Themordynamics Cengel & Boles 5th edition - Chapter 9 - Solutions

9–1C Why is the Carnot cycle not suitable as an ideal cycle for all power-producing cyclic devices? Get 9.1 exercise solution

9–2C How does the thermal efficiency of an ideal cycle, in general, compare to that of a Carnot cycle operating between the same temperature limits? Get 9.2 exercise solution

9–3C What does the area enclosed by the cycle represent on a P-v diagram? How about on a T-s diagram? Get 9.3 exercise solution

9–4C What is the difference between air-standard assumptions and the cold-air-standard assumptions? Get 9.4 exercise solution

9–5C How are the combustion and exhaust processes modeled under the air-standard assumptions? Get 9.5 exercise solution

9–6C What are the air-standard assumptions? Get 9.6 exercise solution

9–7C What is the difference between the clearance volume and the displacement volume of reciprocating engines? Get 9.7 exercise solution

9–8C Define the compression ratio for reciprocating engines. Get 9.8 exercise solution

9–9C How is the mean effective pressure for reciprocating engines defined? Get 9.9 exercise solution

9–10C Can the mean effective pressure of an automobile engine in operation be less than the atmospheric pressure? Get 9.10 exercise solution

9–11C As a car gets older, will its compression ratio change? How about the mean effective pressure? Get 9.11 exercise solution

9–12C What is the difference between spark-ignition and compression-ignition engines? Get 9.12 exercise solution

9–13C Define the following terms related to reciprocating engines: stroke, bore, top dead center, and clearance volume. Get 9.13 exercise solution

9–14 An air-standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes: 1-2 Isentropic compression from 100 kPa and 27°C to 800 kPa 2-3 v constant heat addition to 1800 K 3-4 Isentropic expansion to 100 kPa 4-1 P constant heat rejection to initial state (a) Show the cycle on P-v and T-s diagrams. (b) Calculate the net work output per unit mass. (c) Determine the thermal efficiency. Get 9.14 exercise solution

9–15 Reconsider Problem 9–14. Using EES (or other) software, study the effect of varying the temperature after the constant-volume heat addition from 1500 K to 2500 K. Plot the net work output and thermal efficiency as a function of the maximum temperature of the cycle. Plot the T-s and P-v diagrams for the cycle when the maximum temperature of the cycle is 1800 K. Get 9.15 exercise solution

9–16 An air-standard cycle is executed in a closed system and is composed of the following four processes: 1-2 Isentropic compression from 100 kPa and 27°C to 1 MPa 2-3 P constant heat addition in amount of 2800 kJ/kg 3-4 v constant heat rejection to 100 kPa 4-1 P constant heat rejection to initial state (a) Show the cycle on P-v and T-s diagrams. (b) Calculate the maximum temperature in the cycle. (c) Determine the thermal efficiency. Assume constant specific heats at room temperature. Get 9.16 exercise solution

9–17E An air-standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes: 1-2 v constant heat addition from 14.7 psia and 80°F in the amount of 300 Btu/lbm 2-3 P constant heat addition to 3200 R 3-4 Isentropic expansion to 14.7 psia 4-1 P constant heat rejection to initial state (a) Show the cycle on P-v and T-s diagrams. (b) Calculate the total heat input per unit mass. (c) Determine the thermal efficiency. Answers: (b) 612.4 Btu/lbm, (c) 24.2 percent Get 9.17 exercise solution

9–18E Repeat Problem 9–17E using constant specific heats at room temperature. Get 9.18 exercise solution

9–19 An air-standard cycle is executed in a closed system with 0.004 kg of air and consists of the following three processes: 1-2 Isentropic compression from 100 kPa and 27°C to 1 MPa 2-3 P constant heat addition in the amount of 2.76 kJ 3-1 P c1v + c2 heat rejection to initial state (c1 and c2 are constants) (a) Show the cycle on P-v and T-s diagrams. (b) Calculate the heat rejected. (c) Determine the thermal efficiency. Assume constant specific heats at room temperature. Get 9.19 exercise solution

9–20 An air-standard cycle with variable specific heats is executed in a closed system with 0.003 kg of air and consists of the following three processes: 1-2 v = constant heat addition from 95 kPa and 17°C to 380 kPa 2-3 Isentropic expansion to 95 kPa 3-1 P = constant heat rejection to initial state (a) Show the cycle on P-v and T-s diagrams. (b) Calculate the net work per cycle, in kJ. (c) Determine the thermal efficiency. Get 9.20 exercise solution

9–21 Repeat Problem 9–20 using constant specific heats at room temperature. Get 9.21 exercise solution

9–22 Consider a Carnot cycle executed in a closed system with 0.003 kg of air. The temperature limits of the cycle are 300 and 900 K, and the minimum and maximum pressures that occur during the cycle are 20 and 2000 kPa. Assuming constant specific heats, determine the net work output per cycle. Get 9.22 exercise solution

9–23 An air-standard Carnot cycle is executed in a closed system between the temperature limits of 350 and 1200 K. The pressures before and after the isothermal compression are 150 and 300 kPa, respectively. If the net work output per cycle is 0.5 kJ, determine (a) the maximum pressure in the cycle, (b) the heat transfer to air, and (c) the mass of air. Assume variable specific heats for air. Get 9.23 exercise solution

9–24 Repeat Problem 9–23 using helium as the working fluid. Get 9.24 exercise solution

9–25 Consider a Carnot cycle executed in a closed system with air as the working fluid. The maximum pressure in the cycle is 800 kPa while the maximum temperature is 750 K. If the entropy increase during the isothermal heat rejection process is 0.25 kJ/kg . K and the net work output is 100 kJ/kg, determine (a) the minimum pressure in the cycle, (b) the heat rejection from the cycle, and (c) the thermal efficiency of the cycle. (d) If an actual heat engine cycle operates between the same temperature limits and produces 5200 kW of power for an air flow rate of 90 kg/s, determine the second law efficiency of this cycle. Get 9.25 exercise solution

9–26C What four processes make up the ideal Otto cycle? Get 9.26 exercise solution

9–27C How do the efficiencies of the ideal Otto cycle and the Carnot cycle compare for the same temperature limits? Explain. Get 9.27 exercise solution

9–28C How is the rpm (revolutions per minute) of an actual four-stroke gasoline engine related to the number of thermodynamic cycles? What would your answer be for a two-stroke engine? Get 9.28 exercise solution

9–29C Are the processes that make up the Otto cycle analyzed as closed-system or steady-flow processes? Why? Get 9.29 exercise solution

9–30C How does the thermal efficiency of an ideal Otto cycle change with the compression ratio of the engine and the specific heat ratio of the working fluid? Get 9.30 exercise solution

9–31C Why are high compression ratios not used in sparkignition engines? Get 9.31 exercise solution

9–32C An ideal Otto cycle with a specified compression ratio is executed using (a) air, (b) argon, and (c) ethane as the working fluid. For which case will the thermal efficiency be the highest? Why? Get 9.32 exercise solution

9–33C What is the difference between fuel-injected gasoline engines and diesel engines? Get 9.33 exercise solution

9–34 An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, air is at 95 kPa and 27°C, and 750 kJ/kg of heat is transferred to air during the constant-volume heat-addition process. Taking into account the variation of specific heats with temperature, determine (a) the pressure and temperature at the end of the heataddition process, (b) the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for the cycle. Get 9.34 exercise solution

9–35 Reconsider Problem 9–34. Using EES (or other) software, study the effect of varying the compression ratio from 5 to 10. Plot the net work output and thermal efficiency as a function of the compression ratio. Plot the T-s and P-v diagrams for the cycle when the compression ratio is 8. Get 9.35 exercise solution

9–36 Repeat Problem 9–34 using constant specific heats at room temperature. Get 9.36 exercise solution

9–37 The compression ratio of an air-standard Otto cycle is 9.5. Prior to the isentropic compression process, the air is at 100 kPa, 35°C, and 600 cm3. The temperature at the end of the isentropic expansion process is 800 K. Using specific heat values at room temperature, determine (a) the highest temperature and pressure in the cycle; (b) the amount of heat transferred in, in kJ; (c) the thermal efficiency; and (d) the mean effective pressure. Get 9.37 exercise solution

9–38 Repeat Problem 9–37, but replace the isentropic expansion process by a polytropic expansion process with the polytropic exponent n 1.35. Get 9.38 exercise solution

9–39E An ideal Otto cycle with air as the working fluid has a compression ratio of 8. The minimum and maximum temperatures in the cycle are 540 and 2400 R. Accounting for the variation of specific heats with temperature, determine (a) the amount of heat transferred to the air during the heat-addition process, (b) the thermal efficiency, and (c) the thermal efficiency of a Carnot cycle operating between the same temperature limits. Get 9.39 exercise solution

9–40E Repeat Problem 9–39E using argon as the working fluid. Get 9.40 exercise solution

9–41 A four-cylinder, four-stroke, 2.2-L gasoline engine operates on the Otto cycle with a compression ratio of 10. The air is at 100 kPa and 60°C at the beginning of the compression process, and the maximum pressure in the cycle is 8 MPa. The compression and expansion processes may be modeled as polytropic with a polytropic constant of 1.3. Using constant specific heats at 850 K, determine (a) the temperature at the end of the expansion process, (b) the net work output and the thermal efficiency, (c) the mean effective pressure, (d) the engine speed for a net power output of 70 kW, and (e) the specific fuel consumption, in g/kWh, defined as the ratio of the mass of the fuel consumed to the net work produced. The air–fuel ratio, defined as the amount of air divided by the amount of fuel intake, is 16. Get 9.41 exercise solution

9–42C How does a diesel engine differ from a gasoline engine? Get 9.42 exercise solution

9–43C How does the ideal Diesel cycle differ from the ideal Otto cycle? Get 9.43 exercise solution

9–44C For a specified compression ratio, is a diesel or gasoline engine more efficient? Get 9.44 exercise solution

9–45C Do diesel or gasoline engines operate at higher compression ratios? Why? Get 9.45 exercise solution

9–46C What is the cutoff ratio? How does it affect the thermal efficiency of a Diesel cycle? Get 9.46 exercise solution

9–47 An air-standard Diesel cycle has a compression ratio of 16 and a cutoff ratio of 2. At the beginning of the compression process, air is at 95 kPa and 27°C. Accounting for the variation of specific heats with temperature, determine (a) the temperature after the heat-addition process, (b) the thermal efficiency, and (c) the mean effective pressure. Answers: (a) 1724.8 K, (b) 56.3 percent, (c) 675.9 kPa Get 9.47 exercise solution

9–48 Repeat Problem 9–47 using constant specific heats at room temperature. Get 9.48 exercise solution

9–49E An air-standard Diesel cycle has a compression ratio of 18.2. Air is at 80°F and 14.7 psia at the beginning of the compression process and at 3000 R at the end of the heataddition process. Accounting for the variation of specific heats with temperature, determine (a) the cutoff ratio, (b) the heat rejection per unit mass, and (c) the thermal efficiency. Get 9.49 exercise solution

9–50E Repeat Problem 9–49E using constant specific heats at room temperature. Get 9.50 exercise solution

9–51 An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is 95 kPa and 20°C. If the maximum temperature in the cycle is not to exceed 2200 K, determine (a) the thermal efficiency and (b) the mean effective pressure. Assume constant specific heats for air at room temperature. Answers: (a) 63.5 percent, (b) 933 kPa Get 9.51 exercise solution

9–52 Repeat Problem 9–51, but replace the isentropic expansion process by polytropic expansion process with the polytropic exponent n 1.35. Get 9.52 exercise solution

9–53 Reconsider Problem 9–52. Using EES (or other) software, study the effect of varying the compression ratio from 14 to 24. Plot the net work output, mean effective pressure, and thermal efficiency as a function of the compression ratio. Plot the T-s and P-v diagrams for the cycle when the compression ratio is 20. Get 9.53 exercise solution

9–54 A four-cylinder two-stroke 2.4-L diesel engine that operates on an ideal Diesel cycle has a compression ratio of 17 and a cutoff ratio of 2.2. Air is at 55°C and 97 kPa at the beginning of the compression process. Using the cold-airstandard assumptions, determine how much power the engine will deliver at 1500 rpm. Get 9.54 exercise solution

9–55 Repeat Problem 9–54 using nitrogen as the working fluid. Get 9.55 exercise solution

9–56 The compression ratio of an ideal dual cycle is 14. Air is at 100 kPa and 300 K at the beginning of the compression process and at 2200 K at the end of the heat-addition process. Heat transfer to air takes place partly at constant volume and partly at constant pressure, and it amounts to 1520.4 kJ/kg. Assuming variable specific heats for air, determine (a) the fraction of heat transferred at constant volume and (b) the thermal efficiency of the cycle. Get 9.56 exercise solution

9–57 Reconsider Problem 9–56. Using EES (or other) software, study the effect of varying the compression ratio from 10 to 18. For the compression ratio equal to 14, plot the T-s and P-v diagrams for the cycle. Get 9.57 exercise solution

9–58 Repeat Problem 9–56 using constant specific heats at room temperature. Is the constant specific heat assumption reasonable in this case? Get 9.58 exercise solution

9–59 A six-cylinder, four-stroke, 4.5-L compression-ignition engine operates on the ideal diesel cycle with a compression ratio of 17. The air is at 95 kPa and 55°C at the beginning of the compression process and the engine speed is 2000 rpm. The engine uses light diesel fuel with a heating value of 42,500 kJ/kg, an air–fuel ratio of 24, and a combustion efficiency of 98 percent. Using constant specific heats at 850 K, determine (a) the maximum temperature in the cycle and the cutoff ratio (b) the net work output per cycle and the thermal efficiency, (c) the mean effective pressure, (d) the net power output, and (e) the specific fuel consumption, in g/kWh, defined as the ratio of the mass of the fuel consumed to the net work produced. Get 9.59 exercise solution

9–60C Consider the ideal Otto, Stirling, and Carnot cycles operating between the same temperature limits. How would you compare the thermal efficiencies of these three cycles? Get 9.60 exercise solution

9–61C Consider the ideal Diesel, Ericsson, and Carnot cycles operating between the same temperature limits. How would you compare the thermal efficiencies of these three cycles? Get 9.61 exercise solution

9–62C What cycle is composed of two isothermal and two constant-volume processes? Get 9.62 exercise solution

9–63C How does the ideal Ericsson cycle differ from the Carnot cycle? Get 9.63 exercise solution

9–64E An ideal Ericsson engine using helium as the working fluid operates between temperature limits of 550 and 3000 R and pressure limits of 25 and 200 psia. Assuming a mass flow rate of 14 lbm/s, determine (a) the thermal efficiency of the cycle, (b) the heat transfer rate in the regenerator, and (c) the power delivered. Get 9.64 exercise solution

9–65 Consider an ideal Ericsson cycle with air as the working fluid executed in a steady-flow system. Air is at 27°C and 120 kPa at the beginning of the isothermal compression process, during which 150 kJ/kg of heat is rejected. Heat transfer to air occurs at 1200 K. Determine (a) the maximum pressure in the cycle, (b) the net work output per unit mass of air, and (c) the thermal efficiency of the cycle. Get 9.65 exercise solution

9–66 An ideal Stirling engine using helium as the working fluid operates between temperature limits of 300 and 2000 K and pressure limits of 150 kPa and 3 MPa. Assuming the mass of the helium used in the cycle is 0.12 kg, determine (a) the thermal efficiency of the cycle, (b) the amount of heat transfer in the regenerator, and (c) the work output per cycle. Get 9.66 exercise solution

9–67C Why are the back work ratios relatively high in gasturbine engines? Get 9.67 exercise solution

9–68C What four processes make up the simple ideal Brayton cycle? Get 9.68 exercise solution

9–69C For fixed maximum and minimum temperatures, what is the effect of the pressure ratio on (a) the thermal efficiency and (b) the net work output of a simple ideal Brayton cycle? Get 9.69 exercise solution

9–70C What is the back work ratio? What are typical back work ratio values for gas-turbine engines? Get 9.70 exercise solution

9–71C How do the inefficiencies of the turbine and the compressor affect (a) the back work ratio and (b) the thermal efficiency of a gas-turbine engine? Get 9.71 exercise solution

9–72E A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10. The air enters the compressor at 520 R and the turbine at 2000 R. Accounting for the variation of specific heats with temperature, determine (a) the air temperature at the compressor exit, (b) the back work ratio, and (c) the thermal efficiency. Get 9.72 exercise solution

9–73 A simple Brayton cycle using air as the working fluid has a pressure ratio of 8. The minimum and maximum temperatures in the cycle are 310 and 1160 K. Assuming an isentropic efficiency of 75 percent for the compressor and 82 percent for the turbine, determine (a) the air temperature at the turbine exit, (b) the net work output, and (c) the thermal efficiency. Get 9.73 exercise solution

9–74 Reconsider Problem 9–73. Using EES (or other) software, allow the mass flow rate, pressure ratio, turbine inlet temperature, and the isentropic efficiencies of the turbine and compressor to vary. Assume the compressor inlet pressure is 100 kPa. Develop a general solution for the problem by taking advantage of the diagram window method for supplying data to EES software. Get 9.74 exercise solution

9–75 Repeat Problem 9–73 using constant specific heats at room temperature. Get 9.75 exercise solution

9–76 Air is used as the working fluid in a simple ideal Brayton cycle that has a pressure ratio of 12, a compressor inlet temperature of 300 K, and a turbine inlet temperature of 1000 K. Determine the required mass flow rate of air for a net power output of 70 MW, assuming both the compressor and the turbine have an isentropic efficiency of (a) 100 percent and (b) 85 percent. Assume constant specific heats at room temperature. Answers: (a) 352 kg/s, (b) 1037 kg/s Get 9.76 exercise solution

9–77 A stationary gas-turbine power plant operates on a simple ideal Brayton cycle with air as the working fluid. The air enters the compressor at 95 kPa and 290 K and the turbine at 760 kPa and 1100 K. Heat is transferred to air at a rate of 35,000 kJ/s. Determine the power delivered by this plant (a) assuming constant specific heats at room temperature and (b) accounting for the variation of specific heats with temperature. Get 9.77 exercise solution

9–78 Air enters the compressor of a gas-turbine engine at 300 K and 100 kPa, where it is compressed to 700 kPa and 580 K. Heat is transferred to air in the amount of 950 kJ/kg before it enters the turbine. For a turbine efficiency of 86 percent, determine (a) the fraction of the turbine work output used to drive the compressor and (b) the thermal efficiency. Assume variable specific heats for air. Get 9.78 exercise solution

9–79 Repeat Problem 9–78 using constant specific heats at room temperature. Get 9.79 exercise solution

9–80E A gas-turbine power plant operates on a simple Brayton cycle with air as the working fluid. The air enters the turbine at 120 psia and 2000 R and leaves at 15 psia and 1200 R. Heat is rejected to the surroundings at a rate of 6400 Btu/s, and air flows through the cycle at a rate of 40 lbm/s. Assuming the turbine to be isentropic and the compresssor to have an isentropic efficiency of 80 percent, determine the net power output of the plant. Account for the variation of specific heats with temperature. Get 9.80 exercise solution

9–81E For what compressor efficiency will the gas-turbine power plant in Problem 9–80E produce zero net work? Get 9.81 exercise solution

9–82 A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 32 MW of power. The minimum and maximum temperatures in the cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the value at the compressor inlet. Assuming an isentropic efficiency of 80 percent for the compressor and 86 percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heats with temperature. Get 9.82 exercise solution

9–83 Repeat Problem 9–82 using constant specific heats at room temperature. Get 9.83 exercise solution

9–84 A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1200 kPa. The working fluid is air, which enters the compressor at 30°C at a rate of 150 m3/min and leaves the turbine at 500°C. Using variable specific heats for air and assuming a compressor isentropic efficiency of 82 percent and a turbine isentropic efficiency of 88 percent, determine (a) the net power output, (b) the back work ratio, and (c) the thermal efficiency. Get 9.84 exercise solution

9–85C How does regeneration affect the efficiency of a Brayton cycle, and how does it accomplish it? Get 9.85 exercise solution

9–86C Somebody claims that at very high pressure ratios, the use of regeneration actually decreases the thermal efficiency of a gas-turbine engine. Is there any truth in this claim? Explain. Get 9.86 exercise solution

9–87C Define the effectiveness of a regenerator used in gas-turbine cycles. Get 9.87 exercise solution

9–88C In an ideal regenerator, is the air leaving the compressor heated to the temperature at (a) turbine inlet, (b) turbine exit, (c) slightly above turbine exit? Get 9.88 exercise solution

9–89C In 1903, Aegidius Elling of Norway designed and built an 11-hp gas turbine that used steam injection between the combustion chamber and the turbine to cool the combustion gases to a safe temperature for the materials available at the time. Currently there are several gas-turbine power plants that use steam injection to augment power and improve thermal efficiency. For example, the thermal efficiency of the General Electric LM5000 gas turbine is reported to increase from 35.8 percent in simple-cycle operation to 43 percent when steam injection is used. Explain why steam injection increases the power output and the efficiency of gas turbines. Also, explain how you would obtain the steam. Get 9.89 exercise solution

9–90E The idea of using gas turbines to power automobiles was conceived in the 1930s, and considerable research was done in the 1940s and 1950s to develop automotive gas turbines by major automobile manufacturers such as the Chrysler and Ford corporations in the United States and Rover in the United Kingdom. The world’s first gas-turbinepowered automobile, the 200-hp Rover Jet 1, was built in 1950 in the United Kingdom. This was followed by the production of the Plymouth Sport Coupe by Chrysler in 1954 under the leadership of G. J. Huebner. Several hundred gasturbine-powered Plymouth cars were built in the early 1960s for demonstration purposes and were loaned to a select group of people to gather field experience. The users had no complaints other than slow acceleration. But the cars were never mass-produced because of the high production (especially material) costs and the failure to satisfy the provisions of the 1966 Clean Air Act. A gas-turbine-powered Plymouth car built in 1960 had a turbine inlet temperature of 1700°F, a pressure ratio of 4, and a regenerator effectiveness of 0.9. Using isentropic efficiencies of 80 percent for both the compressor and the turbine, determine the thermal efficiency of this car. Also, determine the mass flow rate of air for a net power output of 95 hp. Assume the ambient air to be at 540 R and 14.5 psia. Get 9.90 exercise solution

9–91 The 7FA gas turbine manufactured by General Electric is reported to have an efficiency of 35.9 percent in the simple-cycle mode and to produce 159 MW of net power. The pressure ratio is 14.7 and the turbine inlet temperature is 1288°C. The mass flow rate through the turbine is 1,536,000 kg/h. Taking the ambient conditions to be 20°C and 100 kPa, determine the isentropic efficiency of the turbine and the compressor. Also, determine the thermal efficiency of this gas turbine if a regenerator with an effectiveness of 80 percent is added. Get 9.91 exercise solution

9–92 Reconsider Problem 9–91. Using EES (or other) software, develop a solution that allows different isentropic efficiencies for the compressor and turbine and study the effect of the isentropic efficiencies on net work done and the heat supplied to the cycle. Plot the T-s diagram for the cycle. Get 9.92 exercise solution

9–93 An ideal Brayton cycle with regeneration has a pressure ratio of 10. Air enters the compressor at 300 K and the turbine at 1200 K. If the effectiveness of the regenerator is 100 percent, determine the net work output and the thermal efficiency of the cycle. Account for the variation of specific heats with temperature. Get 9.93 exercise solution

9–94 Reconsider Problem 9–93. Using EES (or other) software, study the effects of varying the isentropic efficiencies for the compressor and turbine and regenerator effectiveness on net work done and the heat supplied to the cycle for the variable specific heat case. Plot the T-s diagram for the cycle. Get 9.94 exercise solution

9–95 Repeat Problem 9–93 using constant specific heats at room temperature. Get 9.95 exercise solution

9–96 A Brayton cycle with regeneration using air as the working fluid has a pressure ratio of 7. The minimum and maximum temperatures in the cycle are 310 and 1150 K. Assuming an isentropic efficiency of 75 percent for the compressor and 82 percent for the turbine and an effectiveness of 65 percent for the regenerator, determine (a) the air temperature at the turbine exit, (b) the net work output, and (c) the thermal efficiency. Get 9.96 exercise solution

9–97 A stationary gas-turbine power plant operates on an ideal regenerative Brayton cycle (P = 100 percent) with air as the working fluid. Air enters the compressor at 95 kPa and 290 K and the turbine at 760 kPa and 1100 K. Heat is transferred to air from an external source at a rate of 75,000 kJ/s. Determine the power delivered by this plant (a) assuming constant specific heats for air at room temperature and (b) accounting for the variation of specific heats with temperature. Get 9.97 exercise solution

9–98 Air enters the compressor of a regenerative gas-turbine engine at 300 K and 100 kPa, where it is compressed to 800 kPa and 580 K. The regenerator has an effectiveness of 72 percent, and the air enters the turbine at 1200 K. For a turbine efficiency of 86 percent, determine (a) the amount of heat transfer in the regenerator and (b) the thermal efficiency. Assume variable specific heats for air. Get 9.98 exercise solution

9–99 Repeat Problem 9–98 using constant specific heats at room temperature. Get 9.99 exercise solution

9–100 Repeat Problem 9–98 for a regenerator effectiveness of 70 percent. Brayton Cycle with Intercooling, Reheating, and Regeneration Get 9.100 exercise solution

9–101C Under what modifications will the ideal simple gas-turbine cycle approach the Ericsson cycle? Get 9.101 exercise solution

9–102C The single-stage compression process of an ideal Brayton cycle without regeneration is replaced by a multistage compression process with intercooling between the same pressure limits. As a result of this modification, (a) Does the compressor work increase, decrease, or remain the same? (b) Does the back work ratio increase, decrease, or remain the same? (c) Does the thermal efficiency increase, decrease, or remain the same? Get 9.102 exercise solution

9–103C The single-stage expansion process of an ideal Brayton cycle without regeneration is replaced by a multistage expansion process with reheating between the same pressure limits. As a result of this modification, (a) Does the turbine work increase, decrease, or remain the same? (b) Does the back work ratio increase, decrease, or remain the same? (c) Does the thermal efficiency increase, decrease, or remain the same? Get 9.103 exercise solution

9–104C A simple ideal Brayton cycle without regeneration is modified to incorporate multistage compression with intercooling and multistage expansion with reheating, without changing the pressure or temperature limits of the cycle. As a result of these two modifications, (a) Does the net work output increase, decrease, or remain the same? (b) Does the back work ratio increase, decrease, or remain the same? (c) Does the thermal efficiency increase, decrease, or remain the same? (d) Does the heat rejected increase, decrease, or remain the same? Get 9.104 exercise solution

9–105C A simple ideal Brayton cycle is modified to incorporate multistage compression with intercooling, multistage expansion with reheating, and regeneration without changing the pressure limits of the cycle. As a result of these modifications, (a) Does the net work output increase, decrease, or remain the same? (b) Does the back work ratio increase, decrease, or remain the same? (c) Does the thermal efficiency increase, decrease, or remain the same? (d) Does the heat rejected increase, decrease, or remain the same? Get 9.105 exercise solution

9–106C For a specified pressure ratio, why does multistage compression with intercooling decrease the compressor work, and multistage expansion with reheating increase the turbine work? Get 9.106 exercise solution

9–107C In an ideal gas-turbine cycle with intercooling, reheating, and regeneration, as the number of compression and expansion stages is increased, the cycle thermal efficiency approaches (a) 100 percent, (b) the Otto cycle efficiency, or (c) the Carnot cycle efficiency. Get 9.107 exercise solution

9–108 Consider an ideal gas-turbine cycle with two stages of compression and two stages of expansion. The pressure ratio across each stage of the compressor and turbine is 3. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Determine the back work ratio and the thermal efficiency of the cycle, assuming (a) no regenerator is used and (b) a regenerator with 75 percent effectiveness is used. Use variable specific heats. Get 9.108 exercise solution

9–109 Repeat Problem 9–108, assuming an efficiency of 80 percent for each compressor stage and an efficiency of 85 percent for each turbine stage. Get 9.109 exercise solution

9–110 Consider a regenerative gas-turbine power plant with two stages of compression and two stages of expansion. The overall pressure ratio of the cycle is 9. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Accounting for the variation of specific heats with temperature, determine the minimum mass flow rate of air needed to develop a net power output of 110 MW. Get 9.110 exercise solution

9–111 Repeat Problem 9–110 using argon as the working fluid. Jet-Propulsion Cycles Get 9.111 exercise solution

9–112C What is propulsive power? How is it related to thrust? Get 9.112 exercise solution

9–113C What is propulsive efficiency? How is it determined? Get 9.113 exercise solution

9–114C Is the effect of turbine and compressor irreversibilities of a turbojet engine to reduce (a) the net work, (b) the thrust, or (c) the fuel consumption rate? Get 9.114 exercise solution

9–115E A turbojet is flying with a velocity of 900 ft/s at an altitude of 20,000 ft, where the ambient conditions are 7 psia and 10°F. The pressure ratio across the compressor is 13, and the temperature at the turbine inlet is 2400 R. Assuming ideal operation for all components and constant specific heats for air at room temperature, determine (a) the pressure at the turbine exit, (b) the velocity of the exhaust gases, and (c) the propulsive efficiency. Get 9.115 exercise solution

9–116E Repeat Problem 9–115E accounting for the variation of specific heats with temperature. Get 9.116 exercise solution

9–117 A turbojet aircraft is flying with a velocity of 320 m/s at an altitude of 9150 m, where the ambient conditions are 32 kPa and -32°C. The pressure ratio across the compressor is 12, and the temperature at the turbine inlet is 1400 K. Air enters the compressor at a rate of 60 kg/s, and the jet fuel has a heating value of 42,700 kJ/kg. Assuming ideal operation for all components and constant specific heats for air at room temperature, determine (a) the velocity of the exhaust gases, (b) the propulsive power developed, and (c) the rate of fuel consumption. Get 9.117 exercise solution

9–118 Repeat Problem 9–117 using a compressor efficiency of 80 percent and a turbine efficiency of 85 percent. Get 9.118 exercise solution

9–119 Consider an aircraft powered by a turbojet engine that has a pressure ratio of 12. The aircraft is stationary on the ground, held in position by its brakes. The ambient air is at 27°C and 95 kPa and enters the engine at a rate of 10 kg/s. The jet fuel has a heating value of 42,700 kJ/kg, and it is burned completely at a rate of 0.2 kg/s. Neglecting the effect of the diffuser and disregarding the slight increase in mass at the engine exit as well as the inefficiencies of engine components, determine the force that must be applied on the brakes to hold the plane stationary. Get 9.119 exercise solution

9–120 Reconsider Problem 9–119. In the problem statement, replace the inlet mass flow rate by an inlet volume flow rate of 9.063 m3/s. Using EES (or other) software, investigate the effect of compressor inlet temperature in the range of –20 to 30°C on the force that must be applied to the brakes to hold the plane stationary. Plot this force as a function in compressor inlet temperature. Get 9.120 exercise solution

9–121 Air at 7°C enters a turbojet engine at a rate of 16 kg/s and at a velocity of 300 m/s (relative to the engine).Air is heated in the combustion chamber at a rate 15,000 kJ/s and it leaves the engine at 427°C. Determine the thrust produced by this turbojet engine. (Hint: Choose the entire engine as your control volume.) Get 9.121 exercise solution

9–122 Determine the total exergy destruction associated with the Otto cycle described in Problem 9–34, assuming a source temperature of 2000 K and a sink temperature of 300 K. Also, determine the exergy at the end of the power stroke. Get 9.122 exercise solution

9–123 Determine the total exergy destruction associated with the Diesel cycle described in Problem 9–47, assuming a source temperature of 2000 K and a sink temperature of 300 K. Also, determine the exergy at the end of the isentropic compression process. Get 9.123 exercise solution

9–124E Determine the exergy destruction associated with the heat rejection process of the Diesel cycle described in Problem 9–49E, assuming a source temperature of 3500 R and a sink temperature of 540 R. Also, determine the exergy at the end of the isentropic expansion process. Get 9.124 exercise solution

9–125 Calculate the exergy destruction associated with each of the processes of the Brayton cycle described in Problem 9–73, assuming a source temperature of 1600 K and a sink temperature of 290 K. Get 9.125 exercise solution

9–126 Determine the total exergy destruction associated with the Brayton cycle described in Problem 9–93, assuming a source temperature of 1800 K and a sink temperature of 300 K. Also, determine the exergy of the exhaust gases at the exit of the regenerator. Get 9.126 exercise solution

9–127 Reconsider Problem 9–126. Using EES (or other) software, investigate the effect of varying the cycle pressure ratio from 6 to 14 on the total exergy destruction for the cycle and the exergy of the exhaust gas leaving the regenerator. Plot these results as functions of pressure ratio. Discuss the results. Get 9.127 exercise solution

9–128 Determine the exergy destruction associated with each of the processes of the Brayton cycle described in Problem 9–98, assuming a source temperature of 1260 K and a sink temperature of 300 K. Also, determine the exergy of the exhaust gases at the exit of the regenerator. Take Pexhaust = P0 = 100 kPa. Get 9.128 exercise solution

9–129 A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 700 kPa. Air enters the compressor at 30°C at a rate of 12.6 kg/s and leaves at 260°C. A diesel fuel with a heating value of 42,000 kJ/kg is burned in the combustion chamber with an air–fuel ratio of 60 and a combustion efficiency of 97 percent. Combustion gases leave the combustion chamber and enter the turbine whose isentropic efficiency is 85 percent. Treating the combustion gases as air and using constant specific heats at 500°C, determine (a) the isentropic efficiency of the compressor, (b) the net power output and the back work ratio, (c) the thermal efficiency, and (d) the second-law efficiency. Get 9.129 exercise solution

9–130 A four-cylinder, four-stroke, 2.8-liter modern, highspeed compression-ignition engine operates on the ideal dual cycle with a compression ratio of 14. The air is at 95 kPa and 55°C at the beginning of the compression process and the engine speed is 3500 rpm. Equal amounts of fuel are burned at constant volume and at constant pressure. The maximum allowable pressure in the cycle is 9 MPa due to material strength limitations. Using constant specific heats at 850 K, determine (a) the maximum temperature in the cycle, (b) the net work output and the thermal efficiency, (c) the mean effective pressure, and (d) the net power output. Also, determine (e) the second-law efficiency of the cycle and the rate of exergy output with the exhaust gases when they are purged. Get 9.130 exercise solution

9–131 A gas-turbine power plant operates on the regenerative Brayton cycle between the pressure limits of 100 and 700 kPa. Air enters the compressor at 30°C at a rate of 12.6 kg/s and leaves at 260°C. It is then heated in a regenerator to 400°C by the hot combustion gases leaving the turbine. A diesel fuel with a heating value of 42,000 kJ/kg is burned in the combustion chamber with a combustion efficiency of 97 percent. The combustion gases leave the combustion chamber at 871°C and enter the turbine whose isentropic efficiency is 85 percent. Treating combustion gases as air and using constant specific heats at 500°C, determine (a) the isentropic efficiency of the compressor, (b) the effectiveness of the regenerator, (c) the air–fuel ratio in the combustion chamber, (d) the net power output and the back work ratio, (e) the thermal efficiency, and (f) the second-law efficiency of the plant. Also determine (g) the second-law (exergetic) efficiencies of the compressor, the turbine, and the regenerator, and (h) the rate of the exergy flow with the combustion gases at the regenerator exit. Get 9.131 exercise solution

9–132 A four-stroke turbocharged V-16 diesel engine built by GE Transportation Systems to power fast trains produces 3500 hp at 1200 rpm. Determine the amount of power produced per cylinder per (a) mechanical cycle and (b) thermodynamic cycle. Get 9.132 exercise solution

9–133 Consider a simple ideal Brayton cycle operating between the temperature limits of 300 and 1500 K. Using constant specific heats at room temperature, determine the pressure ratio for which the compressor and the turbine exit temperatures of air are equal. Get 9.133 exercise solution

9–134 An air-standard cycle with variable coefficients is executed in a closed system and is composed of the following four processes: 1-2 v = constant heat addition from 100 kPa and 27°C to 300 kPa 2-3 P = constant heat addition to 1027°C 3-4 Isentropic expansion to 100 kPa 4-1 P = constant heat rejection to initial state (a) Show the cycle on P-v and T-s diagrams. (b) Calculate the net work output per unit mass. (c) Determine the thermal efficiency. Get 9.134 exercise solution

9–135 Repeat Problem 9–134 using constant specific heats at room temperature. Get 9.135 exercise solution

9–136 An air-standard cycle with variable specific heats is executed in a closed system with 0.003 kg of air, and it consists of the following three processes: 1-2 Isentropic compression from 100 kPa and 27°C to 700 kPa 2-3 P = constant heat addition to initial specific volume 3-1 v = constant heat rejection to initial state (a) Show the cycle on P-v and T-s diagrams. (b) Calculate the maximum temperature in the cycle. (c) Determine the thermal efficiency. Get 9.136 exercise solution

9–137 Repeat Problem 9–136 using constant specific heats at room temperature. Get 9.137 exercise solution

9–138 A Carnot cycle is executed in a closed system and uses 0.0025 kg of air as the working fluid. The cycle efficiency is 60 percent, and the lowest temperature in the cycle is 300 K. The pressure at the beginning of the isentropic expansion is 700 kPa, and at the end of the isentropic compression it is 1 MPa. Determine the net work output per cycle. Get 9.138 exercise solution

9–139 A four-cylinder spark-ignition engine has a compression ratio of 8, and each cylinder has a maximum volume of 0.6 L. At the beginning of the compression process, the air is at 98 kPa and 17°C, and the maximum temperature in the cycle is 1800 K. Assuming the engine to operate on the ideal Otto cycle, determine (a) the amount of heat supplied per cylinder, (b) the thermal efficiency, and (c) the number of revolutions per minute required for a net power output of 60 kW. Assume variable specific heats for air. Get 9.139 exercise solution

9–140 Reconsider Problem 9–139. Using EES (or other) software, study the effect of varying the compression ratio from 5 to 11 on the net work done and the efficiency of the cycle. Plot the P-v and T-s diagrams for the cycle, and discuss the results. Get 9.140 exercise solution

9–141 An ideal Otto cycle has a compression ratio of 9.2 and uses air as the working fluid. At the beginning of the compression process, air is at 98 kPa and 27°C. The pressure is doubled during the constant-volume heat-addition process. Accounting for the variation of specific heats with temperature, determine (a) the amount of heat transferred to the air, (b) the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for the cycle. Get 9.141 exercise solution

9–142 Repeat Problem 9–141 using constant specific heats at room temperature. Get 9.142 exercise solution

9–143 Consider an engine operating on the ideal Diesel cycle with air as the working fluid. The volume of the cylinder is 1200 cm3 at the beginning of the compression process, 75 cm3 at the end, and 150 cm3 after the heat-addition process. Air is at 17°C and 100 kPa at the beginning of the compression process. Determine (a) the pressure at the beginning of the heat-rejection process, (b) the net work per cycle, in kJ, and (c) the mean effective pressure. Get 9.143 exercise solution

9–144 Repeat Problem 9–143 using argon as the working fluid. Get 9.144 exercise solution

9–145E An ideal dual cycle has a compression ratio of 12 and uses air as the working fluid. At the beginning of the compression process, air is at 14.7 psia and 90°F, and occupies a volume of 75 in3. During the heat-addition process, 0.3 Btu of heat is transferred to air at constant volume and 1.1 Btu at constant pressure. Using constant specific heats evaluated at room temperature, determine the thermal efficiency of the cycle. Get 9.145 exercise solution

9–146 Consider an ideal Stirling cycle using air as the working fluid. Air is at 350 K and 200 kPa at the beginning of the isothermal compression process, and heat is supplied to air from a source at 1800 K in the amount of 900 kJ/kg. Determine (a) the maximum pressure in the cycle and (b) the net work output per unit mass of air. Get 9.146 exercise solution

9–147 Consider a simple ideal Brayton cycle with air as the working fluid. The pressure ratio of the cycle is 6, and the minimum and maximum temperatures are 300 and 1300 K, respectively. Now the pressure ratio is doubled without changing the minimum and maximum temperatures in the cycle. Determine the change in (a) the net work output per unit mass and (b) the thermal efficiency of the cycle as a result of this modification. Assume variable specific heats for air. Get 9.147 exercise solution

9–148 Repeat Problem 9–147 using constant specific heats at room temperature. Get 9.148 exercise solution

9–149 Helium is used as the working fluid in a Brayton cycle with regeneration. The pressure ratio of the cycle is 8, the compressor inlet temperature is 300 K, and the turbine inlet temperature is 1800 K. The effectiveness of the regenerator is 75 percent. Determine the thermal efficiency and the required mass flow rate of helium for a net power output of 60 MW, assuming both the compressor and the turbine have an isentropic efficiency of (a) 100 percent and (b) 80 percent. Get 9.149 exercise solution

9–150 A gas-turbine engine with regeneration operates with two stages of compression and two stages of expansion. The pressure ratio across each stage of the compressor and turbine is 3.5. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. The compressor and turbine efficiencies are 78 and 86 percent, respectively, and the effectiveness of the regenerator is 72 percent. Determine the back work ratio and the thermal efficiency of the cycle, assuming constant specific heats for air at room temperature. Answers: 53.2 percent, 39.2 percent Get 9.150 exercise solution

9–151 Reconsider Problem 9–150. Using EES (or other) software, study the effects of varying the isentropic efficiencies for the compressor and turbine and regenerator effectiveness on net work done and the heat supplied to the cycle for the variable specific heat case. Let the isentropic efficiencies and the effectiveness vary from 70 percent to 90 percent. Plot the T-s diagram for the cycle. Get 9.151 exercise solution

9–152 Repeat Problem 9–150 using helium as the working fluid. Get 9.152 exercise solution

9–153 Consider the ideal regenerative Brayton cycle. Determine the pressure ratio that maximizes the thermal efficiency of the cycle and compare this value with the pressure ratio that maximizes the cycle net work. For the same maximumto-minimum temperature ratios, explain why the pressure ratio for maximum efficiency is less than the pressure ratio for maximum work. Get 9.153 exercise solution

9–154 Consider an ideal gas-turbine cycle with one stage of compression and two stages of expansion and regeneration. The pressure ratio across each turbine stage is the same. The high-pressure turbine exhaust gas enters the regenerator and then enters the low-pressure turbine for expansion to the compressor inlet pressure. Determine the thermal efficiency of this cycle as a function of the compressor pressure ratio and the high-pressure turbine to compressor inlet temperature ratio. Compare your result with the efficiency of the standard regenerative cycle. Get 9.154 exercise solution

9–155 A four-cylinder, four-stroke spark-ignition engine operates on the ideal Otto cycle with a compression ratio of 11 and a total displacement volume of 1.8 liter. The air is at 90 kPa and 50°C at the beginning of the compression process. The heat input is 1.5 kJ per cycle per cylinder. Accounting for the variation of specific heats of air with temperature, determine (a) the maximum temperature and pressure that occur during the cycle, (b) the net work per cycle per cyclinder and the thermal efficiency of the cycle, (c) the mean effective pressure, and (d) the power output for an engine speed of 3000 rpm. Get 9.155 exercise solution

9–156 A gas-turbine plant operates on the regenerative Brayton cycle with two stages of reheating and two-stages of intercooling between the pressure limits of 100 and 1200 kPa. The working fluid is air. The air enters the first and the second stages of the compressor at 300 K and 350 K, respectively, and the first and the second stages of the turbine at 1400 K and 1300 K, respectively. Assuming both the compressor and the turbine have an isentropic efficiency of 80 percent and the regenerator has an effectiveness of 75 percent and using variable specific heats, determine (a) the back work ratio and the net work output, (b) the thermal efficiency, and (c) the second-law efficiency of the cycle. Also determine (d) the exergies at the exits of the combustion chamber (state 6) and the regenerator (state 10) (See Figure 9–43 in the text). Answers: (a) 0.523, 317 kJ/kg, (b) 0.553, (c) 0.704, (d) 931 kJ/kg, 129 kJ/kg Get 9.156 exercise solution

9–157 Electricity and process heat requirements of a manufacturing facility are to be met by a cogeneration plant consisting of a gas turbine and a heat exchanger for steam production The plant operates on the simple Brayton cycle between the pressure limits of 100 and 1200 kPa with air as the working fluid. Air enters the compressor at 30°C. Combustion gases leave the turbine and enter the heat exchanger at 500°C, and leave the heat exchanger of 350°C, while the liquid water enters the heat exchanger at 25°C and leaves at 200°C as a saturated vapor. The net power produced by the gas-turbine cycle is 800 kW. Assuming a compressor isentropic efficiency of 82 percent and a turbine isentropic efficiency of 88 percent and using variable specific heats, determine (a) the mass flow rate of air, (b) the back work ratio and the thermal efficiency, and (c) the rate at which steam is produced in the heat exchanger. Also determine (d) the utilization efficiency of the cogeneration plant, defined as the ratio of the total energy utilized to the energy supplied to the plant. Get 9.157 exercise solution

9–158 A turbojet aircraft flies with a velocity of 900 km/h at an altitude where the air temperature and pressure are -35°C and 40 kPa. Air leaves the diffuser at 50 kPa with a velocity of 15 m/s, and combustion gases enter the turbine at 450 kPa and 950°C. The turbine produces 500 kW of power, all of which is used to drive the compressor. Assuming an isentropic efficiency of 83 percent for the compressor, turbine, and nozzle, and using variable specific heats, determine (a) the pressure of combustion gases at the turbine exit, (b) the mass flow rate of air through the compressor, (c) the velocity of the gases at the nozzle exit, and (d) the propulsive power and the propulsive efficiency for this engine. Answers: (a) 147 kPa, (b) 1.76 kg/s, (c) 719 m/s, (d) 206 kW, 0.156 Get 9.158 exercise solution

9–159 Using EES (or other) software, study the effect of variable specific heats on the thermal efficiency of the ideal Otto cycle using air as the working fluid. At the beginning of the compression process, air is at 100 kPa and 300 K. Determine the percentage of error involved in using constant specific heat values at room temperature for the following combinations of compression ratios and maximum cycle temperatures: r = 6, 8, 10, 12, and Tmax = 1000, 1500, 2000, 2500 K. Get 9.159 exercise solution

9–160 Using EES (or other) software, determine the effects of compression ratio on the net work output and the thermal efficiency of the Otto cycle for a maximum cycle temperature of 2000 K. Take the working fluid to be air that is at 100 kPa and 300 K at the beginning of the compression process, and assume variable specific heats. Vary the compression ratio from 6 to 15 with an increment of 1. Tabulate and plot your results against the compression ratio. Get 9.160 exercise solution

9–161 Using EES (or other) software, determine the effects of pressure ratio on the net work output and the thermal efficiency of a simple Brayton cycle for a maximum cycle temperature of 1800 K. Take the working fluid to be air that is at 100 kPa and 300 K at the beginning of the compression process, and assume variable specific heats. Vary the pressure ratio from 5 to 24 with an increment of 1. Tabulate and plot your results against the pressure ratio. At what pressure ratio does the net work output become a maximum? At what pressure ratio does the thermal efficiency become a maximum? Get 9.161 exercise solution

9–162 Repeat Problem 9–161 assuming isentropic efficiencies of 85 percent for both the turbine and the compressor. Get 9.162 exercise solution

9–163 Using EES (or other) software, determine the effects of pressure ratio, maximum cycle temperature, and compressor and turbine efficiencies on the net work output per unit mass and the thermal efficiency of a simple Brayton cycle with air as the working fluid. Air is at 100 kPa and 300 K at the compressor inlet. Also, assume constant specific heats for air at room temperature. Determine the net work output and the thermal efficiency for all combinations of the following parameters, and draw conclusions from the results. Pressure ratio: 5, 8, 14 Maximum cycle temperature: 800, 1200, 1600 K Compressor isentropic efficiency: 80, 100 percent Turbine isentropic efficiency: 80, 100 percent Get 9.163 exercise solution

9–164 Repeat Problem 9–163 by considering the variation of specific heats of air with temperature. Get 9.164 exercise solution

9–165 Repeat Problem 9–163 using helium as the working fluid. Get 9.165 exercise solution

9–166 Using EES (or other) software, determine the effects of pressure ratio, maximum cycle temperature, regenerator effectiveness, and compressor and turbine efficiencies on the net work output per unit mass and on the thermal efficiency of a regenerative Brayton cycle with air as the working fluid. Air is at 100 kPa and 300 K at the compressor inlet. Also, assume constant specific heats for air at room temperature. Determine the net work output and the thermal efficiency for all combinations of the following parameters. Pressure ratio: 6, 10 Maximum cycle temperature: 1500, 2000 K Compressor isentropic efficiency: 80, 100 percent Turbine isentropic efficiency: 80, 100 percent Regenerator effectiveness: 70, 90 percent Get 9.166 exercise solution

9–167 Repeat Problem 9–166 by considering the variation of specific heats of air with temperature. Get 9.167 exercise solution

9–168 Repeat Problem 9–166 using helium as the working fluid. Get 9.168 exercise solution

9–169 Using EES (or other) software, determine the effect of the number of compression and expansion stages on the thermal efficiency of an ideal regenerative Brayton cycle with multistage compression and expansion. Assume that the overall pressure ratio of the cycle is 12, and the air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Using constant specific heats for air at room temperature, determine the thermal efficiency of the cycle by varying the number of stages from 1 to 22 in increments of 3. Plot the thermal efficiency versus the number of stages. Compare your results to the efficiency of an Ericsson cycle operating between the same temperature limits. Get 9.169 exercise solution

9–170 Repeat Problem 9–169 using helium as the working fluid Get 9.170 exercise solution

9–171 An Otto cycle with air as the working fluid has a compression ratio of 8.2. Under cold-air-standard conditions, the thermal efficiency of this cycle is (a) 24 percent (b) 43 percent (c) 52 percent (d) 57 percent (e) 75 percent Get 9.171 exercise solution

9–172 For specified limits for the maximum and minimum temperatures, the ideal cycle with the lowest thermal efficiency is (a) Carnot (b) Stirling (c) Ericsson (d) Otto (e) All are the same Get 9.172 exercise solution

9–173 A Carnot cycle operates between the temperature limits of 300 and 2000 K, and produces 600 kW of net power. The rate of entropy change of the working fluid during the heat addition process is (a) 0 ( b) 0.300 kW/K (c) 0.353 kW/K (d) 0.261 kW/K (e) 2.0 kW/K Get 9.173 exercise solution

9–174 Air in an ideal Diesel cycle is compressed from 3 to 0.15 L, and then it expands during the constant pressure heat addition process to 0.30 L. Under cold air standard conditions, the thermal efficiency of this cycle is (a) 35 percent (b) 44 percent (c) 65 percent (d) 70 percent (e) 82 percent Get 9.174 exercise solution

9–175 Helium gas in an ideal Otto cycle is compressed from 20°C and 2.5 to 0.25 L, and its temperature increases by an additional 700°C during the heat addition process. The temperature of helium before the expansion process is (a) 1790°C (b) 2060°C (c) 1240°C (d) 620°C (e) 820°C Get 9.175 exercise solution

9–176 In an ideal Otto cycle, air is compressed from 1.20 kg/m3 and 2.2 to 0.26 L, and the net work output of the cycle is 440 kJ/kg. The mean effective pressure (MEP) for this cycle is (a) 612 kPa (b) 599 kPa (c) 528 kPa (d) 416 kPa (e) 367 kPa Get 9.176 exercise solution

9–177 In an ideal Brayton cycle, air is compressed from 95 kPa and 25°C to 800 kPa. Under cold-air-standard conditions, the thermal efficiency of this cycle is (a) 46 percent (b) 54 percent (c) 57 percent (d) 39 percent (e) 61 percent Get 9.177 exercise solution

9–178 Consider an ideal Brayton cycle executed between the pressure limits of 1200 and 100 kPa and temperature limits of 20 and 1000°C with argon as the working fluid. The net work output of the cycle is (a) 68 kJ/kg (b) 93 kJ/kg (c) 158 kJ/kg (d) 186 kJ/kg (e) 310 kJ/kg Get 9.178 exercise solution

9–179 An ideal Brayton cycle has a net work output of 150 kJ/kg and a back work ratio of 0.4. If both the turbine and the compressor had an isentropic efficiency of 85 percent, the net work output of the cycle would be (a) 74 kJ/kg (b) 95 kJ/kg (c) 109 kJ/kg (d) 128 kJ/kg (e) 177 kJ/kg Get 9.179 exercise solution

9–180 In an ideal Brayton cycle, air is compressed from 100 kPa and 25°C to 1 MPa, and then heated to 1200°C before entering the turbine. Under cold-air-standard conditions, the air temperature at the turbine exit is (a) 490°C (b) 515°C (c) 622°C (d) 763°C (e) 895°C Get 9.180 exercise solution

9–181 In an ideal Brayton cycle with regeneration, argon gas is compressed from 100 kPa and 25°C to 400 kPa, and then heated to 1200°C before entering the turbine. The highest temperature that argon can be heated in the regenerator is (a) 246°C (b) 846°C (c) 689°C (d) 368°C (e) 573°C Get 9.181 exercise solution

9–182 In an ideal Brayton cycle with regeneration, air is compressed from 80 kPa and 10°C to 400 kPa and 175°C, is heated to 450°C in the regenerator, and then further heated to 1000°C before entering the turbine. Under cold-air-standard conditions, the effectiveness of the regenerator is (a) 33 percent (b) 44 percent (c) 62 percent (d) 77 percent (e) 89 percent Get 9.182 exercise solution

9–183 Consider a gas turbine that has a pressure ratio of 6 and operates on the Brayton cycle with regeneration between the temperature limits of 20 and 900°C. If the specific heat ratio of the working fluid is 1.3, the highest thermal efficiency this gas turbine can have is (a) 38 percent (b) 46 percent (c) 62 percent (d) 58 percent (e) 97 percent Get 9.183 exercise solution

9–184 An ideal gas turbine cycle with many stages of compression and expansion and a regenerator of 100 percent effectiveness has an overall pressure ratio of 10. Air enters every stage of compressor at 290 K, and every stage of turbine at 1200 K. The thermal efficiency of this gas-turbine cycle is (a) 36 percent (b) 40 percent (c) 52 percent (d) 64 percent (e) 76 percent Get 9.184 exercise solution

9–185 Air enters a turbojet engine at 260 m/s at a rate of 30 kg/s, and exits at 800 m/s relative to the aircraft. The thrust developed by the engine is (a) 8 kN (b) 16 kN (c) 24 kN (d) 20 kN (e) 32 kN Get 9.185 exercise solution

Themordynamics Cengel & Boles 5th edition - Chapter 8 - Solutions

8–1C How does reversible work differ from useful work? Get 8.1 exercise solution

8–2C Under what conditions does the reversible work equal irreversibility for a process? Get 8.2 exercise solution

8–3C What final state will maximize the work output of a device? Get 8.3 exercise solution

8–4C Is the exergy of a system different in different environments? Get 8.4 exercise solution

8–5C How does useful work differ from actual work? For what kind of systems are these two identical? Get 8.5 exercise solution

8–6C Consider a process that involves no irreversibilities. Will the actual useful work for that process be equal to the reversible work? Get 8.6 exercise solution

8–7C Consider two geothermal wells whose energy contents are estimated to be the same. Will the exergies of these wells necessarily be the same? Explain. Get 8.7 exercise solution

8–8C 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? Get 8.8 exercise solution

8–9C Consider an environment of zero absolute pressure (such as outer space). How will the actual work and the useful work compare in that environment? Get 8.9 exercise solution

8–10C What is the second-law efficiency? How does it differ from the first-law efficiency? Get 8.10 exercise solution

8–11C 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. Get 8.11 exercise solution

8–12C Does a refrigerator that has a higher COP necessarily have a higher second-law efficiency than one with a lower COP? Explain. Get 8.12 exercise solution

8–13C Can a process for which the reversible work is zero be reversible? Can it be irreversible? Explain. Get 8.13 exercise solution

8–14C Consider a process during which no entropy is generated (Sgen = 0). Does the exergy destruction for this process have to be zero? Get 8.14 exercise solution

8–15 The electric power needs of a community are to be met by windmills with 10-m-diameter rotors. The windmills are to be located where the wind is blowing steadily at an average velocity of 8 m/s. Determine the minimum number of windmills that need to be installed if the required power output is 600 kW. Get 8.15 exercise solution

8–16 One method of meeting the extra electric power demand at peak periods is to pump some water from a large body of water (such as a lake) to a water reservoir at a higher elevation at times of low demand and to generate electricity at times of high demand by letting this water run down and rotate a turbine (i.e., convert the electric energy to potential energy and then back to electric energy). For an energy storage capacity of 5 x 106 kWh, determine the minimum amount of water that needs to be stored at an average elevation (relative to the ground level) of 75 m. Get 8.16 exercise solution

8–17 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. Get 8.17 exercise solution

8–18 A heat engine receives heat from a source at 1500 K at a rate of 700 kJ/s, and it rejects the waste heat to a medium at 320 K. The measured power output of the heat engine is 320 kW, and the environment temperature is 25°C. Determine (a) the reversible power, (b) the rate of irreversibility, and (c) the second-law efficiency of this heat engine. Answers: (a) 550.7 kW, (b) 230.7 kW, (c) 58.1 percent Get 8.18 exercise solution

8–19 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 298 K, and plot the results. Get 8.19 exercise solution

8–20E A heat engine that rejects waste heat to a sink at 530 R has a thermal efficiency of 36 percent and a second-law efficiency of 60 percent. Determine the temperature of the source that supplies heat to this engine. Get 8.20 exercise solution

8–21 How much of the 100 kJ of thermal energy at 800 K can be converted to useful work? Assume the environment to be at 25°C. Get 8.21 exercise solution

8–22 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. Get 8.22 exercise solution

8–23 A house that is losing heat at a rate of 80,000 kJ/h when the outside temperature drops to 15°C is to be heated by electric resistance heaters. If the house is to be maintained at 22°C at all times, determine the reversible work input for this process and the irreversibility. Get 8.23 exercise solution

8–24E 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. Get 8.24 exercise solution

8–25 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. Get 8.25 exercise solution

8–26 A geothermal power plant uses geothermal liquid water at 160°C at a rate of 440 kg/s as the heat source, and produces 14 MW of net power in an environment at 25°C. If 18.5 MW of exergy entering the plant with the geothermal water is destructed within the plant, determine (a) the exergy of the geothermal water entering the plant, (b) the second-law efficiency, and (c) the exergy of the heat rejected from the plant. Get 8.26 exercise solution

8–27C Is a process during which no entropy is generated (Sgen = 0) necessarily reversible? Get 8.27 exercise solution

8–28C Can a system have a higher second-law efficiency than the first-law efficiency during a process? Give examples. Get 8.28 exercise solution

8–29 A piston–cylinder device initially contains 2 L of air at 100 kPa and 25°C. Air is now compressed to a final state of 600 kPa and 150°C. The useful work input is 1.2 kJ. Assuming the surroundings are at 100 kPa and 25°C, 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. Get 8.29 exercise solution

8–30 A piston–cylinder device contains 5 kg of refrigerant134a at 0.7 MPa and 60°C. The refrigerant is now cooled at constant pressure until it exists as a liquid at 24°C. If the surroundings are at 100 kPa and 24°C, determine (a) the exergy of the refrigerant at the initial and the final states and (b) the exergy destroyed during this process. Get 8.30 exercise solution

8–31 The radiator of a steam heating system has a volume of 20 L and is filled with superheated water vapor at 200 kPa and 200°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 80°C as a result of heat transfer to the room air, which is at 21°C. Assuming the surroundings to be at 0°C, 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. Get 8.31 exercise solution

8–32 Reconsider Prob. 8–31. Using EES (or other) software, 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 21°C and plot the actual and maximum heat transferred to the room as functions of final steam temperature. Get 8.32 exercise solution

8–33E A well-insulated rigid tank contains 6 lbm 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. Assuming 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. Get 8.33 exercise solution

8–34 A rigid tank is divided into two equal parts by a partition. One part of the tank contains 1.5 kg of compressed liquid water at 300 kPa and 60°C and the other side is evacuated. Now the partition is removed, and the water expands to fill the entire tank. If the final pressure in the tank is 15 kPa, determine the exergy destroyed during this process. Assume the surroundings to be at 25°C and 100 kPa. Get 8.34 exercise solution

8–35 Reconsider Prob. 8–34. Using EES (or other) software, study the effect of final pressure in the tank on the exergy destroyed during the process. Plot the exergy destroyed as a function of the final pressure for final pressures between 25 and 15 kPa, and discuss the results. Get 8.35 exercise solution

8–36 An insulated piston–cylinder device contains 2 L of saturated liquid water at a constant pressure of 150 kPa. An electric resistance heater inside the cylinder is turned on, and electrical work is done on the water in the amount of 2200 kJ. Assuming the surroundings to be at 25°C and 100 kPa, determine (a) the minimum work with which this process could be accomplished and (b) the exergy destroyed during this process. Get 8.36 exercise solution

8–37 Reconsider Prob. 8–36. 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 2200 kJ, and plot your results. Get 8.37 exercise solution

8–38 An insulated piston–cylinder device contains 0.05 m3 of saturated refrigerant-134a vapor at 0.8 MPa pressure. The refrigerant is now allowed to expand in a reversible manner until the pressure drops to 0.2 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. Get 8.38 exercise solution

8–39E 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. Get 8.39 exercise solution

8–40 A 1.2-m3 insulated rigid tank contains 2.13 kg of carbon dioxide at 100 kPa. Now paddle-wheel work is done on the system until the pressure in the tank rises to 120 kPa. Determine (a) the actual paddle-wheel work done during this process and (b) the minimum paddle-wheel work with which this process (between the same end states) could be accomplished. Take T0 = 298 K. Get 8.40 exercise solution

8–41 An insulated piston–cylinder device initially contains 30 L of air at 120 kPa and 27°C. Air is now heated for 5 min by a 50-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. Get 8.41 exercise solution

8–42 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. Get 8.42 exercise solution

8–43 An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains 3 kg of argon gas at 300 kPa and 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. Get 8.43 exercise solution

8–44E A 70-lbm copper block initially at 250°F is dropped into an insulated tank that contains 1.5 ft3 of water at 75°F. Determine (a) the final equilibrium temperature and (b) the work potential wasted during this process. Assume the surroundings to be at 75°F. Get 8.44 exercise solution

8–45 An iron block of unknown mass at 85°C is dropped into an insulated tank that contains 100 L of water at 20°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°C. Assuming the surroundings to be at 20°C, determine (a) the mass of the iron block and (b) the exergy destroyed during this process. Get 8.45 exercise solution

8–46 A 50-kg iron block and a 20-kg copper block, both initially at 80°C, are dropped into a large lake at 15°C. Thermal equilibrium is established after a while as a result of heat transfer between the blocks and the lake water. Assuming the surroundings to be at 20°C, determine the amount of work that could have been produced if the entire process were executed in a reversible manner. Get 8.46 exercise solution

8–47E A 12-ft3 rigid tank contains refrigerant-134a at 40 psia and 55 percent quality. Heat is transferred now to the refrigerant from a source at 120°F until the pressure rises to 60 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. Get 8.47 exercise solution

8–48 Chickens with an average mass of 2.2 kg and average specific heat of 3.54 kJ/kg · °C are to be cooled by chilled water that enters a continuous-flow-type immersion chiller at 0.5°C and leaves at 2.5°C. Chickens are dropped into the chiller at a uniform temperature of 15°C at a rate of 500 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 200 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. Get 8.48 exercise solution

8–49 An ordinary egg can be approximated as a 5.5-cmdiameter sphere. The egg is initially at a uniform temperature of 8°C and is dropped into boiling water at 97°C. Taking the properties of egg to be r = 1020 kg/m3 and cp = 3.32 kJ/kg · °C, determine how much heat is transferred to the egg by the time the average temperature of the egg rises to 70°C and the amount of exergy destruction associated with this heat transfer process. Take T0 = 25°C. Get 8.49 exercise solution

8–50 Stainless steel ball bearings (r = 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. Get 8.50 exercise solution

8–51 Carbon steel balls (r = 7833 kg/m3 and cp = 0.465 kJ/kg · °C) 8 mm in diameter are annealed by heating them first to 900°C in a furnace and then allowing them to cool slowly to 100°C in ambient air at 35°C. If 1200 balls are to be annealed per hour, determine (a) the rate of heat transfer from the balls to the air and (b) the rate of exergy destruction due to heat loss from the balls to the air. Get 8.51 exercise solution

8–52 A 0.04-m3 tank initially contains air at ambient conditions of 100 kPa and 22°C. Now, a 15-liter tank containing liquid water at 85°C is placed into the tank without causing any air to escape. After some heat transfer from the water to the air and the surroundings, both the air and water are measured to be at 44°C. Determine (a) the amount of heat lost to the surroundings and (b) the exergy destruction during this process. Get 8.52 exercise solution

8–53 A piston–cylinder device initially contains 1.4 kg of refrigerant-134a at 140 kPa and 20°C. Heat is now transferred to the refrigerant, and the piston, which is resting on a set of stops, starts moving when the pressure inside reaches 180 kPa. Heat transfer continues until the temperature reaches 120°C. Assuming the surroundings to be at 25°C 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. Get 8.53 exercise solution

8–54 Steam is throttled from 8 MPa and 450°C to 6 MPa. Determine the wasted work potential during this throttling process. Assume the surroundings to be at 25°C. Get 8.54 exercise solution

8–55 Air is compressed steadily by an 8-kW compressor from 100 kPa and 17°C to 600 kPa and 167°C 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 17°C. Get 8.55 exercise solution

8–56 Reconsider Prob. 8–55. 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°C. Explain the values of heat transfer, exergy destroyed, and efficiency when the outlet temperature is set to 209.31°C and mass flow rate to 2.466 kg/min. Get 8.56 exercise solution

8–57 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. Get 8.57 exercise solution

8–58 Reconsider Prob. 8–57. 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. Get 8.58 exercise solution

8–59 Air enters a nozzle steadily at 300 kPa and 87°C with a velocity of 50 m/s and exits at 95 kPa and 300 m/s. The heat loss from the nozzle to the surrounding medium at 17°C is estimated to be 4 kJ/kg. Determine (a) the exit temperature and (b) the exergy destroyed during this process. Get 8.59 exercise solution

8–60 Reconsider Prob. 8–59. 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. Get 8.60 exercise solution

8–61 Steam enters a diffuser at 10 kPa and 50°C with a velocity of 300 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. Get 8.61 exercise solution

8–62E 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. Get 8.62 exercise solution

8–63 Steam enters an adiabatic turbine at 6 MPa, 600°C, and 80 m/s and leaves at 50 kPa, 100°C, 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 25°C. Get 8.63 exercise solution

8–64 Steam is throttled from 9 MPa and 500°C to a pressure of 7 MPa. Determine the decrease in exergy of the steam during this process. Assume the surroundings to be at 25°C. Get 8.64 exercise solution

8–65 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? Get 8.65 exercise solution

8–66E Refrigerant-134a enters an adiabatic compressor as saturated vapor at 30 psia at a rate of 20 ft3/min and exits at 70 psia pressure. If the isentropic efficiency of the compressor is 80 percent, determine (a) the actual power input and (b) the second-law efficiency of the compressor. Assume the surroundings to be at 75°F. Get 8.66 exercise solution

8–67 Refrigerant-134a at 140 kPa and -10°C is compressed by an adiabatic 0.5-kW compressor to an exit state of 700 kPa and 60°C. Neglecting the changes in kinetic and potential energies and assuming the surroundings to be at 27°C, determine (a) the isentropic efficiency and (b) the second-law efficiency of the compressor. Get 8.67 exercise solution

8–68 Air is compressed by a compressor from 95 kPa and 27°C to 600 kPa and 277°C at a rate of 0.06 kg/s. Neglecting the changes in kinetic and potential energies and assuming the surroundings to be at 25°C, determine the reversible power input for this process. Get 8.68 exercise solution

8–69 Reconsider Prob. 8–68. Using EES (or other) software, investigate the effect of compressor exit pressure on reversible power. Vary the compressor exit pressure from 200 to 600 kPa while keeping the exit temperature at 277°C. Plot the reversible power input for this process as a function of the compressor exit pressure. Get 8.69 exercise solution

8–70 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. Get 8.70 exercise solution

8–71 Steam expands in a turbine steadily at a rate of 15,000 kg/h, entering at 8 MPa and 450°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. Get 8.71 exercise solution

8–72E 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. Determine (a) the mass flow rate of air and (b) the portion of the power input that is used just to overcome the irreversibilities. Get 8.72 exercise solution

8–73 Hot combustion gases enter the nozzle of a turbojet engine at 260 kPa, 747°C, and 80 m/s and exit at 70 kPa and 500°C. Assuming the nozzle to be adiabatic and the surroundings to be at 20°C, determine (a) the exit velocity and (b) the decrease in the exergy of the gases. Take k = 1.3 and cp = 1.15 kJ/kg · °C for the combustion gases. Get 8.73 exercise solution

8–74 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. Get 8.74 exercise solution

8–75 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. Get 8.75 exercise solution

8–76E 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. Answers: (a) 5.0 lbm/s, (b) 14.6 Btu/s Get 8.76 exercise solution

8–77 Liquid water at 200 kPa and 20°C is heated in a chamber by mixing it with superheated steam at 200 kPa and 300°C. Liquid water enters the mixing chamber at a rate of 2.5 kg/s, and the chamber is estimated to lose heat to the surrounding air at 25°C at a rate of 600 kJ/min. If the mixture leaves the mixing chamber at 200 kPa and 60°C, determine (a) the mass flow rate of the superheated steam and (b) the wasted work potential during this mixing process. Get 8.77 exercise solution

8–78 Air enters the evaporator section of a window air conditioner at 100 kPa and 27°C with a volume flow rate of 6m 3/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. Get 8.78 exercise solution

8–79 A 0.1-m3 rigid tank initially contains refrigerant-134a at 1.2 MPa and 100 percent quality. The tank is connected by a valve to a supply line that carries refrigerant-134a at 1.6 MPa and 30°C. The valve is now opened, allowing the refrigerant to enter the tank, and it is closed when the tank contains only saturated liquid at 1.4 MPa. The refrigerant exchanges heat with its surroundings at 45°C and 100 kPa during this process. Determine (a) the mass of the refrigerant that entered the tank and (b) the exergy destroyed during this process. Get 8.79 exercise solution

8–80 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 tank 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. Answers: (a) 2545 kJ, (b) 141.2 kJ, 141.2 kJ Get 8.80 exercise solution

8–81E An insulated 150-ft3 rigid tank contains air at 75 psia and 140°F. A valve connected to the tank is opened, and air is allowed to escape until the pressure inside drops to 30 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. Answers: (a) 1249 Btu, (b) 1068 Btu Get 8.81 exercise solution

8–82 A 0.1-m3 rigid tank contains saturated refrigerant134a 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. Get 8.82 exercise solution

8–83 A vertical piston–cylinder device initially contains 0.1 m3 of helium at 20°C. The mass of the piston is such that it maintains a constant pressure of 300 kPa inside. A valve is now opened, and helium is allowed to escape until the volume inside the cylinder is decreased by one-half. Heat transfer takes place between the helium and its surroundings at 20°C 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. Get 8.83 exercise solution

8–84 A 0.2-m3 rigid tank initially contains saturated refrigerant-134a vapor at 1 MPa. The tank is connected by a valve to a supply line that carries refrigerant-134a at 1.4 MPa and 60°C. The valve is now opened, and the refrigerant is allowed to enter the tank. The valve is closed when one-half of the volume of the tank is filled with liquid and the rest with vapor at 1.2 MPa. The refrigerant exchanges heat during this process with the surroundings at 25°C. Determine (a) the amount of heat transfer and (b) the exergy destruction associated with this process. Get 8.84 exercise solution

8–85 An insulated vertical piston–cylinder device initially contains 15 kg of water, 9 kg of which is in the vapor phase. The mass of the piston is such that it maintains a constant pressure of 200 kPa inside the cylinder. Now steam at 1 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. Get 8.85 exercise solution

8–86 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. Get 8.86 exercise solution

8–87 Ambient air at 100 kPa and 300 K is compressed isentropically in a steady-flow device to 1 MPa. Determine (a) the work input to the compressor, (b) the exergy of the air at the compressor exit, and (c) the exergy of compressed air after it is cooled to 300 K at 1 MPa pressure. Get 8.87 exercise solution

8–88 Cold water (cp = 4.18 kJ/kg · °C) leading to a shower enters a well-insulated, thin-walled, double-pipe, counter-flow heat exchanger at 15°C at a rate of 0.25 kg/s and is heated to 45°C by hot water (cp = 4.19 kJ/kg · °C) that enters at 100°C 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 = 25°C. Get 8.88 exercise solution

8–89 Outdoor air (cp = 1.005 kJ/kg · °C) 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 95 kPa and 20°C at a rate of 0.8 m3/s. The combustion gases (cp = 1.10 kJ/kg · °C) enter at 180°C at a rate of 1.1 kg/s and leave at 95°C. Determine the rate of heat transfer to the air and the rate of exergy destruction in the heat exchanger. Get 8.89 exercise solution

8–90 A well-insulated shell-and-tube heat exchanger is used to heat water (cp = 4.18 kJ/kg · °C) in the tubes from 20 to 70°C at a rate of 4.5 kg/s. Heat is supplied by hot oil (cp = 2.30 kJ/kg · °C) that enters the shell side at 170°C at a rate of 10 kg/s. Disregarding any heat loss from the heat exchanger, determine (a) the exit temperature of oil and (b) the rate of exergy destruction in the heat exchanger. Take T0 = 25°C. Get 8.90 exercise solution

8–91E 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. Get 8.91 exercise solution

8–92 Steam enters a turbine at 12 MPa, 550°C, and 60 m/s and leaves at 20 kPa and 130 m/s with a moisture content of 5 percent. The turbine is not adequately insulated and it estimated that heat is lost from the turbine at a rate of 150 kW. The power output of the turbine is 2.5 MW. Assuming the surroundings to be at 25°C, determine (a) the reversible power output of the turbine, (b) the exergy destroyed within the turbine, and (c) the second-law efficiency of the turbine. (d) Also, estimate the possible increase in the power output of the turbine if the turbine were perfectly insulated. Get 8.92 exercise solution

8–93 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. Get 8.93 exercise solution

8–94 Liquid water at 15°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 kg/s and the saturated steam enters at a rate of 0.23 kg/s. The mixture leaves the mixing chamber as a liquid at 45°C. If the surroundings are at 15°C, 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. Get 8.94 exercise solution

8–95 Refrigerant-134a is expanded adiabatically in an expansion valve from 1.2 MPa and 40°C to 180 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. Get 8.95 exercise solution

8–96 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. Get 8.96 exercise solution

8–97 A 30-L electrical radiator containing heating oil is placed in a well-sealed 50-m3 room. Both the air in the room and the oil in the radiator are initially at the environment temperature of 10°C. Electricity with a rating of 1.8 kW is now turned on. Heat is also lost from the room at an average rate of 0.35 kW. The heater is turned off after some time when the temperatures of the room air and oil are measured to be 20°C and 50°C, respectively. Taking the density and the specific heat of oil to be 950 kg/m3 and 2.2 kJ/kg . °C, determine (a) how long the heater is kept on, (b) the exergy destruction, and (c) the second-law efficiency for this process. Get 8.97 exercise solution

8–98 Hot exhaust gases leaving an internal combustion engine at 400°C and 150 kPa at a rate of 0.8 kg/s is to be used to produce saturated steam at 200°C in an insulated heat exchanger. Water enters the heat exchanger at the ambient temperature of 20°C, and the exhaust gases leave the heat exchanger at 350°C. 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. Get 8.98 exercise solution

8–99 The inner and outer surfaces of a 5-m x 6-m brick wall of thickness 30 cm are maintained at temperatures of 20°C and 5°C, 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 = 0°C. Get 8.99 exercise solution

8–100 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. Get 8.100 exercise solution

8–101 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. Get 8.101 exercise solution

8–102 The inner and outer surfaces of a 0.5-cm-thick, 2-m x 2-m window glass in winter are 10°C and 3°C, respectively. If the rate of heat loss through the window is 3.2 kJ/s, determine the amount of heat loss, in kJ, through the glass over a period of 5 h. Also, determine the exergy destruction associated with this process. Take T0 = 5°C. Get 8.102 exercise solution

8–103 An aluminum pan has a flat bottom whose diameter is 20 cm. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of 800 W. If the temperatures of the inner and outer surfaces of the bottom of the pan are 104°C and 105°C, respectively, determine the rate of exergy destruction within the bottom of the pan during this process, in W. Take T0 = 25°C. Get 8.103 exercise solution

8–104 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. Get 8.104 exercise solution

8–105E A refrigerator has a second-law efficiency of 45 percent, and heat is removed from the refrigerated space at a rate of 200 Btu/min. If the space is maintained at 35°F while the surrounding air temperature is 75°F, determine the power input to the refrigerator. Get 8.105 exercise solution

8–106 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.) Get 8.106 exercise solution

8–107 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 in the amount 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.) Get 8.107 exercise solution

8–108 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 Q0 as well as a heat reservoir at TR in the amount of QR. (Hint: Eliminate Q0 between the two equations.) Get 8.108 exercise solution

8–109 A 50-cm-long, 800-W electric resistance heating element whose diameter is 0.5 cm is immersed in 40 kg of water initially at 20°C. Assuming the water container is wellinsulated, determine how long it will take for this heater to raise the water temperature to 80°C. Also, determine the minimum work input required and exergy destruction for this process, in kJ. Take T0 = 20°C. Get 8.109 exercise solution

8–110 A 5-cm-external-diameter, 10-m-long hot water pipe at 80°C is losing heat to the surrounding air at 5°C by natural convection at a rate of 45 W. Determine the rate at which the work potential is wasted during this process as a result of this heat loss. Get 8.110 exercise solution

8–111 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 250°C. 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 0°C. 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. Get 8.111 exercise solution

8–112E A piston–cylinder device initially contains 15 ft3 of helium gas at 25 psia and 70°F. Helium is now compressed in a polytropic process (PVn = constant) to 70 psia and 300°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. Get 8.112 exercise solution

8–113 A well-insulated 4-m x 4-m x 5-m room initially at 10°C 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 200°C. 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 = 10°C. Get 8.113 exercise solution

8–114 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. Get 8.114 exercise solution

8–115 Steam at 9 MPa and 500°C 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 1.4 MPa for other use. The remainder of the steam is further expanded in the second stage and leaves the turbine at 50 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. Get 8.115 exercise solution

8–116 Steam enters a two-stage adiabatic turbine at 8 MPa and 500°C. It expands in the first stage to a state of 2 MPa and 350°C. Steam is then reheated at constant pressure to a temperature of 500°C 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 25°C, determine the reversible power output and the rate of exergy destruction within this turbine. Get 8.116 exercise solution

8–117 One ton of liquid water at 80°C is brought into a well-insulated and well-sealed 4-m x 5-m x 6-m room initially at 22°C and 100 kPa. Assuming constant specific heats for both the air and water at room temperature, determine (a) the final equilibrium temperature in the room, (b) the exergy destruction, (c) the maximum amount of work that can be produced during this process, in kJ. Take T0 = 10°C. Get 8.117 exercise solution

8–118 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 80°C while the other side contains 1 m3 of He gas at 500 kPa and 25°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 (b) the wasted work potential during this process. What would your answer be if the piston were not free to move? Take T0 = 25°C. Get 8.118 exercise solution

8–119 Repeat Prob. 8–118 by assuming the piston is made of 5 kg of copper initially at the average temperature of the two gases on both sides. Get 8.119 exercise solution

8–120E Argon gas enters an adiabatic turbine at 1500°F and 200 psia at a rate of 40 lbm/min and exhausts at 30 psia. If the power output of the turbine is 95 hp, determine (a) the isentropic efficiency and (b) the second-law efficiency of the turbine. Assume the surroundings to be at 77°F. Get 8.120 exercise solution

8–121 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 MPa and 200°C and leaves as saturated liquid at the same pressure. Feedwater enters the heater at 2.5 MPa and 50°C and leaves 10°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 (b) the reversible work for this process per unit mass of the feedwater. Assume the surroundings to be at 25°C. Get 8.121 exercise solution

8–122 Reconsider Prob. 8–121. 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. Assume the entropy of the extracted steam is constant at the value for 1 MPa, 200°C and decrease the extracted steam pressure from 1 MPa to 100 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. Get 8.122 exercise solution

8–123 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 333.7 kJ/kg, respectively. Take T0 = 20°C. Get 8.123 exercise solution

8–124 Consider a 12-L evacuated rigid bottle that is surrounded by the atmosphere at 100 kPa and 17°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. Get 8.124 exercise solution

8–125 Two constant-volume tanks, each filled with 30 kg of air, have temperatures of 900 K and 300 K. A heat engine placed between the two tanks extracts heat from the hightemperature tank, produces work, and rejects heat to the lowtemperature tank. Determine the maximum work that can be produced by the heat engine and the final temperatures of the tanks. Assume constant specific heats at room temperature. Get 8.125 exercise solution

8–126 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 hightemperature device, produces work, and rejects heat to the lowtemperature 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. Get 8.126 exercise solution

8–127 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 25°C 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. Get 8.127 exercise solution

8–128 What would your answer to Prob. 8–127 be if heat were supplied to the pressure cooker from a heat source at 180°C instead of the electrical heating unit? Get 8.128 exercise solution

8–129 A constant-volume tank contains 20 kg of nitrogen at 1000 K, and a constant-pressure device contains 10 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. Get 8.129 exercise solution

8–130 A constant-volume tank has a temperature of 800 K and a constant-pressure device has a temperature of 290 K. Both the tank and device are filled with 20 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. Get 8.130 exercise solution

8–131 Can closed-system exergy be negative? How about flow exergy? Explain using an incompressible substance as an example. Get 8.131 exercise solution

8–132 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. Get 8.132 exercise solution

8–133E In a production facility, 1.2-in-thick, 2-ft x 2-ft square brass plates (r = 532.5 lbm/ft3 and cp = 0.091 Btu/lbm · °F) that are initially at a uniform temperature of 75°F are heated by passing them through an oven at 1300°F at a rate of 300 per minute. If the plates remain in the oven until their average temperature rises to 1000°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. Get 8.133 exercise solution

8–134 Long cylindrical steel rods (r = 7833 kg/m3 and cp = 0.465 kJ/kg · °C) of 10-cm diameter are heat-treated by drawing them at a velocity of 3 m/min through a 6-m-long oven maintained at 900°C. If the rods enter the oven at 30°C and leave at 700°C, determine (a) the rate of heat transfer to the rods in the oven and (b) the rate of exergy destruction associated with this heat transfer process. Take T0 = 25°C. Get 8.134 exercise solution

8–135 Steam is to be condensed in the condenser of a steam power plant at a temperature of 60°C with cooling water from a nearby lake that enters the tubes of the condenser at 15°C at a rate of 140 kg/s and leaves at 25°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. Get 8.135 exercise solution

8–136 A well-insulated heat exchanger is to heat water (cp = 4.18 kJ/kg · °C) from 25°C to 60°C at a rate of 0.4 kg/s. The heating is to be accomplished by geothermal water (cp = 4.31 kJ/kg · °C) available at 140°C at a mass flow rate of 0.3 kg/s. The inner tube is thin-walled and has a diameter of 0.6 cm. Determine (a) the rate of heat transfer and (b) the rate of exergy destruction in the heat exchanger. Get 8.136 exercise solution

8–137 An adiabatic heat exchanger is to cool ethylene glycol (cp =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. Get 8.137 exercise solution

8–138 A well-insulated, thin-walled, counter-flow heat exchanger is to be used to cool oil (cp = 2.20 kJ/kg · °C) from 150 to 40°C at a rate of 2 kg/s by water (cp = 4.18 kJ/kg · °C) that enters at 22°C 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 Get 8.138 exercise solution

8–139 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 $1.04/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. Get 8.139 exercise solution

8–140 Combustion gases enter a gas turbine at 750°C and 1.2 MPa at a rate of 3.4 kg/s and leave at 630°C and 500 kPa. It is estimated that heat is lost from the turbine at a rate of 30 kW. Using air properties for the combustion gases and assuming the surroundings to be at 25°C 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. Get 8.140 exercise solution

8–141 Refrigerant-134a enters an adiabatic compressor at 160 kPa superheated by 3°C, and leaves at 1.0 MPa. If the compressor has a second-law efficiency of 80 percent, determine (a) the actual work input, (b) the isentropic efficiency, and (c) the exergy destruction. Take the environment temperature to be 25°C. Get 8.141 exercise solution

8–142 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 frictional heating, (c) the exergy destruction, and (d) the second-law efficiency for an environment temperature of 20°C. Get 8.142 exercise solution

8–143 Argon gas expands from 3.5 MPa and 100°C to 500 kPa in an adiabatic expansion valve. For environment conditions of 100 kPa and 25°C, determine (a) the exergy of argon at the inlet, (b) the exergy destruction during the process, and (c) the second-law efficiency. Get 8.143 exercise solution

8–144 Nitrogen gas enters a diffuser at 100 kPa and 150°C with a velocity of 180 m/s, and leaves at 110 kPa and 25 m/s. It is estimated that 4.5 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 0.06 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. Get 8.144 exercise solution

8–145 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 temperature is 0°C, 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 Get 8.145 exercise solution

8–146 Liquid water enters an adiabatic piping system at 15°C at a rate of 5 kg/s. It is observed that the water temperature rises by 0.5°C in the pipe due to friction. If the environment temperature is also 15°C, the rate of exergy destruction in the pipe is (a) 8.36 kW (b) 10.4 kW (c) 197 kW (d) 265 kW (e) 2410 kW Get 8.146 exercise solution

8–147 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% Get 8.147 exercise solution

8–148 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 Get 8.148 exercise solution

8–149 A house is maintained at 25°C in winter by electric resistance heaters. If the outdoor temperature is 2°C, the second-law efficiency of the resistance heaters is (a) 0% (b) 7.7% (c) 8.7% (d) 13% (e) 100% Get 8.149 exercise solution

8–150 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) 0 kJ (c) 4.6 kJ (d) 55 kJ (e) 1008 kJ Get 8.150 exercise solution

8–151 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. Get 8.151 exercise solution

8–152 A furnace can supply heat steadily at a 1600 K at a rate of 800 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) 150 kW (b) 210 kW (c) 325 kW (d) 650 kW (e) 984 kW Get 8.152 exercise solution

8–153 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) 0.20 kW (c) 47 kW (d) 59 kW (e) 119 kW Get 8.153 exercise solution

8–154 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 Get 8.154 exercise solution