ________________ (b) 17,500 W ________________ (c)765W ________________ (d) 32,800 W ________________ (e)0W

Problem 138P A heat engine receives heat from a source at 1500 K at a rate of 600 kJ/s and rejects the waste heat to a sink at 300 K. If the power output of the engine is 400 kW, the second-law efficiency of this heat engine is (a) 42% ________________ (b) 53% ________________ (c) 83% ________________ (d)67% ________________ (e) 80%

Problem 140P A house is maintained at 21°C in winter by electric resistance heaters. If the outdoor temperature is 9°C, the second-law efficiency of the resistance heaters is (a)0% ________________ (b)4.1% ________________ (c) 5.7% ________________ (d) 25% ________________ (e) 100%

Problem 137P Liquid water enters an adiabatic piping system at 5°C at a rate of 3 kg/s. It is observed that the water temper-iture rises by 0.3°C in the pipe due to friction. If the environ-nent temperature is also 15°C, the rate of exergy destruction n the pipe is (a) 3.8 kW ________________ (b) 24 kW ________________ (c) 72 kW ________________ (d) 98 kW ________________ (e) 124 kW

Problem 141P A 12-kg solid whose specific heat is 2.8 kJ/kg?°C is at a uniform temperature of ? 10°C. For an environment temperature of 20°C, the exergy content of this solid is (a) Less than zero ________________ (b)0kJ ________________ (c) 4.6 kJ ________________ (d) 55 kJ ________________ (e) 1008 kJ

Problem 142P Keeping the limitations imposed by the second law I of thermodynamics in mind, choose the wrong statement below: (a) A heat engine cannot have a thermal efficiency of 100%. ________________ (b) For all reversible processes, the second-law efficiency is 100%. ________________ (c) The second-law efficiency of a heat engine cannot be greater than its thermal efficiency. ________________ (d) The second-law efficiency of a process is 100% if no entropy is generated during that process. ________________ (e) The coefficient of performance of a refrigerator can be greater than 1.

Problem 143P A furnace can supply heat steadily at a 1300 K at a rate of 500 kJ/s. The maximum amount of power that can be produced by using the heat supplied by this furnace in an environment at 300 K is (a)115kW ________________ (b)192kW ________________ (c) 385 kW ________________ (d)5C0kW ________________ (e)650kW

Problem 9P Does a refrigerator that has a higher COP necessarily have a higher second-law efficiency than one with a lower COP? Explain.

Problem 144P Air is throttled from 50°C and 800 kPa to a pressure of 200 kPa at a rate of 0.5 kg/s in an environment at 25°C. The change in kinetic energy is negligible, and no heat transfer occurs during the process. The power potential wasted during this process is (a)0 ________________ (b)0.20kW ________________ (c)47kW ________________ (d)59kW ________________ (e)119kW

Problem 8.81C Outdoor air is to be preheated by hot exhaust gases in a cross-flow heat exchanger before it enters the furnace. Air enters the heat exchanger at 101 kPa and at a rate of . The combustion gases enter at at a rate of and leave at . Determine the rate of heat transfer to the air and the rate of energy destruction in the heat exchanger.

Is the exergy of a system different in different environments?

Air enters a compressor at ambient conditions of and at a rate of with a low velocity, and exits at , , and . The compressor is cooled by cooling water that experiences a temperature rise of . The isothermal efficiency of the compressor is 70 percent. Determine (a) the actual and reversible power inputs, (b) the second-law efficiency, and (c) the mass flow rate of the cooling water.

A hot-water stream at enters an adiabatic mixing chamber with a mass flow rate of , where it is mixed with a stream of cold water at . If the mixture leaves the chamber at , determine (a) the mass flow rate of the cold water and (b) the exergy destroyed during this adiabatic mixing process. Assume all the streams are at a pressure of and the surroundings are at .

Liquid water at is heated in a chamber by mixing it with saturated steam. Liquid water enters the chamber at the steam pressure at a rate of and the saturated steam enters at a rate of . The mixture leaves the mixing chamber as a liquid at . If the surroundings are at , determine (a) the temperature of saturated steam entering the chamber, (b) the exergy destruction during this mixing process, and (c) the second-law efficiency of the mixing chamber.

A refrigerator has a second-law efficiency of 28 percent, and heat is removed from the refrigerated space at a rate of . If the space is maintained at while the surrounding air temperature is , determine the power input to the refrigerator.

Problem 8.87 Refrigerant-134a is expanded adiabatically in an expansion valve from and to . For environment conditions of and , determine (a) the work potential of R-134a at the inlet, (b) the exergy destruction during the process, and (c) the second-law efficiency.

Steam enters an adiabatic nozzle at and with a low velocity and leaves at and at a rate of . If the ambient state is and , determine (a) the exit velocity, (b) the rate of exergy destruction, and (c) the second-law efficiency.

Problem 8.89 Steam is condensed in a closed system at a constant pressure of from a saturated vapor to a saturated liquid by rejecting heat to a thermal energy reservoir at . Determine the second-law efficiency of this process. Take and .

Can a process for which the reversible work is zero be reversible? Can it be irreversible? Explain.

Consider a process during which no entropy is generated . Does the exergy destruction for this process have to be zero?

The electric power needs of a community are to be met by windmills with 40-m-diameter rotors. The windmills are to be located where the wind is blowing steadily at an average velocity of . Determine the minimum number of windmills that need to be installed if the required power output is .

Saturated steam is generated in a boiler by converting a saturated liquid to a saturated vapor at . This is done by transferring heat from the combustion gases, which are at , 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 the steam stream? Take and .

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 , determine the minimum amount of water that needs to be stored at an average elevation (relative to the ground level) of 75 m.

How much of the of thermal energy at can be converted to useful work? Assume the environment to be at .

A heat engine that receives heat from a furnace at and rejects waste heat to a river at has a thermal efficiency of 40 percent. Determine the second-law efficiency of this power plant.

Consider a thermal energy reservoir at e that can supply heat at a rate of . Determine the exergy of this supplied energy, assuming an environmental temperature of .

A heat engine receives heat from a source at 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 258C. Determine (a) the reversible power, (b) the rate of irreversibility, and (c) the second-law efficiency of this heat engine.

Reconsider Prob. 818. 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.

A heat engine that rejects waste heat to a sink at has a thermal efficiency of 25 percent and a second-law efficiency of 50 percent. Determine the temperature of the source that supplies heat to this engine.

A house that is losing heat at a rate of when the outside temperature drops to is to be heated by electric resistance heaters. If the house is to be maintained at at all times, determine the reversible work input for this process and the irreversibility.

A freezer is maintained at by removing heat from it at a rate of . The power input to the freezer is , and the surrounding air is at . Determine (a) the reversible power, (b) the irreversibility, and (c) the second-law efficiency of this freezer.

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.

Can a system have a higher second-law efficiency than the first-law efficiency during a process? Give examples

A mass of 8 kg of helium undergoes a process from an initial state of 3 m3 /kg and 158C to a final state of 0.5 m3 /kg and 808C. Assuming the surroundings to be at 258C and 100 kPa, determine the increase in the useful work potential of the helium during this process.

Air is expanded in an adiabatic closed system from 180 psia and 1408F to 20 psia with an isentropic expansion efficiency of 95 percent. What is the second-law efficiency of this expansion? Take T0 5 778F and P0 5 14.7 psia.

Which is a more valuable resource for work production in a closed system l5 ft3 of air at 100 psia and 2508F or 20 ft3 of helium at 60 psia and 2008F? Take T0 5 778F and P0 5 14.7 psia.

Which has the capability to produce the most work in a closed system l kg of steam at 800 kPa and 1808C or 1 kg of R134a at 800 kPa and 1808C? Take T0 5 258C and P0 5 100 kPa.

A pistoncylinder device contains 8 kg of refrigerant- 134a at 0.7 MPa and 608C. The refrigerant is now cooled at constant pressure until it exists as a liquid at 208C. If the surroundings are at 100 kPa and 208C, determine (a) the exergy of the refrigerant at the initial and the final states and (b) the exergy destroyed during this process

The radiator of a steam heating system has a volume of 20 L and is filled with superheated water vapor at 200 kPa and 2008C. At this moment both the inlet and the exit valves to the radiator are closed. After a while it is observed that the temperature of the steam drops to 808C as a result of heat transfer to the room air, which is at 218C. Assuming the surroundings to be at 08C, determine (a) the amount of heat transfer to the room and (b) the maximum amount of heat that can be supplied to the room if this heat from the radiator is supplied to a heat engine that is driving a heat pump. Assume the heat engine operates between the radiator and the surroundings.

Reconsider Prob. 830. Using EES (or other) soft ware, investigate the effect of the final steam temperature in the radiator on the amount of actual heat transfer and the maximum amount of heat that can be transferred. Vary the final steam temperature from 80 to 218C and plot the actual and maximum heat transferred to the room as functions of final steam temperature.

A well-insulated rigid tank contains 6 lbm of saturated liquidvapor mixture of water at 35 psia. Initially, three-quarters 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 758F and 14.7 psia, determine (a) the exergy destruction and (b) the second-law efficiency for this process.

An insulated pistoncylinder 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 258C and 100 kPa, determine (a) the minimum work with which this process could be accomplished and (b) the exergy destroyed during this process.

Reconsider Prob. 833. Using EES (or other) 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.

An insulated pistoncylinder device contains 0.03 m3 of saturated refrigerant-134a vapor at 0.6 MPa pressure. The refrigerant is now allowed to expand in a reversible manner until the pressure drops to 0.16 MPa. Determine the change in the exergy of the refrigerant during this process and the reversible work. Assume the surroundings to be at 258C and 100 kPa.

Oxygen gas is compressed in a pistoncylinder device from an initial state of 12 ft3 /lbm and 758F to a final state of 1.5 ft3 /lbm and 5258F. 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 758F.

A pistoncylinder device initially contains 2 L of air at 100 kPa and 258C. Air is now compressed to a final state of 600 kPa and 1508C. The useful work input is 1.2 kJ. Assuming the surroundings are at 100 kPa and 258C, 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.

A 0.8-m3 insulated rigid tank contains 1.54 kg of carbon dioxide at 100 kPa. Now paddle-wheel work is done on the system until the pressure in the tank rises to 135 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 5 298 K.

An insulated pistoncylinder device initially contains 20 L of air at 140 kPa and 278C. 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 278C and 100 kPa. Determine the exergy destroyed during this process.

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 708C, and the other side is evacuated. The partition is now removed, and the gas fills the entire tank. Assuming the surroundings to be at 258C, determine the exergy destroyed during this process.

A 70-lbm copper block initially at 2208F is dropped into an insulated tank that contains 1.2 ft3 of water at 658F. Determine (a) the final equilibrium temperature and (b) the work potential wasted during this process. Assume the surroundings to be at 658F

An iron block of unknown mass at 858C is dropped into an insulated tank that contains 100 L of water at 208C. 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 248C. Assuming the surroundings to be at 208C, determine (a) the mass of the iron block and (b) the exergy destroyed during this process.

A 12-ft3 rigid tank contains refrigerant-134a at 30 psia and 55 percent quality. Heat is transferred now to the refrigerant from a source at 1208F until the pressure rises to 50 psia. Assuming the surroundings to be at 758F, determine (a) the amount of heat transfer between the source and the refrigerant and (b) the exergy destroyed during this process.

Stainless steel ball bearings (r 5 8085 kg/m3 and cp 5 0.480 kJ/kg8C) having a diameter of 1.2 cm are to be quenched in water at a rate of 1400 per minute. The balls leave the oven at a uniform temperature of 9008C and are exposed to air at 308C for a while before they are dropped into the water. If the temperature of the balls drops to 8508C prior to quenching, 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.

An ordinary egg can be approximated as a 5.5-cmdiameter sphere. The egg is initially at a uniform temperature of 88C and is dropped into boiling water at 978C. Taking the properties of egg to be r 5 1020 kg/m3 and cp 5 3.32 kJ/kg8C, determine how much heat is transferred to the egg by the time the average temperature of the egg rises to 708C and the amount of exergy destruction associated with this heat transfer process. Take T0 5 258C.

Chickens with an average mass of 1.6 kg and average specific heat of 3.54 kJ/kg8C are to be cooled by chilled water that enters a continuous-flow-type immersion chiller at 0.58C and leaves at 2.58C. Chickens are dropped into the chiller at a uniform temperature of 158C at a rate of 700 chickens per hour and are cooled to an average temperature of 38C 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 5 258C.

A pistoncylinder device initially contains 1.4 kg of refrigerant-134a at 100 kPa and 208C. Heat is now transferred to the refrigerant from a source at 1508C, and the piston which is resting on a set of stops, starts moving when the pressure inside reaches 120 kPa. Heat transfer continues until the temperature reaches 808C. Assuming the surroundings to be at 258C 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. A

Refrigerant-134a at 1 MPa and 1008C is throttled to a pressure of 0.8 MPa. Determine the reversible work and exergy destroyed during this throttling process. Assume the surroundings to be at 308C.

Reconsider Prob. 848. Using EES (or other) software, investigate the effect of exit pressure on the reversible work and exergy destruction. Vary the throttle exit pressure from 1 to 0.1 MPa and plot the reversible work and exergy destroyed as functions of the exit pressure. Discuss the results.

Helium is expanded in a turbine from 1500 kPa and 3008C to 100 kPa and 258C. Determine the maximum work this turbine can produce, in kJ/kg. Does the maximum work require an adiabatic turbine?

Air is compressed steadily by an 8-kW compressor from 100 kPa and 178C to 600 kPa and 1678C 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 178C.

Reconsider Prob. 851. Using EES (or other) software, 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 second-law efficiency. Then interpret the results when the outlet temperature is set to, say, 3008C. Explain the values of heat transfer, exergy destroyed, and efficiency when the outlet temperature is set to 209.318C and mass flow rate to 2.466 kg/min.

Air enters a nozzle steadily at 200 kPa and 658C 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 178C is estimated to be 3 kJ/kg. Determine (a) the exit temperature and (b) the exergy destroyed during this process.

Reconsider Prob. 853. 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.

Steam enters a diffuser at 10 kPa and 608C with a velocity of 375 m/s and exits as saturated vapor at 508C 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 258C.

Air is compressed steadily by a compressor from 14.7 psia and 608F to 100 psia and 4808F at a rate of 22 lbm/min. Assuming the surroundings to be at 608F, 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.

Argon gas enters an adiabatic compressor at 120 kPa and 308C with a velocity of 20 m/s and exits at 1.2 MPa, 5308C, and 80 m/s. The inlet area of the compressor is 130 cm2 . Assuming the surroundings to be at 258C, determine the reversible power input and exergy destroyed.

Steam enters an adiabatic turbine at 6 MPa, 6008C, and 80 m/s and leaves at 50 kPa, 1008C, 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 258C.

Steam is throttled from 7 MPa and 5008C to a pressure of 1 MPa. Determine the decrease in exergy of the steam during this process. Assume the surroundings to be at 258C.

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 258C.

Combustion gases enter a gas turbine at 9008C, 800 kPa, and 100 m/s and leave at 6508C, 400 kPa, and 220 m/s. Taking cp 5 1.15 kJ/kg8C and k 5 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 258C and 100 kPa. Can this turbine be adiabatic?

Refrigerant-134a enters an adiabatic compressor at 2308C as a saturated vapor at a rate of 0.45 m3 /min and leaves at 900 kPa and 558C. 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 T0 5 278C.

Refrigerant-134a is condensed in a refrigeration system by rejecting heat to ambient air at 258C. R-134a enters the condenser at 700 kPa and 508C 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 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.

Air enters the evaporator section of a window air conditioner at 100 kPa and 278C with a volume flow rate of 6 m3 /min. Refrigerant-134a at 120 kPa with a quality of 0.3 enters the evaporator at a rate of 2 kg/min and leaves as saturated vapor at the same pressure. Determine the exit temperature of the air and the exergy destruction for this process, assuming (a) the outer surfaces of the air conditioner are insulated and (b) heat is transferred to the evaporator of the air conditioner from the surrounding medium at 328C at a rate of 30 kJ/min.

Refrigerant-22 absorbs heat from a cooled space at 508F as it flows through an evaporator of a refrigeration system. R-22 enters the evaporator at 108F 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 5 778F. The properties of R-22 at the inlet and exit of the evaporator are: h1 5 107.5 Btu/lbm, s1 5 0.2851 Btu/lbmR, h2 5 172.1 Btu/lbm, s2 5 0.4225 Btu/lbmR.

How much exergy is lost in a rigid vessel filled with 1 kg of liquid R-134a, whose temperature remains constant at 248C, as R-134a vapor is released from the vessel? This vessel may exchange heat with the surrounding atmosphere, which is at 100 kPa and 248C. The vapor is released until the last of the liquid inside the vessel disappears.

A 40-ft3 adiabatic container is initially evacuated. The supply line contains air that is maintained at 150 psia and 908F. 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 5 808F.

What is the work potential of the air in the filled container of Prob. 8-67E 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 808F. Note that the container cannot be adiabatic in this case, and it can exchange heat with the natural environment.

Steam expands in a turbine steadily at a rate of 18,000 kg/h, entering at 7 MPa and 6008C and leaving at 50 kPa as saturated vapor. Assuming the surroundings to be at 100 kPa and 258C, 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.

Air enters a compressor at ambient conditions of 15 psia and 608F with a low velocity and exits at 150 psia, 6208F, and 350 ft/s. The compressor is cooled by the ambient air at 608F 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.

Hot combustion gases enter the nozzle of a turbojet engine at 230 kPa, 6278C, and 60 m/s and exit at 70 kPa and 4508C. Assuming the nozzle to be adiabatic and the surroundings to be at 208C, determine (a) the exit velocity and (b) the decrease in the exergy of the gases. Take k 5 1.3 and cp 5 1.15 kJ/kg8C for the combustion gases.

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 5008C with a velocity of 70 m/s and exits at 5 MPa and 4508C. Assuming the surroundings to be at 258C, determine (a) the exit velocity of the steam, (b) the isentropic efficiency, and (c) the exergy destroyed within the nozzle.

Ambient air at 100 kPa and 300 K is compressed isentropically in a steady-flow device to 0.8 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 0.8 MPa pressure.

A 0.6-m3 rigid tank is filled with saturated liquid water at 1708C. 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 2108C 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 258C and 100 kPa.

A 0.1-m3 rigid tank contains saturated refrigerant- 134a at 800 kPa. Initially, 30 percent of the volume is occupied by liquid and the rest by vapor. A valve at the bottom of the tank is opened, and liquid is withdrawn from the tank. Heat is transferred to the refrigerant from a source at 608C so that the pressure inside the tank remains constant. The valve is closed when no liquid is left in the tank and vapor starts to come out. Assuming the surroundings to be at 258C, determine (a) the final mass in the tank and (b) the reversible work associated with this process.

An insulated 260-ft3 rigid tank contains air at 40 psia and 1808F. 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 708F.

A vertical pistoncylinder device initially contains 0.12 m3 of helium at 208C. The mass of the piston is such that it maintains a constant pressure of 200 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 208C 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.

An insulated vertical pistoncylinder 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 4008C 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 258C and 100 kPa, determine (a) the amount of steam that has entered and (b) the exergy destroyed during this process.

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 158C is heated to 558C in an electric water heater and tempered to 428C 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 5 258C.

Cold water (cp 5 4.18 kJ/kg8C) leading to a shower enters a well-insulated, thin-walled, double-pipe, counterflow heat exchanger at 158C at a rate of 0.25 kg/s and is heated to 458C by hot water (cp 5 4.19 kJ/kg8C) that enters at 1008C at a rate of 3 kg/s. Determine (a) the rate of heat transfer and (b) the rate of exergy destruction in the heat exchanger. Take T0 5 258C.

Outdoor air (cp 5 1.005 kJ/kg8C) is to be preheated by hot exhaust gases in a cross-flow heat exchanger before it enters the furnace. Air enters the heat exchanger at 101 kPa and 308C at a rate of 0.5 m3 /s. The combustion gases (cp 5 1.10 kJ/kg8C) enter at 3508C at a rate of 0.85 kg/s and leave at 2608C. Determine the rate of heat transfer to the air and the rate of exergy destruction in the heat exchanger.

Steam is to be condensed on the shell side of a heat exchanger at 1208F. Cooling water enters the tubes at 608F at a rate of 115.3 lbm/s and leaves at 738F. Assuming the heat exchanger to be well insulated, determine (a) the rate of heat transfer in the heat exchanger and (b) the rate of exergy destruction in the heat exchanger. Take T0 5 778F.

Steam is to be condensed on the shell side of a heat exchanger at 1208F. Cooling water enters the tubes at 608F at a rate of 115.3 lbm/s and leaves at 738F. Assuming the heat exchanger to be well insulated, determine (a) the rate of heat transfer in the heat exchanger and (b) the rate of exergy destruction in the heat exchanger. Take T0 5 778F.

Air enters a compressor at ambient conditions of 100 kPa and 208C at a rate of 4.5 m3 /s with a low velocity, and exits at 900 kPa, 608C, and 80 m/s. The compressor is cooled by cooling water that experiences a temperature rise of 108C. The isothermal efficiency of the compressor is 70 percent. Determine (a) the actual and reversible power inputs, (b) the second-law efficiency, and (c) the mass flow rate of the cooling water.

A hot-water stream at 1608F enters an adiabatic mixing chamber with a mass flow rate of 4 lbm/s, where it is mixed with a stream of cold water at 708F. If the mixture leaves the chamber at 1108F, determine (a) the mass flow rate of the cold water and (b) the exergy destroyed during this adiabatic mixing process. Assume all the streams are at a pressure of 50 psia and the surroundings are at 758F.

Liquid water at 208C is heated in a chamber by mixing it with saturated steam. Liquid water enters the chamber at the steam pressure at a rate of 4.6 kg/s and the saturated steam enters at a rate of 0.19 kg/s. The mixture leaves the mixing chamber as a liquid at 458C. If the surroundings are at 208C, determine (a) the temperature of saturated steam entering the chamber, (b) the exergy destruction during this mixing process, and (c) the second-law efficiency of the mixing chamber.

A refrigerator has a second-law efficiency of 28 percent, and heat is removed from the refrigerated space at a rate of 800 Btu/min. If the space is maintained at 258F while the surrounding air temperature is 908F, determine the power input to the refrigerator.

Refrigerant-134a is expanded adiabatically in an expansion valve from 700 kPa and 258C to 160 kPa. For environment conditions of 100 kPa and 208C, determine (a) the work potential of R-134a at the inlet, (b) the exergy destruction during the process, and (c) the second-law efficiency.

Steam enters an adiabatic nozzle at 3.5 MPa and 3008C with a low velocity and leaves at 1.6 MPa and 2508C at a rate of 0.4 kg/s. If the ambient state is 100 kPa and 188C, determine (a) the exit velocity, (b) the rate of exergy destruction, and (c) the second-law efficiency.

Steam is condensed in a closed system at a constant pressure of 75 kPa from a saturated vapor to a saturated liquid by rejecting heat to a thermal energy reservoir at 378C. Determine the second-law efficiency of this process. Take T0 5 258C and P0 5 100 kPa.

Refrigerant-134a is converted from a saturated liquid to a saturated vapor in a closed system using a reversible constant pressure process by transferring heat from a heat reservoir at 68C. From second-law point of view, is it more effective to do this phase change at 100 kPa or 180 kPa? Take T0 5 258C and P0 5 100 kPa.

An adiabatic heat exchanger is to cool ethylene glycol (cp 5 2.56 kJ/kg8C) flowing at a rate of 2 kg/s from 80 to 408C by water (cp 5 4.18 kJ/kg8C) that enters at 208C and leaves at 558C. Determine (a) the rate of heat transfer and (b) the rate of exergy destruction in the heat exchanger.

A well-insulated, thin-walled, counter-flow heat exchanger is to be used to cool oil (cp 5 2.20 kJ/kg8C) from 150 to 408C at a rate of 2 kg/s by water (cp 5 4.18 kJ/kg8C) that enters at 228C at a rate of 1.5 kg/s. The diameter of the tube is 2.5 cm, and its length is 6 m. Determine (a) the rate of heat transfer and (b) the rate of exergy destruction in the heat exchanger.

Hot exhaust gases leaving an internal combustion engine at 4008C and 150 kPa at a rate of 0.8 kg/s is to be used to produce saturated steam at 2008C in an insulated heat exchanger. Water enters the heat exchanger at the ambient temperature of 208C, and the exhaust gases leave the heat exchanger at 3508C. Determine (a) the rate of steam production, (b) the rate of exergy destruction in the heat exchanger, and (c) the second-law efficiency of the heat exchanger.

A crater lake has a base area of 20,000 m2 , and the water it contains is 12 m deep. The ground surrounding the crater is nearly flat and is 140 m below the base of the lake. Determine the maximum amount of electrical work, in kWh, that can be generated by feeding this water to a hydroelectric power plant.

The inner and outer surfaces of a 5-m 3 6-m brick wall of thickness 30 cm are maintained at temperatures of 208C and 58C, respectively, and the rate of heat transfer through the wall is 900 W. Determine the rate of exergy destruction associated with this process. Take T0 5 08C.

A 1000-W iron is left on the ironing board with its base exposed to the air at 208C. If the temperature of the base of the iron is 1508C, determine the rate of exergy destruction for this process due to heat transfer, in steady operation.

A 30-cm-long, 1500-W electric resistance heating element whose diameter is 1.2 cm is immersed in 70 kg of water initially at 208C. Assuming the water container is wellinsulated, determine how long it will take for this heater to raise the water temperature to 808C. Also, determine the minimum work input required and exergy destruction for this process, in kJ. Take T0 5 208C.

An adiabatic steam nozzle has steam entering at 300 kPa, 1508C, and 45 m/s, and leaving as a saturated vapor at 150 kPa. Calculate the actual and maximum outlet velocity. Take T0 5 258C.

A steam turbine is equipped to bleed 6 percent of the inlet steam for feedwater heating. It is operated with 500 psia and 6008F steam at the inlet, a bleed pressure of 100 psia, and an exhaust pressure of 5 psia. The turbine efficiency between the inlet and bleed point is 97 percent, and the efficiency between the bleed point and exhaust is 95 percent. Calculate this turbines second-law efficiency. Take T0 5 778F.

To control an isentropic steam turbine, a throttle valve is placed in the steam line leading to the turbine inlet. Steam at 6 MPa and 6008C is supplied to the throttle inlet, and the turbine exhaust pressure is set at 40 kPa. What is the effect on the stream exergy at the turbine inlet when the throttle valve is partially closed such that the pressure at the turbine inlet is 2 MPa. Compare the second-law efficiency of this system when the valve is partially open to when it is fully open. Take T0 5 258C.

Two rigid tanks are connected by a valve. Tank A is insulated and contains 0.2 m3 of steam at 400 kPa and 80 percent quality. Tank B is uninsulated and contains 3 kg of steam at 200 kPa and 2508C. The valve is now opened, and steam flows from tank A to tank B until the pressure in tank A drops to 300 kPa. During this process 900 kJ of heat is transferred from tank B to the surroundings at 08C. Assuming the steam remaining inside tank A to have undergone a reversible adiabatic process, determine (a) the final temperature in each tank and (b) the work potential wasted during this process.

A pistoncylinder device initially contains 8 ft3 of helium gas at 40 psia and 708F. Helium is now compressed in a polytropic process (Pv n 5 constant) to 140 psia and 3208F. Assuming the surroundings to be at 14.7 psia and 708F, determine (a) the actual useful work consumed and (b) the minimum useful work input needed for this process.

Steam at 7 MPa and 4008C enters a two-stage adiabatic turbine at a rate of 15 kg/s. Ten percent of the steam is extracted at the end of the first stage at a pressure of 1.8 MPa for other use. The remainder of the steam is further expanded in the second stage and leaves the turbine at 10 kPa. If the turbine has an isentropic efficiency of 88 percent, determine the wasted power potential during this process as a result of irreversibilities. Assume the surroundings to be at 258C.

Steam enters a two-stage adiabatic turbine at 8 MPa and 5008C. It expands in the first stage to a state of 2 MPa and 3508C. Steam is then reheated at constant pressure to a temperature of 5008C before it is routed to the second stage, where it exits at 30 kPa and a quality of 97 percent. The work output of the turbine is 5 MW. Assuming the surroundings to be at 258C, determine the reversible power output and the rate of exergy destruction within this turbine.

A well-insulated 4-m 3 4-m 3 5-m room initially at 108C is heated by the radiator of a steam heating system. The radiator has a volume of 15 L and is filled with superheated vapor at 200 kPa and 2008C. At this moment both the inlet and the exit valves to the radiator are closed. A 150-W fan is used to distribute the air in the room. The pressure of the steam is observed to drop to 100 kPa after 30 min as a result of heat transfer to the room. Assuming constant specific heats for air at room temperature, determine (a) the average temperature of room air in 24 min, (b) the entropy change of the steam, (c) the entropy change of the air in the room, and (d) the exergy destruction for this process, in kJ. Assume the air pressure in the room remains constant at 100 kPa at all times, and take T0 5 108C.

Consider a well-insulated horizontal rigid cylinder that is divided into two compartments by a piston that is free to move but does not allow either gas to leak into the other side. Initially, one side of the piston contains 1 m3 of N2 gas at 500 kPa and 808C while the other side contains 1 m3 of He gas at 500 kPa and 258C. Now thermal equilibrium is established in the cylinder as a result of heat transfer through the piston. Using constant specific heats at room temperature, determine (a) the final equilibrium temperature in the cylinder and (b) the wasted work potential during this process. What would your answer be if the piston were not free to move? Take T0 5 258C.

Repeat Prob. 8106 by assuming the piston is made of 5 kg of copper initially at the average temperature of the two gases on both sides.

Argon gas enters an adiabatic turbine at 13008F and 200 psia at a rate of 40 lbm/min and exhausts at 20 psia. If the power output of the turbine is 105 hp, determine (a) the isentropic efficiency and (b) the second-law efficiency of the turbine. Assume the surroundings to be at 778F.

In large steam power plants, the feedwater is frequently heated in closed feedwater heaters, which are basically heat exchangers, by steam extracted from the turbine at some stage. Steam enters the feedwater heater at 1.6 MPa and 2508C and leaves as saturated liquid at the same pressure. Feedwater enters the heater at 4 MPa and 308C and leaves 108C below the exit temperature of the steam. Neglecting any heat losses from the outer surfaces of the heater, determine (a) the ratio of the mass flow rates of the extracted steam and the feedwater heater and (b) the reversible work for this process per unit mass of the feedwater. Assume the surroundings to be at 258C.

Reconsider Prob. 8109. Using EES (or other) software, investigate the effect of the state of the steam at the inlet of the feedwater heater on the ratio of mass flow rates and the reversible power. Vary the extracted steam pressure between 200 and 2000 kPa. Plot both the ratio of the mass flow rates of the extracted steam and the feedwater heater and the reversible work for this process per unit mass of feedwater as functions of the extraction pressure.

In order to cool 1 ton of water at 208C in an insulated tank, a person pours 80 kg of ice at 258C into the water. Determine (a) the final equilibrium temperature in the tank and (b) the exergy destroyed during this process. The melting temperature and the heat of fusion of ice at atmospheric pressure are 08C and 333.7 kJ/kg, respectively. Take T0 5 208C.

One method of passive solar heating is to stack gallons of liquid water inside the buildings and expose them to the sun. The solar energy stored in the water during the day is released at night to the room air, providing some heating. Consider a house that is maintained at 228C and whose heating is assisted by a 350-L water storage system. If the water is heated to 458C during the day, determine the amount of heating this water will provide to the house at night. Assuming an outside temperature of 58C, determine the exergy destruction associated with this process.

A passive solar house that is losing heat to the outdoors at 58C at an average rate of 50,000 kJ/h is maintained at 228C at all times during a winter night for 10 h. The house is to be heated by 50 glass containers, each containing 20 L of water that is heated to 808C during the day by absorbing solar energy. A thermostat-controlled 15-kW back-up electric resistance heater turns on whenever necessary to keep the house at 228C. Determine (a) how long the electric heating system was on that night, (b) the exergy destruction, and (c) the minimum work input required for that night, in kJ.

Consider a 20-L evacuated rigid bottle that is surrounded by the atmosphere at 100 kPa and 258C. A valve at the neck of the bottle is now opened and the atmospheric air is allowed to flow into the bottle. The air trapped in the bottle eventually reaches thermal equilibrium with the atmosphere as a result of heat transfer through the wall of the bottle. The valve remains open during the process so that the trapped air also reaches mechanical equilibrium with the atmosphere. Determine the net heat transfer through the wall of the bottle and the exergy destroyed during this filling process.

A frictionless piston-cylinder device, shown in Fig. P8-115, initially contains 0.01 m3 of argon gas at 400 K and 350 kPa. Heat is now transferred to the argon from a furnace at 1200 K, and the argon expands isothermally until its volume is doubled. No heat transfer takes place between the argon and the surrounding atmospheric air, which is at 300 K and 100 kPa. Determine (a) the useful work output, (b) the exergy destroyed, and (c) the maximum work that can be produced during this process.

Two constant-pressure devices, each filled with 30 kg of air, have temperatures of 900 K and 300 K. A heat engine placed between the two devices extracts heat from the high-temperature device, produces work, and rejects heat to the low-temperature device. Determine the maximum work that can be produced by the heat engine and the final temperatures of the devices. Assume constant specific heats at room temperature.

A constant-volume tank contains 30 kg of nitrogen at 900 K, and a constant-pressure device contains 15 kg of argon at 300 K. A heat engine placed between the tank and device extracts heat from the high-temperature tank, produces work, and rejects heat to the low-temperature device. Determine the maximum work that can be produced by the heat engine and the final temperatures of the nitrogen and argon. Assume constant specific heats at room temperature.

A 100-L well-insulated rigid tank is initially filled with nitrogen at 1000 kPa and 208C. Now a valve is opened and one-half of nitrogens mass is allowed to escape. Determine the change in the exergy content of the tank.

A 4-L pressure cooker has an operating pressure of 175 kPa. Initially, one-half of the volume is filled with liquid water and the other half by water vapor. The cooker is now placed on top of a 750-W electrical heating unit that is kept on for 20 min. Assuming the surroundings to be at 258C and 100 kPa, determine (a) the amount of water that remained in the cooker and (b) the exergy destruction associated with the entire process, including the conversion of electric energy to heat energy.

What would your answer to Prob. 8119 be if heat were supplied to the pressure cooker from a heat source at 1808C instead of the electrical heating unit?

Steam is to be condensed in the condenser of a steam power plant at a temperature of 508C with cooling water from a nearby lake that enters the tubes of the condenser at 128C at a rate of 240 kg/s and leaves at 208C. Assuming the condenser to be perfectly insulated, determine (a) the rate of condensation of the steam and (b) the rate of exergy destruction in the condenser.

The compressed-air storage tank shown in Fig. P8122 has a volume of 500,000 m3 , and it initially contains air at 100 kPa and 208C. The isentropic compressor proceeds to compress air that enters the compressor at 100 kPa and 208C until the tank is filled at 600 kPa and 208C. All heat exchanges are with the surrounding air at 208C. Calculate the change in the work potential of the air stored in the tank. How does this compare to the work required to compress the air as the tank was being filled?

The air stored in the tank of Prob. 8122 is now released through the isentropic turbine until the tank contents are at 100 kPa and 208C. The pressure is always 100 kPa at the turbine outlet, and all heat exchanges are with the surrounding air, which is at 208C. How does the total work produced by the turbine compare to the change in the work potential of the air in the storage tank?

A constant-volume tank has a temperature of 600 K and a constant-pressure device has a temperature of 280 K. Both the tank and device are filled with 40 kg of air. A heat engine placed between the tank and device receives heat from the high-temperature tank, produces work, and rejects heat to the low-temperature device. Determine the maximum work that can be produced by the heat engine and the final temperatures of the tank and device. Assume constant specific heats at room temperature.

In a production facility, 1.5-in-thick, 1-ft 3 3-ft square brass plates (r 5 532.5 lbm/ft3 and cp 5 0.091 Btu/lbm8F) that are initially at a uniform temperature of 758F are heated by passing them through an oven at 13008F at a rate of 175 per minute. If the plates remain in the oven until their average temperature rises to 10008F, determine the rate of heat transfer to the plates in the furnace and the rate of exergy destruction associated with this heat transfer process.

In a dairy plant, milk at 48C is pasteurized continuously at 728C at a rate of 12 L/s for 24 h/day and 365 days/yr. The milk is heated to the pasteurizing temperature by hot water heated in a natural gas-fired boiler having an efficiency of 82 percent. The pasteurized milk is then cooled by cold water at 188C before it is finally refrigerated back to 48C. To save energy and money, the plant installs a regenerator that has an effectiveness of 82 percent. If the cost of natural gas is $1.30/therm (1 therm 5 105,500 kJ), determine how much energy and money the regenerator will save this company per year and the annual reduction in exergy destruction.

Combustion gases enter a gas turbine at 6278C and 1.2 MPa at a rate of 2.5 kg/s and leave at 5278C and 500 kPa. It is estimated that heat is lost from the turbine at a rate of 20 kW. Using air properties for the combustion gases and assuming the surroundings to be at 258C and 100 kPa, determine (a) the actual and reversible power outputs of the turbine, (b) the exergy destroyed within the turbine, and (c) the second-law efficiency of the turbine.

Refrigerant-134a enters an adiabatic compressor at 120 kPa superheated by 2.38C, and leaves at 0.7 MPa. If the compressor has a second-law efficiency of 85 percent, determine (a) the actual work input, (b) the isentropic efficiency, and (c) the exergy destruction. Take the environment temperature to be 258C.

Water enters a pump at 100 kPa and 308C at a rate of 1.35 kg/s, and leaves at 4 MPa. If the pump has an isentropic efficiency of 70 percent, determine (a) the actual power input, (b) the rate of frictional heating, (c) the exergy destruction, and (d) the second-law efficiency for an environment temperature of 208C.

Argon gas expands from 3.5 MPa and 1008C to 500 kPa in an adiabatic expansion valve. For environment conditions of 100 kPa and 258C, determine (a) the exergy of argon at the inlet, (b) the exergy destruction during the process, and (c) the second-law efficiency.

Nitrogen gas enters a diffuser at 100 kPa and 1108C with a velocity of 205 m/s, and leaves at 110 kPa and 45 m/s. It is estimated that 2.5 kJ/kg of heat is lost from the diffuser to the surroundings at 100 kPa and 278C. The exit area of the diffuser is 0.04 m2 . Accounting for the variation of the specific heats with temperature, determine (a) the exit temperature, (b) the rate of exergy destruction, and (c) the second-law efficiency of the diffuser.

Obtain a relation for the second-law efficiency of a heat engine that receives heat QH from a source at temperature TH and rejects heat QL to a sink at TL , which is higher than T0 (the temperature of the surroundings), while producing work in the amount of W.

Writing the first- and second-law relations and simplifying, obtain the reversible work relation for a closed system that exchanges heat with the surrounding medium at T0 in the amount of Q0 as well as a heat reservoir at TR in the amount of QR. (Hint: Eliminate Q0 between the two equations.)

Writing the first- and second-law relations and simplifying, obtain the reversible work relation for a steady-flow system that exchanges heat with the surrounding medium at T0 a rate of Q # 0 as well as a thermal reservoir at TR at a rate of Q # R. (Hint: Eliminate Q # 0 between the two equations.)

Writing the first- and second-law relations and simplifying, obtain the reversible work relation for a uniformflow system that exchanges heat with the surrounding medium at T0 in the amount of Q0 as well as a heat reservoir at TR in the amount of QR. (Hint: Eliminate Q0 between the two equations.)

Heat is lost through a plane wall steadily at a rate of 800 W. If the inner and outer surface temperatures of the wall are 208C and 58C, respectively, and the environment temperature is 08C, the rate of exergy destruction within the wall is (a) 40 W (b) 17,500 W (c) 765 W (d) 32,800 W (e) 0 W

Liquid water enters an adiabatic piping system at 158C at a rate of 3 kg/s. It is observed that the water temperature rises by 0.38C in the pipe due to friction. If the environment temperature is also 158C, the rate of exergy destruction in the pipe is (a) 3.8 kW (b) 24 kW (c) 72 kW (d) 98 kW (e) 124 kW

A heat engine receives heat from a source at 1500 K at a rate of 600 kJ/s and rejects the waste heat to a sink at 300 K. If the power output of the engine is 400 kW, the second-law efficiency of this heat engine is (a) 42% (b) 53% (c) 83% (d) 67% (e) 80%

A water reservoir contains 100 tons of water at an average elevation of 60 m. The maximum amount of electric power that can be generated from this water is (a) 8 kWh (b) 16 kWh (c) 1630 kWh (d) 16,300 kWh (e) 58,800 kWh

A house is maintained at 218C in winter by electric resistance heaters. If the outdoor temperature is 98C, the second-law efficiency of the resistance heaters is (a) 0% (b) 4.1% (c) 5.7% (d) 25% (e) 100%

A 12-kg solid whose specific heat is 2.8 kJ/kg8C is at a uniform temperature of 2108C. For an environment temperature of 208C, the exergy content of this solid is (a) Less than zero (b) 0 kJ (c) 4.6 kJ (d) 55 kJ (e) 1008 kJ

Keeping the limitations imposed by the second law of thermodynamics in mind, choose the wrong statement below: (a) A heat engine cannot have a thermal efficiency of 100%. (b) For all reversible processes, the second-law efficiency is 100%. (c) The second-law efficiency of a heat engine cannot be greater than its thermal efficiency. (d) The second-law efficiency of a process is 100% if no entropy is generated during that process. (e) The coefficient of performance of a refrigerator can be greater than 1.

A furnace can supply heat steadily at a 1300 K at a rate of 500 kJ/s. The maximum amount of power that can be produced by using the heat supplied by this furnace in an environment at 300 K is (a) 115 kW (b) 192 kW (c) 385 kW (d) 500 kW (e) 650 kW

Air is throttled from 508C and 800 kPa to a pressure of 200 kPa at a rate of 0.5 kg/s in an environment at 258C. The change in kinetic energy is negligible, and no heat transfer occurs during the process. The power potential wasted during this process is (a) 0 (b) 0.20 kW (c) 47 kW (d) 59 kW (e) 119 kW

Obtain the following information about a power plant that is closest to your town: the net power output; the type and amount of fuel used; the power consumed by the pumps, fans, and other auxiliary equipment; stack gas losses; temperatures at several locations; and the rate of heat rejection at the condenser. Using these and other relevant data, determine the rate of irreversibility in that power plant.

Human beings are probably the most capable creatures, and they have a high level of physical, intellectual, emotional, and spiritual potentials or exergies. Unfortunately people make little use of their exergies, letting most of their exergies go to waste. Draw four exergy versus time charts, and plot your physical, intellectual, emotional, and spiritual exergies on each of these charts for a 24-h period using your best judgment based on your experience. On these four charts, plot your respective exergies that you have utilized during the last 24 h. Compare the two plots on each chart and determine if you are living a full life or if you are wasting your life away. Can you think of any ways to reduce the mismatch between your exergies and your utilization of them?

The domestic hot-water systems involve a high level of irreversibility and thus they have low second-law efficiencies. The water in these systems is heated from about 158C to about 608C, and most of the hot water is mixed with cold water to reduce its temperature to 458C or even lower before it is used for any useful purpose such as taking a shower or washing clothes at a warm setting. The water is discarded at about the same temperature at which it was used and replaced by fresh cold water at 158C. Redesign a typical residential hot-water system such that the irreversibility is greatly reduced. Draw a sketch of your proposed design.

Consider natural gas, electric resistance, and heat pump heating systems. For a specified heating load, which one of these systems will do the job with the least irreversibility? Explain.

The temperature of the air in a building can be maintained at a desirable level during winter by using different methods of heating. Compare heating this air in a heat exchanger unit with condensing steam to heating it with an electric-resistance heater. Perform a second-law analysis to determine the heating method that generates the least entropy and thus causes the least exergy destruction.