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Home , Isentropic process

CHAPTER 7 – PROBLEMS

1. Calculate the rate of change of all the components of a refrigerator that uses 10 kW of , rejects 14 kW of , and has a high- thermal- reservoir at 400 K and a low-temperature thermal-energy reservoir at 200 K. (source: -0.02 kJ/s-K, sink: 0.035 kJ/s-K) 2. A accepts 200 kBtu of heat from an energy source at 1500 oR and rejects 100 kBtu to a sink at 600 oR. Calculate the entropy change of all the engine components. 3. When a system is adiabatic, what can be said about the entropy change of the substance in the system? (it must either remain fixed or increase) 4. A completely reversible heat engine operates with a source thermal-energy reservoir at 1500 oR and a sink thermal-energy reservoir at 500 oR. If the entropy of the sink reservoir increases by 10 Btu/oR, how much heat is transferred from the source thermal-energy reservoir? What is the change in the source thermal- energy reservoir entropy? 5. A thermal-energy reservoir at 1000 K transfer’s heat to a completely reversible heat engine. This engine also transfers heat to a thermal-energy reservoir at 300 K. How much heat must be transferred from the high-temperature reservoir to increase the entropy of the low-temperature reservoir by 20 kJ/K? (18 MJ) 6. One hundred Btu of heat are transferred directly from a thermal-energy reservoir at 1200 oR to one at 600 oR. Calculate the entropy change of the two reservoirs and determine if the increase in entropy principle has been satisfied. 7. In Problem 6, assume that the heat is transferred directly from the cold reservoir to the hot reservoir contrary to the Clausius statement of the second law. Prove that this also violates the increase in entropy principle. (total entropy change: - 0.833 Btu/oR) 8. Heat is transferred from an 800 K thermal-energy reservoir to a 300 K thermal- energy reservoir. What is the rate at which this produces entropy? Does this satisfy the second law? 9. A completely reversible air conditioner provides a 36 kBtu/hr cooling effect for a space maintained at 70 oF while rejecting heat to the surrounding air at 110 oF. What is the total rate at which this system changes its entropy? Does this satisfy the second law? (0 Btu/oR-s, yes) 10. A general heat engine whose is 40% uses a hot thermal-energy reservoir at 1300 K and a cold thermal energy reservoir at 500 K. Does this engine satisfy the increase in entropy principle? Hint: Calculate the total entropy change for 1 kJ of heat transfer from the hot reservoir. If the thermal efficiency of this engine is 70%, does it still satisfy the increase in entropy principle? 11. A refrigerator with a COP of 4 transfers heat from a cold region at -20 oC to a hot region at 30 oC. Does this satisfy the second law? Hint: Calculate the total entropy change for 1 kJ of heat transfer from the cold region. Is the second law still satisfied if the COP of this refrigerator is 6? (4-yes, 6-no) 12. A heat creates a 100 kBtu/hr heating effect for a space maintained at 530 oR while using 3 kW of electrical power. What is the minimum temperature of the source thermal-energy reservoir that satisfies the second law of ? 13. Complete this table of water states:

P (kPa) T (oC) v (m3/kg) u (kJ/kg) x (%) s (kJ/kg-K) 500 0.20 500 100 500 0.57 500 600 14. One kilogram of R-134a at 200 kPa fills the 0.08825 m3 left-chamber of two chambers connected by a valve. The right-chamber has twice the of the left-chamber and is initially evacuated. Determine the total change in the entropy of the R-134a after the valve has been opened and enough heat has been transferred such that the temperature of the R-134a is 10 oC. 15. Two pounds-mass of water fill a rigid container whose volume is 0.4 ft3. Initially, the in this container is 40 psia. The container is now heated until the pressure of the water is 100 psia. Calculate the change in the water's total entropy. (0.211 Btu/oR) 16. Two pounds-mass of water at 300 psia fill a weighted piston-cylinder device whose initial volume is 2.5 ft3. The device is now heated until the temperature is 500 oF. Determine the resulting change in the water's total entropy. 17. Saturated R-134a vapor enters a steady-flow, adiabatic at 30 oC. At the compressor exit, the R-134a entropy is the same as at the inlet and the pressure is 1.6 MPa. Determine the temperature at the compressor exit and the required to operate this compressor. (60 oC, 14.7 kJ/kg) 18. A spring loaded piston-cylinder device is initially filled with 0.2 kg of R-134a liquid-vapor mixture whose temperature is 40 oC and whose quality is 80%. The spring constant is 234 N/cm and the piston diameter is 25 cm. The R-134a is now cooled until its volume is increased by 20%. Determine the final temperature and specific entropy of the R-134a. 19. How much error would one expect in determining the specific entropy by applying the incompressible medium assumption to water at 10 Mpa, 280 oC? (0.4%)

20. What is the total amount of heat transfer for reversible processes 1- 3 of Figure A above? 21. What is the specific amount of closed system heat transfer for reversible processes 1-3 of Figure B above? The temperature scale is oC. (170 kJ/kg) 22. What is the total amount of closed system heat transfer for reversible processes 1- 2 of Figure C above? 23. What is the specific amount of closed system heat transfer for reversible processes 1-3 of Figure D above? Temperature scale is oC. (471 kJ/kg) 24. One pound-mass of R-134a is expanded in a closed system isentropic process from 100 psia, 100 oF to 10 psia. Determine the total heat transfer and work production for this process. 25. One-half kilogram of R-134a is expanded in an isentropic process from 600 kPa, 30 oC to 140 kPa. Determine the total heat transfer and work production for this process. (0 and 25.9 kJ) 26. Water at 50 oF, 81.4% quality is compressed in a closed system isentropic process to 500 psia. How much work does this require? 27. Water at 80 kPa, 100 oC is compressed in a closed system isentropic process to 4 MPa. Determine the final temperature and work required for this compression. (665 oC, 888 kJ/kg) 28. Refrigerant-134a at 240 kPa, 20 oC undergoes an in a closed system until its quality is 20%. How much work and heat transfer does this require? 29. Using the definition of entropy, calculate the entropy change for air initially at 15 psia, 70 oF and finally at 40 psia, 250 oF. (0.002855 Btu/lbm-oR) 30. Repeat Problem 29 using a Gibbs equation. 31. Using the definition of entropy, calculate the entropy difference between oxygen at 150 kPa, 39 oC and oxygen at 150 kPa, 337 oC. (0.6161 kJ/kg-K) 32. Repeat Problem 31 using a Gibbs equation. 33. Calculate the change in the specific entropy as water is cooled at a constant pressure of 50 psia from a saturated vapor to a saturated liquid. Use the water property tables to verify your result. (-1.248 Btu/lbm-oR) 34. Air is expanded from 200 psia, 500 oF to 100 psia, 50 oF. Determine the change in the air's specific entropy using a Gibbs equation. 35. Air is expanded from 2 MPa, 500 oC to 100 kPa, 50 oC. Determine the change in the air's specific entropy using a Gibbs equation. (-0.01595 kJ/kg-K) 36. Determine the final temperature of air when it is expanded in an isentropic process from 1 MPa, 477 oC to 100 kPa in a piston-cylinder device. 37. A mixture of ideal gases has a specific heat ratio of 1.35 and an apparent molecular weight of 32. Determine the work required to compress this mixture in a closed system isentropic process from 15 psia, 70 oF to 150 psia. (-103.6 Btu/lbm) 38. Air is expanded in an isentropic process from 100 psia, 500 oF to 20 psia. What is the final temperature of this air? 39. Nitrogen is compressed in an isentropic process from 100 kPa, 27 oC to 1 MPa. What is the final temperature of this nitrogen? (579 K) 40. Which of the two gases - neon or air - has the lowest final temperature when it is adiabatically and reversibly expanded from 1 MPa, 500 oC to 100 kPa in a closed system? 41. Air is expanded in a with n = 1.5 from 200 psia, 600 oF to 10 psia in a piston-cylinder device. Determine the final temperature of the air, the work produced, and the heat transfer for this process. (391 oR, 91.8 Btu/lbm, - 22.7 Btu/lbm) 42. Argon is compressed in a polytropic process with n = 1.2 from 120 kPa, 30 oC to 1.2 MPa in a piston-cylinder device. Determine the final temperature of the argon, the work produced, and the heat transfer for this process. 43. Which of the two gases - neon or air - produces the greatest amount of work when expanded from P1, T1 to P2 in a closed system polytropic process with n = 1.2? (neon) 44. What is the minimum specific that water can achieve as it is expanded adiabatically from 1.5 MPa, 320 oC to 100 kPa? 45. Is it possible to expand water at 30 psia, 70% quality to 10 psia in a closed system undergoing an isothermal, reversible process while exchanging heat with an isothermal energy reservoir at 300 oF? Hint: Apply the increase in entropy principle. (yes) 46. Is it possible to cool and condense R-134a to a saturated liquid from 1000 kPa, 200 oC in a closed system undergoing an isobaric, reversible process while exchanging heat with an isothermal reservoir at 100 oC? Hint: Apply the increase in entropy principle. 47. Ten grams of computer chips with a specific heat of 0.3 kJ/kg-K are initially at 20 oC. These chips are cooled by being placed in 5 grams of -40 oC saturated liquid R-134a inside a well insulated, weighted (isobaric) piston-cylinder device. Determine the entropy change of (a) the chips, (b) the R-134a, and (c) the entire system. Is this process possible? (-0.344 J/kg-K, 0.84 J/kg-K, 0.499 J/kg-k, yes according to the increase in entropy principle) 48. One kilogram of air is in a piston-cylinder apparatus that can only exchange heat with a thermal-energy reservoir at 300 K. Initially, this air is at 250 kPa, 27 oC. Someone claims that this air can be compressed to 2 MPa, 27 oC. Calculate the entropy change of the (a) air and (b) reservoir. Is this claim valid? 49. Refrigerant-134a at 700 kPa, 40 oC is expanded adiabatically in a closed system to 60 kPa. Determine the work produced by and the final temperature of this system for an isentropic expansion efficiency of 80%. (33.49 kJ/kg, 4 oC) 50. Three kilograms of helium at 100 kPa, 27 oC are adiabatically compressed to 900 kPa. If the isentropic compression efficiency is 80%, how much work is required and what is the final helium temperature? 51. You are to expand a gas adiabatically from 300 psia, 400 oF to 10 psia in a closed system. Which of the two choices - air with an isentropic efficiency of 90% or helium with an isentropic efficiency of 80% - will produce the most work? (air with 90% efficiency) 52. An adiabatic open-feedwater heater in an electrical generation plant mixes 0.2 kg/s of steam at 100 kPa, 160 oC with 10 kg/s of feedwater at 100 kPa, 50 oC to produce saturated liquid feedwater at 100 kPa at the outlet. Determine the outlet mass flow rate and velocity when the outlet pipe diameter is 0.03 m. 53. A steady-flow air compressor compresses 10 liters/s of air at 120 kPa, 20 oC to 1MPa, 300 oC and uses 4.5 kW of power. How much of this power is required to move the air through the compressor and how much is required to increase the air's pressure? (1.15 kW, 3.35 kW) 54. Two streams of water at 100 kPa are mixed in an insulated steady-flow device to form a third 100 kPa stream at the outlet. The first stream has a temperature of 90 oC and flow rate of 30 kg/s while the second stream has a temperature of 50 oC and flow rate of 200 kg/s. What is the temperature of the stream leaving this device? 55. An adiabatic steady-flow air compressor compresses 10 liters/s of air at 120 kPa, 20 oC to 1000 kPa, 300 oC. How much power does this require? 56. An adiabatic steady-flow expands air at 500 psia, 800 oF to 60 psia, 250 oF. If the volume flow rate at the turbine exit is 50 ft3/s, the inlet area is 0.6 ft2, and the outlet area is 1.2 ft2, how much power is produced by this turbine? (2130 hp) 57. Carbon dioxide is compressed in a reversible, from 15 psia, 70 oF to 60 psia using a steady-flow device with a single inlet and single outlet. How much work is produced by and how much heat is transferred into this device? (- 39.15 Btu/lbm, 0 Btu/lbm) 58. Repeat Problem 57 when the process is a reversible, isothermal process. 59. Is it possible for an adiabatic liquid-vapor separator to separate wet steam at 100 psia, 90 % quality into a saturated liquid stream and a saturated vapor stream both at a pressure greater than 100 psia? (no according to the increase in entropy principle) 60. Steam is expanded in an isentropic, steady-flow turbine. At the inlet, the steam is at 2 MPa, 360 oC. The steam pressure at the outlet is 100 kPa. How much work is produced by this turbine? 61. Air enters an isentropic, steady-flow turbine at 150 psia, 900 oF through a 0.5 ft2 pipe with a velocity of 500 ft/s. It leaves at 15 psia with a velocity of 100 ft/s. What is the air temperature at the turbine exit and how much power is produced by this turbine? (704 oR, 17,060 hp) 62. The steady-flow compressor in a refrigerator compresses saturated R-134a vapor at 0 oF to 200 psia. How much work is required by this compressor if the compression process is isentropic? 63. Five kilograms of steam per second enter an isentropic at 4 MPa and are exhausted at 70 kPa, 100 oC. Five percent of this flow is removed from this turbine at 700 kPa for the purposes of feedwater heating. How much power is produced by this turbine? (5600 kW) 64. Air at 500 psia, 700 oF is expanded in an adiabatic, steady-flow gas turbine to 20 psia. What is the maximum amount of work that this turbine can produce? 65. Nitrogen at 120 kPa, 30 oC is to be compressed in an adiabatic, steady-flow compressor to 600 kPa. What is the minimum amount of work required for this process? (-183.7 kJ/kg) 66. Oxygen at 50 psia, 200 oF with a velocity of 10 ft/s is expanded in an adiabatic, steady-flow nozzle to 20 psia. What is the maximum possible velocity of the oxygen at the nozzle exit? 67. Steam enters an adiabatic, steady-flow diffuser at 150 kPa, 120 oC with a velocity of 800 m/s. What is the minimum steam velocity at the nozzle exit when the exit pressure is 300 kPa? (608.3 m/s) 68. An inventor claims to have invented an adiabatic, steady-flow device that produces 100 kW of power when expanding 1 kg/s of air from 900 kPa, 300 oC to 100 kPa. Is this claim valid? 69. A chilled water heat exchanger is designed to cool 5000 liters/s of air at 100 kPa, 30 oC to 100 kPa, 18 oC by using water at 100 kPa, 8 oC. If the two streams (air and water) are not mixed, the mass flow rate of the water is 2 kg/s, and the water outlet pressure is 100 kPa, what is the maximum possible temperature of the water at its outlet? (16 oC) 70. Air is compressed in a steady-flow isentropic compressor from 15 psia, 70 oF to 200 psia. What is the outlet temperature and work consumption of this compressor? 71. Nitrogen is compressed in a steady-flow isothermal compressor from 100 kPa, 17 oC to 600 kPa. What is the specific entropy generation for this process? 72. Air is expanded in an adiabatic nozzle by a reversible polytropic process with n = 1.3. It enters this nozzle at 100 psia, 200 oF with a velocity of 100 ft/s and exits at 25 psia. Calculate the exit temperature and velocity of the air. 73. An adiabatic capillary tube is used in some refrigeration systems to reduce the pressure of the saturated liquid in the condenser to the lower pressure in the evaporator. Determine the quality at the exit of this tube and process entropy generation for a steady-flow R-134a system that operates the condenser at 120 oF and the evaporator at 10 oF. (0.4023, 0.01129 Btu/lbm-oR) 74. A throttle valve is placed in the steam line supplying the inlet of an isentropic steam turbine for the purpose of controlling the turbine. Steam at 6 MPa, 400 oC is supplied to the throttle inlet and the turbine exhaust pressure is maintained at 70 kPa by the feedwater . Compare the work produced by this arrangement when the throttle valve is wide open to when it is partially closed such that the pressure at the turbine inlet is 3 MPa.

v should be s(kJ/kg-K) and p should be T(K)

75. What is the total amount of steady-flow system heat transfer for reversible processes 1-3 of Figure A above? (515 Btu) 76. What is the specific amount of steady-flow system heat transfer for reversible processes 1-2 of Figure B above? 77. What is the work production for the steady-flow, single inlet/outlet system undergoing reversible process 1-3 shown in Figure A above? (0 kJ/kg) 78. What is the work production for the steady-flow, single inlet/outlet system undergoing reversible process 1-2 shown in Figure B above? 79. An undergoes a reversible, isothermal process in a steady-flow device. The inlet pressure is 200 kPa and the outlet pressure and specific volume are 600 kPa, 0.002 m3/kg. Determine the work required for this process. Does it matter which ideal gas is passing through this system? (-1.32 kJ/kg, no) 80. Saturated steam vapor at 150 oC is compressed in a steady-flow system to 1 MPa such that its specific volume remains constant. How work does this require? 81. Air is expanded in an adiabatic turbine whose isentropic efficiency is 90%. The air enters the turbine at 2.2 MPa, 300 oC and exits at 200 kPa. What is the temperature of the air at the turbine outlet and how much work does this turbine produce? (317 K, 256.5 kJ/kg) 82. How much entropy is generated by the process of Problem 81? 83. Steam at 450 psia, 550 oF is expanded to 5 psia in an adiabatic turbine whose isentropic efficiency is 92%. How much power is produced by this turbine when the mass flow rate is 2 lbm/s? (853 hp) 84. Air is expanded from 2 MPa, 327 oC to 100 kPa in a steady-flow, adiabatic turbine. What is the isentropic efficiency of this turbine when the air outlet temperature is 0 oC? 85. An adiabatic argon compressor compresses argon at 200 kPa, 27 oC to 2 MPa. If the argon temperature at the compressor outlet is 550 oC, what is the compressor's isentropic efficiency? (0.868) 86. An adiabatic refrigeration compressor compresses saturated R-134a vapor at 0 oC to 600 kPa, 50 oC. What is the isentropic efficiency of this compressor? 87. The exhaust nozzle of a jet engine adiabatically expands air at 300 kPa, 180 oC to 100 kPa. What is the air velocity at the exit of this nozzle when the inlet velocity is negligible and the nozzle efficiency is 96%? (487 m/s) 88. The adiabatic diffuser at the inlet of a jet engine increases the pressure of the air entering this diffuser at 13 psia, 30 oF to 20 psia. What is the air velocity at the diffuser exit if the air enters with a velocity of 1000 ft/s and the diffuser isentropic efficiency is 82%? 89. An adiabatic turbine operates with air entering it at 550kPa, 425 K, 150 m/s and leaving it at 110, 325 K, 50 m/s. What is the maximum and actual work production of this turbine? Why are the maximum and actual work productions not the same? (167.8 kJ/kg, 110.4 kJ/kg, difference is due to internal irreversibilities)