Solved: Using the given heat pump in the previous problem,

Fundamentals of Thermodynamcs | 8th Edition | ISBN: 9781118131992 | Authors: Claus Borgnakke, Richard E. Sonntag

Chapter 5: Problem 1 Fundamentals of Thermodynamcs 8

Problem 1CGP Two heat engines operate between the same two energy reservoirs, and both receive the same QH. One engine is reversible and the other is not. What can you say about the two QL’s?

Chapter 5: Problem 3 Fundamentals of Thermodynamcs 8

Problem 3CGP Suppose we forget the model for heat transfer, Q = CA ?T; canwe drawsome information about the direction of Q from the second law?

Chapter 5: Problem 2 Fundamentals of Thermodynamcs 8

Problem 2CGP Compare two domestic heat pumps (A and B) running with the same work input. If A is better than B, which one provides more heat?

Chapter 5: Problem 5 Fundamentals of Thermodynamcs 8

Problem 5CGP Compare two heat engines receiving the same Q, one at 1200 K and the other at 1800 K, both of which reject heat at 500 K. Which one is better?

Chapter 5: Problem 4 Fundamentals of Thermodynamcs 8

Problem 4CGP A combination of two heat engines is shown in Fig. P5.4. Find the overall thermal efficiency as a function of the two individual efficiencies. FIGURE P5.4

Chapter 5: Problem 161 Fundamentals of Thermodynamcs 8

Problem 161EUP Air in a rigid 40-ft3 box is at 540 R, 30 lbf/in.2. It is heated to 1100Rby heat transfer from a reversible heat pump that receives energy from the ambient at 540 R besides the work input. Use constant specific heat at 540 R. Since the COP changes, write dQ = mair Cv dT and find dW. Integrate dW with temperature to find the required heat pump work

Chapter 5: Problem 6 Fundamentals of Thermodynamcs 8

Problem 6CGP A car engine takes atmospheric air in at 20°C, no fuel, and exhausts the air at?20°C, producingwork in the process. What do the first and second laws say about that?

Chapter 5: Problem 8 Fundamentals of Thermodynamcs 8

Problem 8CGP After you have driven a car on a trip and it is back home, the car’s engine has cooled down and thus is back to the state in which it started. What happened to all the energy released in the burning of gasoline? What happened to all thework the engine gave out?

Chapter 5: Problem 9 Fundamentals of Thermodynamcs 8

Problem 9CGP Does a reversible heat engine burning coal (which in practice cannot be done reversibly) have impacts on our world other than depletion of the coal reserve?

Chapter 5: Problem 10 Fundamentals of Thermodynamcs 8

Problem 10CGP If the efficiency of a power plant goes up as the low temperature drops, why do all power plants not reject energy at, say, ?40°C?

Chapter 5: Problem 7 Fundamentals of Thermodynamcs 8

Problem 7CGP A combination of two refrigerator cycles is shown in Fig. P5.7. Find the overall COP as a function of COP1 and COP2. FIGURE P5.7

Chapter 5: Problem 11 Fundamentals of Thermodynamcs 8

Problem 11CGP If the efficiency of a power plant goes up as the low temperature drops, why not let the heat rejection go to a refrigerator at, say, ?10°C instead of ambient 20°C?

Chapter 5: Problem 12 Fundamentals of Thermodynamcs 8

Problem 12CGP A coal-fired power plant operates with a high temperature of 600°C, whereas a jet engine has about 1400 K. Does this mean that we should replace all power plants with jet engines?

Chapter 5: Problem 13 Fundamentals of Thermodynamcs 8

Problem 13CGP Heat transfer requires a temperature difference (see Chapter 3) to push the Q. What does that imply for a real heat engine? A refrigerator?

Chapter 5: Problem 14 Fundamentals of Thermodynamcs 8

Problem 14CGP Hot combustion gases (air) at 1500 K are used as the heat source in a heat engine where the gas is cooled to 750 K and the ambient is at 300 K. This is not a constant-temperature source. Howdoes that affect the efficiency?

Chapter 5: Problem 16 Fundamentals of Thermodynamcs 8

Problem 16HP A lawnmower tractor engine produces 18 hp using 40 kW of heat transfer from burning fuel. Find the thermal efficiency and the rate of heat transfer rejected to the ambient.

Chapter 5: Problem 15 Fundamentals of Thermodynamcs 8

Problem 15HP A window-mounted air conditioner removes 3.5 kJ from the inside of a home using 1.75 kJ work input. How much energy is released outside and what is its coefficient of performance?

Chapter 5: Problem 17 Fundamentals of Thermodynamcs 8

Problem 17HP Calculate the thermal efficiency of the steam power plant cycle described in Example 4.7. Example 4.7 Consider the simple steam power plant, as shown in Fig. 4.11 The following data are for such a power plant where the states are numbered and there is specific pump work as 4 kJ/kg. State Pressure Temperature or Quality 1 2.0 MPa 300°C 2 1.9 MPa 290°C 3 15 kPa 90% 4 14 kPa 45°C Determine the following quantities per kilogram flowing through the unit: a. Heat transfer in the line between the boiler and turbine. b. Turbine work. c. Heat transfer in the condenser. d. Heat transfer in the boiler. Since there are several control volumes to be considered in the solution to this problem, let us consolidate our solution procedure somewhat in this example. Using the notation of Fig. 4.11, we have: All processes: Steady-state. Model: Steam tables. From the steam tables: h1 = 3023.5 kJ/kg h2 = 3002.5 kJ/kg h3 = 225.9 + 0.9(2373.1) = 2361.7 kJ/kg h4 = 188.4 kJ/kg All analyses: No changes in kinetic or potential energy will be considered in the solution. In each case, the energy equation is given by Eq. Now, we proceed to answer the specific questions raised in the problem statement. a. For the control volume for the pipeline between the boiler and the turbine, the energy equation and solution are 1q2 + h1 = h2 1q2 = h2 ? h1 = 3002.5 ? 3023.5 = ?21.0 kJ/kg b. A turbine is essentially an adiabatic machine. Therefore, it is reasonable to neglect heat transfer in the energy equation, so that h2 = h3 + 2w3 2w3 = 3002.5 ? 2361.7 = 640.8 kJ/kg c. There is no work for the control volume enclosing the condenser. Therefore, the energy equation and solution are 3q4 + h3 = h4 3q4 = 188.4 ? 2361.7 = ?2173.3 kJ/kg d. If we consider a control volume enclosing the boiler, the work is equal to zero, so the energy equation becomes 5q1 + h5 = h1 A solution requires a value for h5, which can be found by taking a control volume around the pump: h4 = h5 + 4w5 h5 = 188.4 ? (?4) = 192.4 kJ/kg Therefore, for the boiler, 5q1 + h5 = h1 5q1 = 3023.5 ? 192.4 = 2831.1 kJ/kg FIGURE 4.11 Simple steam power plant.

Chapter 5: Problem 18 Fundamentals of Thermodynamcs 8

Problem 18HP A refrigerator operates at steady state using 500W of electric power with a COP of 2.5.What is the net effect on the kitchen air?

Chapter 5: Problem 19 Fundamentals of Thermodynamcs 8

Problem 19HP A room is heated with a 1500-W electric heater. How much power can be saved if a heat pump with a COP of 2.5 is used instead?

Chapter 5: Problem 21 Fundamentals of Thermodynamcs 8

Problem 21HP Calculate the thermal efficiency of the steam power plant cycle described in Problem 4.118. Problem 4.118 The following data are for a simple steam power plant as shown in Fig. P4.118 State 6 has x6 =0.92 and velocity of 200 m/s. The rate of steam flowis 25 kg/s, with 300 kW of power input to the pump. Piping diameters are 200mmfrom the steam generator to the turbine and 75 mm from the condenser to the economizer and steam generator. Determine the velocity at state 5 and the power output of the turbine. State 1 2 3 4 5 6 7 P, kPa 6200 6100 5900 5700 5500 10 9 T, °C 45 175 500 490 40 h, kJ/kg 194 744 3426 3404 168 FIGURE P4.118

Chapter 5: Problem 22 Fundamentals of Thermodynamcs 8

Problem 22HP A large coal fired power plant has an efficiency of 45% and produces net 1,500 MW of electricity. Coal releases 25 000 kJ/kg as it burns so how much coal is used per hour?

Chapter 5: Problem 23 Fundamentals of Thermodynamcs 8

Problem 23HP A window air conditioner (Fig. P5.23) discards 1.7 kW to the ambient with a power input of 500 W. Find the rate of cooling and the COP. FIGURE P5.23

Chapter 5: Problem 24 Fundamentals of Thermodynamcs 8

Problem 24HP An industrial machine is being cooled by 0.4 kg/s water at 15°C that is chilled from 35°C by a refrigeration unit with a COP of 3. Find the rate of cooling required and the power input to the unit.

Chapter 5: Problem 25 Fundamentals of Thermodynamcs 8

Problem 25HP Calculate the COP of the R-410a heat pump cycle described in Problem 4.123. Problem 4.123 An R-410a heat pump cycle shown in Fig. P4.123 has an R-410a flow rate of 0.05 kg/s with 5 kW into the compressor. The following data are given: State 1 2 3 4 5 6 P, kPa 3100 3050 3000 420 400 390 T, °C 120 110 45 ?10 ?5 h, kJ/kg 377 367 134 — 280 284 Calculate the heat transfer from the compressor, the heat transfer from the R-410a in the condenser, and the heat transfer to the R-410a in the evaporator. FIGURE P4.123

Chapter 5: Problem 20 Fundamentals of Thermodynamcs 8

Problem 20HP Calculate the COP of the R-134a refrigerator described in Example 4.8. Example 4.8 The refrigerator shown in Fig. 4.12 uses R-134a as the working fluid. The mass flow rate through each component is 0.1 kg/s, and the power input to the compressor is 5.0 kW. The following state data are known, using the state notation of Fig. 4.12: FIGURE 4.12 Refrigerator. P1 = 100 kPa, T1 = ?20° C P2 = 800 kPa, T2 = 50° C T3 = 30° C x3 = 0.0 T4 = ?25° C Determine the following: a. The quality at the evaporator inlet. b. The rate of heat transfer to the evaporator. c. The rate of heat transfer from the compressor. All processes: Steady-state. Model: R-134a tables. All analyses: No changes in kinetic or potential energy. The energy equation in each case is given by Eq.

Chapter 5: Problem 26 Fundamentals of Thermodynamcs 8

Problem 26HP A window-mounted air-conditioner unit is placed on a laboratory bench and tested in cooling mode using 750Wof electric power with a COP of 1.75. What is the cooling power capacity and what is the net effect on the laboratory?

Chapter 5: Problem 27 Fundamentals of Thermodynamcs 8

Problem 27HP A farmer runs a heat pump with a 2-kW motor. It should keep a chicken hatchery at 30°C, which loses energy at a rate of 10 kW to the colder ambient Tamb. What is the minimum COP that will be acceptable for the pump?

Chapter 5: Problem 28 Fundamentals of Thermodynamcs 8

Problem 28HP A sports car engine delivers 100 hp to the driveshaft with a thermal efficiency of 25%. The fuel has a heating value of 40 000 kJ/kg. Find the rate of fuel consumption and the combined power rejected through the radiator and exhaust.

Chapter 5: Problem 29 Fundamentals of Thermodynamcs 8

Problem 29HP R-410a enters the evaporator (the cold heat exchanger) in an air-conditioner unit at ?20°C, x = 28% and leaves at ?20°C, x = 1. The COP of the refrigerator is 1.5 and the mass flow rate is 0.003 kg/s. Find the net work input to the cycle.

Chapter 5: Problem 30 Fundamentals of Thermodynamcs 8

Problem 30HP In a Rankine cycle 0.9MWis taken out in the condenser, 0.63MWis taken out from the turbine, and the pumpwork is 0.03MW. Find the plant’s thermal efficiency. If everything could be reversed, find the COP as a refrigerator.

Chapter 5: Problem 31 Fundamentals of Thermodynamcs 8

Problem 31HP An experimental power plant outputs 130 MW of electrical power. It uses a supply of 1200 MW from a geothermal source and rejects energy to the atmosphere. Find the power to the air and how much air should be flowed to the cooling tower (kg/s) if its temperature cannot be increased more than 12°C.

Chapter 5: Problem 32 Fundamentals of Thermodynamcs 8

Problem 32HP A water cooler for drinking water should cool 25 L/h water from 18°C to 10°C while the water reservoirs also gains 60 W from heat transfer. Assume that a small refrigeration unit with a COP of 2.5 does the cooling. Find the total rate of cooling required and the power input to the unit.

Chapter 5: Problem 33 Fundamentals of Thermodynamcs 8

Problem 33HP A large stationary diesel engine produces 5 MW with a thermal efficiency of 40%. The exhaust gas, which we assume is air, flows out at 800 K and the temperature of the intake air is 290 K. How large a mass flow rate is that, assuming this is the only way we reject heat? Can the exhaust flow energy be used?

Chapter 5: Problem 34 Fundamentals of Thermodynamcs 8

Problem 34HP For each of the cases below, determine if the heat engine satisfies the first law (energy equation) and if it violates the second law. a. ?Q H = 6 kW, ?QL = 4 kW, ?W = 2 kW b. ?Q H = 6 kW, ?QL = 0 kW, ?W = 6 kW c. ?Q H = 6 kW, ?QL = 2 kW, ?W = 5 kW d. ?Q H = 6 kW, ?QL = 6 kW, ?W = 0 kW

Chapter 5: Problem 35 Fundamentals of Thermodynamcs 8

Problem 35HP For each of the cases in Problem 5.34, determine if a heat pump satisfies the first law (energy equation) and if it violates the second law. Problem 5.34 For each of the cases below, determine if the heat engine satisfies the first law (energy equation) and if it violates the second law. a. ?Q H = 6 kW, ?QL = 4 kW, ?W = 2 kW b. ?Q H = 6 kW, ?QL = 0 kW, ?W = 6 kW c. ?Q H = 6 kW, ?QL = 2 kW, ?W = 5 kW d. ?Q H = 6 kW, ?QL = 6 kW, ?W = 0 kW

Chapter 5: Problem 36 Fundamentals of Thermodynamcs 8

Problem 36HP Calculate the amount of work input a refrigerator needs to make ice cubes out of a tray of 0.25 kg liquid water at 10°C. Assume that the refrigerator has ? = 3.5 and a motor-compressor of 750 W. How much time does it take if this is the only cooling load?

Chapter 5: Problem 38 Fundamentals of Thermodynamcs 8

Problem 38HP Discuss the factors thatwould make the power plant cycle described in Problem 4.118 an irreversible cycle. Problem 4.118 The following data are for a simple steam power plant as shown in Fig. P4.118 State 6 has x6 =0.92 and velocity of 200 m/s. The rate of steam flowis 25 kg/s, with 300 kW of power input to the pump. Piping diameters are 200mmfrom the steam generator to the turbine and 75 mm from the condenser to the economizer and steam generator. Determine the velocity at state 5 and the power output of the turbine. State 1 2 3 4 5 6 7 P, kPa 6200 6100 5900 5700 5500 10 9 T, °C 45 175 500 490 40 h, kJ/kg 194 744 3426 3404 168 FIGURE P4.118

Chapter 5: Problem 37 Fundamentals of Thermodynamcs 8

Problem 37HP Prove that a cyclic device that violates the Kelvin– Planck statement of the second lawalso violates the Clausius statement of the second law.

Chapter 5: Problem 40 Fundamentals of Thermodynamcs 8

Problem 40HP Assume a cyclic machine that exchanges 6 kW with a 250°C reservoir and has a. Q L = 0 kW, ?W = 6 kW b. ?Q L = 6 kW, ?W = 0 kW and ?Q L is exchanged with a 30°C ambient. What can you say about the processes in the two cases, a and b, if the machine is a heat engine? Repeat the question for the case of a heat pump.

Chapter 5: Problem 39 Fundamentals of Thermodynamcs 8

Problem 39HP Discuss the factors that would make the heat pump described in Problem 4.123 an irreversible cycle. Problem 4.123 An R-410a heat pump cycle shown in Fig. P4.123 has an R-410a flow rate of 0.05 kg/s with 5 kW into the compressor. The following data are given: State 1 2 3 4 5 6 P, kPa 3100 3050 3000 420 400 390 T, °C 120 110 45 ?10 ?5 h, kJ/kg 377 367 134 — 280 284 Calculate the heat transfer from the compressor, the heat transfer from the R-410a in the condenser, and the heat transfer to the R-410a in the evaporator. FIGURE P4.123

Chapter 5: Problem 41 Fundamentals of Thermodynamcs 8

Problem 41HP Consider a heat engine and heat pump connected as shown in Fig. P5.41. Assume that TH1 = TH2 > Tamb and determine for each of the three cases if the setup satisfies the first law and/or violates the second law. FIGURE P5.41

Chapter 5: Problem 42 Fundamentals of Thermodynamcs 8

Problem 42HP Consider the four cases of a heat engine in Problem 5.34 and determine if any of those are perpetual machines of the first or second kind. Problem 5.34 For each of the cases below, determine if the heat engine satisfies the first law (energy equation) and if it violates the second law. a. ?Q H = 6 kW, ?QL = 4 kW, ?W = 2 kW b. ?Q H = 6 kW, ?QL = 0 kW, ?W = 6 kW c. ?Q H = 6 kW, ?QL = 2 kW, ?W = 5 kW d. ?Q H = 6 kW, ?QL = 6 kW, ?W = 0 kW

Chapter 5: Problem 43 Fundamentals of Thermodynamcs 8

Problem 43HP The simple refrigeration cycle is shown in Problem 5.23 and in Fig. 5.6 Mention a few of the processes that are expected to be irreversible. Problem 5.23 A window air conditioner (Fig) discards 1.7 kW to the ambient with a power input of 500 W. Find the rate of cooling and the COP. FIGURE 5.23 FIGURE 5.6 A simple vapor-compression refrigeration cycle.

Chapter 5: Problem 45 Fundamentals of Thermodynamcs 8

Problem 45HP An ideal (Carnot) heat engine has an efficiency of 40%. If the high temperature is raised 15%, what is the new efficiency keeping the same low temperature?

Chapter 5: Problem 46 Fundamentals of Thermodynamcs 8

Problem 46HP In a few places where the air is very cold in the winter, such as ?30°C, it is possible to find a temperature of 13°C below ground. What efficiency will a heat engine have when operating between these two thermal reservoirs?

Chapter 5: Problem 44 Fundamentals of Thermodynamcs 8

Problem 44HP Calculate the thermal efficiency of a Carnot cycle heat engine operating between reservoirs at 300°C and 45°C. Compare the result to that of Example 4.7. Example 4.7 Consider the simple steam power plant, as shown in Fig. 4.11. The following data are for such a power plant where the states are numbered and there is specific pump work as 4 kJ/kg. State Pressure Temperature or Quality 1 2.0 MPa 300°C 2 1.9 MPa 290°C 3 15 kPa 90% 4 14 kPa 45°C Determine the following quantities per kilogram flowing through the unit: a. Heat transfer in the line between the boiler and turbine. b. Turbine work. c. Heat transfer in the condenser. d. Heat transfer in the boiler. Since there are several control volumes to be considered in the solution to this problem, let us consolidate our solution procedure somewhat in this example. Using the notation of Fig. 4.11, we have: All processes: Steady-state. Model: Steam tables. From the steam tables: h1 = 3023.5 kJ/kg h2 = 3002.5 kJ/kg h3 = 225.9 + 0.9(2373.1) = 2361.7 kJ/kg h4 = 188.4 kJ/kg All analyses: No changes in kinetic or potential energy will be considered in the solution. In each case, the energy equation is given by Eq. Equation 4.13 Now, we proceed to answer the specific questions raised in the problem statement. a. For the control volume for the pipeline between the boiler and the turbine, the energy equation and solution are 1q2 + h1 = h2 1q2 = h2 ? h1 = 3002.5 ? 3023.5 = ?21.0 kJ/kg b. A turbine is essentially an adiabatic machine. Therefore, it is reasonable to neglect heat transfer in the energy equation, so that h2 = h3 + 2w3 2w3 = 3002.5 ? 2361.7 = 640.8 kJ/kg c. There is no work for the control volume enclosing the condenser. Therefore, the energy equation and solution are 3q4 + h3 = h4 3q4 = 188.4 ? 2361.7 = ?2173.3 kJ/kg d. If we consider a control volume enclosing the boiler, the work is equal to zero, so the energy equation becomes 5q1 + h5 = h1 A solution requires a value for h5, which can be found by taking a control volume around the pump: h4 = h5 + 4w5 h5 = 188.4 ? (?4) = 192.4 kJ/kg Therefore, for the boiler, 5q1 + h5 = h1 5q1 = 3023.5 ? 192.4 = 2831.1 kJ/kg FIGURE 4.11 Simple steam power plant.

Chapter 5: Problem 47 Fundamentals of Thermodynamcs 8

Problem 47HP Consider the combination of a heat engine and a heat pump, as in Problem 5.41, with a low temperature of 400 K. What should the high temperature be so that the heat engine is reversible? For that temperature, what is the COP for a reversible heat pump? Problem 5.41 Consider a heat engine and heat pump connected as shown in Fig. P5.41. Assume that TH1 = TH2 > Tamb and determine for each of the three cases if the setup satisfies the first law and/or violates the second law. FIGURE P5.41

Chapter 5: Problem 48 Fundamentals of Thermodynamcs 8

Problem 48HP Find the power output and the low T heat rejection rate for a Carnot cycle heat engine that receives 6 kW at 250° C and rejects heat at 30°C, as in Problem 5.40. Problem 5.40 Assume a cyclic machine that exchanges 6 kW with a 250°C reservoir and has a. Q L = 0 kW, ?W = 6 kW b. ?Q L = 6 kW, ?W = 0 kW and ?Q L is exchanged with a 30°C ambient. What can you say about the processes in the two cases, a and b, if the machine is a heat engine? Repeat the question for the case of a heat pump.

Chapter 5: Problem 49 Fundamentals of Thermodynamcs 8

Problem 49HP A large heat pump should upgrade 4MWof heat at 65°C to be delivered as heat at 145°C. What is the minimum amount of work (power) input that will drive this?

Chapter 5: Problem 50 Fundamentals of Thermodynamcs 8

Problem 50HP A temperature of about 0.01 K can be achieved by magnetic cooling. In this process a strong magnetic field is imposed on a paramagnetic salt, maintained at 1 K by transfer of energy to liquid helium boiling at low pressure. The salt is then thermally isolated from the helium, the magnetic field is removed, and the salt temperature drops. Assume that 1 mJ is removed at an average temperature of 0.1 K to the helium by a Carnot cycle heat pump. Find the work input to the heat pump and theCOPwith an ambient at 300 K.

Chapter 5: Problem 51 Fundamentals of Thermodynamcs 8

Problem 51HP The lowest temperature that has been achieved is about 1 × 10?6 K. To achieve this, an additional stage of cooling is required beyond that described in the previous problem, namely, nuclear cooling. This process is similar to magnetic cooling, but it involves the magnetic moment associated with the nucleus rather than that associated with certain ions in the paramagnetic salt. Suppose that 10 ?J is to be removed from a specimen at an average temperature of 10?5 K(10 mJ is about the potential energy loss of a pin dropping 3 mm). Find the work input to a Carnot cycle heat pump and its COP to do this, assuming that the ambient is at 300 K.

Chapter 5: Problem 53 Fundamentals of Thermodynamcs 8

Problem 53HP Assume the refrigerator in your kitchen runs in a Carnot cycle. Estimate the maximum COP.

Chapter 5: Problem 54 Fundamentals of Thermodynamcs 8

Problem 54HP A car engine burns 5 kg fuel (equivalent to addition of QH) at 1500 K and rejects energy to the radiator and the exhaust at an average temperature of 750 K. If the fuel provides 40 000 kJ/kg, what is the maximum amount of work the engine can provide?

Chapter 5: Problem 52 Fundamentals of Thermodynamcs 8

Problem 52HP Consider the setup with two stacked (temperaturewise) heat engines, as in Fig. P5.4. Let TH =850 K, TM = 600 K, and TL = 350 K. Find the two heat engine efficiencies and the combined overall efficiency assuming Carnot cycles. FIGURE P5.4

Chapter 5: Problem 55 Fundamentals of Thermodynamcs 8

Problem 55HP An air conditioner provides 1 kg/s of air at 15°C cooled by outside atmospheric air at 35°C. Estimate the amount of power needed to operate the air conditioner. Clearly state all assumptions made.

Chapter 5: Problem 56 Fundamentals of Thermodynamcs 8

Problem 56HP A refrigerator should remove 400 kJ from some food. Assume the refrigerator works in a Carnot cycle between ?15°C and 45°C with a motorcompressor of 400 W. How much time does it take if this is the only cooling load?

Chapter 5: Problem 57 Fundamentals of Thermodynamcs 8

Problem 57HP Calculate the amount of work input a freezer needs to make ice cubes out of a tray of 0.25 kg liquid water at 10°C. Assume the freezer works in a Carnot cycle between?8°Cand 35°Cwith a motorcompressor of 600 W. How much time does it take if this is the only cooling load?

Chapter 5: Problem 58 Fundamentals of Thermodynamcs 8

Problem 58HP A heat pump is used to heat a house during the winter. The house is to be maintained at 20°C at all times. When the ambient temperature outside drops to?10°C, the rate at which heat is lost from the house is estimated to be 25 kW. What is the minimum electrical power required to drive the heat pump?

Chapter 5: Problem 61 Fundamentals of Thermodynamcs 8

Problem 61HP A proposal is to build a 1000-MW electric power plant with steam as the working fluid. The condensers are to be cooled with river water (see Fig. P5.61). The maximum steam temperature is 550°C, and the pressure in the condensers will be 10 kPa. Estimate the temperature rise of the river downstream from the power plant. FIGURE P5.61

Chapter 5: Problem 59 Fundamentals of Thermodynamcs 8

Problem 59HP A household freezer operates in a room at 20°C. Heat must be transferred from the cold space at a rate of 2 kW to maintain its temperature at?30°C. What is the theoretically the smallest (power) motor required for operation of this freezer?

Chapter 5: Problem 60 Fundamentals of Thermodynamcs 8

Problem 60HP Thermal storage is made with a rock (granite) bed of 2 m3 that is heated to 400 K using solar energy. A heat engine receives a QH from the bed and rejects heat to the ambient at 290 K. The rock bed therefore cools down, and as it reaches 290 K the process stops. Find the energy the rock bed can give out. What is the heat engine efficiency at the beginning of the process and what is it at the end of the process?

Chapter 5: Problem 63 Fundamentals of Thermodynamcs 8

Problem 63HP A constant temperature of?125°C must be maintained in a cryogenic experiment, although it gains 120 W due to heat transfer. What is the smallest motor you would need for a heat pump absorbing heat from the container and rejecting heat to the room at 20°C?

Chapter 5: Problem 62 Fundamentals of Thermodynamcs 8

Problem 62HP A certain solar-energy collector produces a maximum temperature of 100°C. The energy is used in a cycle heat engine that operates in a 10°C environment. What is the maximum thermal efficiency? If the collector is redesigned to focus the incoming light, what should the maximum temperature be to produce a 25% improvement in engine efficiency?

Chapter 5: Problem 64 Fundamentals of Thermodynamcs 8

Problem 64HP Helium has the lowest normal boiling point of any of the elements at 4.2 K. At this temperature the enthalpy of evaporation is 83.3 kJ/kmol. A Carnot refrigeration cycle is analyzed for the production of 1 kmol of liquid helium at 4.2 K from saturated vapor at the same temperature. What is the work input to the refrigerator and the COP for the cycle with an ambient at 300 K?

Chapter 5: Problem 65 Fundamentals of Thermodynamcs 8

Problem 65HP R-134a fills a 0.1-m3 capsule at 20°C, 200 kPa. It is placed in a deep freezer, where it is cooled to?10°C. The deep freezer sits in a room with ambient temperature of 20°C and has an inside temperature of?10°C. Find the amount of energy the freezer must remove from the R-134a and the extra amount of work input to the freezer to perform the process.

Chapter 5: Problem 67 Fundamentals of Thermodynamcs 8

Problem 67HP A heat pump is driven by the work output of a heat engine, as shown in Fig. P5.67. If we assume ideal devices, find the ratio of the total power ?Q L1 + ?Q H2 that heats the house to the power from the hot-energy source ?Q H1 in terms of the temperatures. FIGURE P5.67

Chapter 5: Problem 66 Fundamentals of Thermodynamcs 8

Problem 66HP A heat engine has a solar collector receiving 0.2 kW/m2 inside which a transfer medium is heated to 450 K. The collected energy powers a heat engine that rejects heat at 40°C. If the heat engine should deliver 2.5 kW, what is the minimum size (area) of the solar collector?

Chapter 5: Problem 68 Fundamentals of Thermodynamcs 8

Problem 68HP Sixty kilograms per hour of water runs through a heat exchanger, entering as saturated liquid at 200 kPa and leaving as saturated vapor. The heat is supplied by a heat pump operating from a lowtemperature reservoir at 16°C with a COP of half that of the similar Carnot unit. Find the rate of work into the heat pump.

Chapter 5: Problem 69 Fundamentals of Thermodynamcs 8

Problem 69HP A power plant with a thermal efficiency of 40% is located on a river similar to the arrangement in Fig. P5.61. With a total river mass flow rate of 1 × 105 kg/s at 15°C, find the maximum power production allowed if the river water should not be heated more than 1 degree. FIGURE P5.61

Chapter 5: Problem 70 Fundamentals of Thermodynamcs 8

Problem 70HP A nuclear reactor provides a flow of liquid sodium at 800°C, which is used as the energy source in a steam power plant. The condenser cooling water comes from a nearby river at 15°C. Determine the maximum thermal efficiency of the power plant. Is it misleading to use the temperatures given to calculate this value?

Chapter 5: Problem 71 Fundamentals of Thermodynamcs 8

Problem 71HP The management at a large factory cannot decide which of two fuels to purchase. The selected fuel will be used in a heat engine operating between the fuel-burning temperature and a low-exhaust temperature. Fuel A burns at 2200 K and exhausts at 450 K, delivering 30 000 kJ/kg, and costs $1.50/kg. Fuel B burns at 1200 K and exhausts at 350 K, delivering 40 000 kJ/kg, and costs $1.30/kg. Which fuel would you buy and why?

Chapter 5: Problem 72 Fundamentals of Thermodynamcs 8

Problem 72HP A salesperson selling refrigerators and deep freezers will guarantee a minimum COP of 4.5 year round. How would you evaluate that performance? Are they all the same?

Chapter 5: Problem 73 Fundamentals of Thermodynamcs 8

Problem 73HP A cyclic machine, shown in Fig. P5.73, receives 325 kJ from a 1000-K energy reservoir. It rejects 125 kJ to a 400-K energy reservoir, and the cycle produces 200 kJ of work as output. Is this cycle reversible, irreversible, or impossible? FIGURE P5.73

Chapter 5: Problem 74 Fundamentals of Thermodynamcs 8

Problem 74HP Consider the previous problem and assume the temperatures and heat input are as given. If the actual machine has an efficiency that is half that of the corresponding Carnot cycle, find the work out and the rejected heat transfer. Reference Problem: A cyclic machine, shown in Fig. P5.73, receives 325 kJ from a 1000-K energy reservoir. It rejects 125 kJ to a 400-K energy reservoir, and the cycle produces 200 kJ of work as output. Is this cycle reversible, irreversible, or impossible?

Chapter 5: Problem 75 Fundamentals of Thermodynamcs 8

Problem 75HP Repeat Problem 5.61 using a more realistic thermal efficiency of 45%. Problem 5.61 A proposal is to build a 1000-MW electric power plant with steam as the working fluid. The condensers are to be cooled with river water (see Fig. P5.61). The maximum steam temperature is 550°C, and the pressure in the condensers will be 10 kPa. Estimate the temperature rise of the river downstream from the power plant. FIGURE P5.61

Chapter 5: Problem 76 Fundamentals of Thermodynamcs 8

Problem 76HP An inventor has developed a refrigeration unit that maintains the cold space at ?10°C while operating in a 25°C room. A COP of 8.5 is claimed. How do you evaluate this?

Chapter 5: Problem 77 Fundamentals of Thermodynamcs 8

Problem 77HP A heat pump receives energy from a source at 80°C and delivers energy to a boiler that operates at 350 kPa. The boiler input is saturated liquid water and the exit is saturated vapor, both at 350 kPa. The heat pump is driven by a 2.5-MW motor and has a COP that is 60% that of a Carnot heat pump. What is the maximum mass flow rate of water the system can deliver?

Chapter 5: Problem 78 Fundamentals of Thermodynamcs 8

Problem 78HP In a remote location, you run a heat engine to provide the power to run a refrigerator. The input to the heat engine is 800 K and the low T is 400 K; it has an actual efficiency equal to half of that of the corresponding Carnot unit. The refrigerator has TL = ?10°C and TH = 35°C, with a COP that is one-third that of the corresponding Carnot unit. Assume a cooling capacity of 2 kW is needed and find the rate of heat input to the heat engine.

Chapter 5: Problem 79 Fundamentals of Thermodynamcs 8

Problem 79HP A car engine with a thermal efficiency of 33% drives the air-conditioner unit (a refrigerator) as well as powering the car and other auxiliary equipment. On a hot (35°C) summer day the air conditioner takes outside air in and cools it to 5°C, sending it into a duct using 2 kW of power input, it is assumed to be half as good as a Carnot refrigeration unit. Find the extra rate of fuel (kW) being burned just to drive the air conditioner unit and its COP. Find the flow rate of cold air the air-conditioner unit can provide.

Chapter 5: Problem 81 Fundamentals of Thermodynamcs 8

Problem 81HP A refrigerator maintaining a 5°C inside temperature is located in a 30°C room. It must have a high temperature ?T above room temperature and a low temperature ?T below the refrigerated space in the cycle to actually transfer the heat. For a ?T of 0°, 5°, and 10°C, respectively, calculate the COP, assuming a Carnot cycle.

Chapter 5: Problem 80 Fundamentals of Thermodynamcs 8

Problem 80HP A large heat pump should upgrade 5 MW of heat at 85°C to be delivered as heat at 150°C. Suppose the actual heat pump has a COP of 2.5. How much power is required to drive the unit? For the same COP, how high a high temperature would a Carnot heat pump have, assuming the same low T?

Chapter 5: Problem 82 Fundamentals of Thermodynamcs 8

Problem 82HP The ocean near Hawaii is 20°C near the surface and 5°C at some depth. A power plant based on this temperature difference is being planned. How large an efficiency could it have? If the two heat transfer terms (QH and QL) both require a 2-degree difference to operate, what is the maximum efficiency?

Chapter 5: Problem 83 Fundamentals of Thermodynamcs 8

Problem 83HP A house is cooled by a heat pump driven by an electric motor using the inside as the lowtemperature reservoir. The house gains energy in direct proportion to the temperature difference as ?Qgain = K(TH ? TL ). Determine the minimum electric power to drive the heat pump as a function of the two temperatures.

Chapter 5: Problem 84 Fundamentals of Thermodynamcs 8

Problem 84HP An air conditioner in a very hot region uses a power input of 2.5 kW to cool a 5°C space with the high temperature in the cycle at 40°C. The QH is pushed to the ambient air at 30°Cin a heat exchangerwhere the transfer coefficient is 50 W/m2K. Find the required minimum heat transfer area.

Chapter 5: Problem 85 Fundamentals of Thermodynamcs 8

Problem 85HP A small house that is kept at 20°C inside loses 12 kW to the outside ambient at 0°C. A heat pump is used to help heat the house together with possible electric heat. The heat pump is driven by a 2.5-kW motor, and it has a COP that is one-fourth that of a Carnot heat pump unit. Find the actual COP for the heat pump and the amount of electric heat that must be used (if any) to maintain the house temperature.

Chapter 5: Problem 87 Fundamentals of Thermodynamcs 8

Problem 87HP A car engine operates with a thermal efficiency of 35%. Assume the air conditioner has a COP of ? = 3 working as a refrigerator cooling the inside using engine shaftwork to drive it. Howmuch extra fuel energy should be spent to remove 1 kJ from the inside?

Chapter 5: Problem 88 Fundamentals of Thermodynamcs 8

Problem 88HP Arctic explorers are unsure if they can use a 5-kW motor-driven heat pump to stay warm. It should keep their shelter at 15°C. The shelter loses energy at a rate of 0.5 kW per degree difference to the colder ambient. The heat pump has a COP that is 50% that of a Carnot heat pump. If the ambient temperature can fall to ?25°C at night, would you recommend this heat pump to the explorers?

Chapter 5: Problem 86 Fundamentals of Thermodynamcs 8

Problem 86HP Consider a room at 20°C that is cooled by an air conditioner with a COP of 3.2 using a power input of 2 kW, and the outside temperature is 35°C. What is the constant in the heat transfer Eq. for the heat transfer from the outside into the room?

Chapter 5: Problem 89 Fundamentals of Thermodynamcs 8

Problem 89HP Using the given heat pump in the previous problem, how warm could it make the shelter in the arctic night?

Chapter 5: Problem 90 Fundamentals of Thermodynamcs 8

Problem 90HP A window air conditioner cools a room at TL =20°C with a maximum of 1.2kWpower input. The room gains 0.6 kW per degree temperature difference to the ambient, and the refrigeration COP is ? =0.6 ?Carnot. Find the maximum outside temperature, TH, for which the air conditioner provides sufficient cooling.

Chapter 5: Problem 91 Fundamentals of Thermodynamcs 8

Problem 91HP A house is cooled by an electric heat pump using the outside as the high-temperature reservoir. For several different summer outdoor temperatures, estimate the percentage savings in electricity if the house is kept at 25°C instead of 20°C. Assume that the house is gaining energy from the outside indirect proportion to the temperature difference, as in Eq.5.14 Equation 5.14

Chapter 5: Problem 92 Fundamentals of Thermodynamcs 8

Problem 92HP A heat pump has a COP that is 50% of the theoretical maximum. It maintains a house at 20°C, which leaks energy of 0.6 kW per degree temperature difference to the ambient. For a maximum of 1.0 kW power input, find the minimum outside temperature for which the heat pump is a sufficient heat source.

Chapter 5: Problem 93 Fundamentals of Thermodynamcs 8

Problem 93HP The room in Problem 5.90 has a combined thermal mass of 2000 kg wood, 250 kg steel, and 500 kg plaster board, Cp = 1kJ/kg-K. Estimate how quickly the room heats up if the air conditioner is turned off on a day when it is 35°C outside. Problem 5.90 A window air conditioner cools a room at TL =20°C with a maximum of 1.2kWpower input. The room gains 0.6 kW per degree temperature difference to the ambient, and the refrigeration COP is ? =0.6 ?Carnot. Find the maximum outside temperature, TH, for which the air conditioner provides sufficient cooling.

Chapter 5: Problem 94 Fundamentals of Thermodynamcs 8

Problem 94HP A window air conditioner cools a room at TL = 22°C, with a maximum of 1.2 kW power input possible. The room gains 0.6 kW per degree temperature difference to the ambient, and the refrigeration COP is ? = 0.6 ?Carnot. Find the actual power required on a day when the temperature is 30°C outside.

Chapter 5: Problem 95 Fundamentals of Thermodynamcs 8

Problem 95HP On a cold (?10°C) winter day, a heat pump provides 20 kW to heat a house maintained at 20°C, and it has a COPHP of 4. How much power does the heat pump require? The next day, a stormbrings the outside temperature to ?15°C, assuming the same COP and the same house heat transfer coefficient for the heat loss to the outside air. Howmuch power does the heat pump require then?

Chapter 5: Problem 96 Fundamentals of Thermodynamcs 8

Problem 96HP In the previous problem, it was assumed that the COP will be the same when the outside temperature drops. Given the temperatures and the actual COP at the ?10°C winter day, give an estimate for a more realistic COP for the outside ?15°C case.

Chapter 5: Problem 98 Fundamentals of Thermodynamcs 8

Problem 98HP Carbon dioxide is used in an ideal gas refrigeration cycle, the reverse of Fig. 5.24. Heat absorption is at 250 K and heat rejection is at 325 K where the pressure changes from 1200 kPa to 2400 kPa. Find the refrigeration COP and the specific heat transfer at the low temperature. FIGURE 5.24 The ideal-gas Carnot cycle.

Chapter 5: Problem 97 Fundamentals of Thermodynamcs 8

Problem 97HP Hydrogen gas is used in a Carnot cycle having an efficiency of 60% with a low temperature of 300 K. During heat rejection, the pressure changes from 90 kPa to 120 kPa. Find the high- and lowtemperature heat transfers and the net cycle work per unit mass of hydrogen.

Chapter 5: Problem 99 Fundamentals of Thermodynamcs 8

Problem 99HP An ideal gas Carnot cycle with air in a piston/ cylinder has a high temperature of 1000 K and heat rejection at 400 K. During heat addition the volume triples. Find the two specific heat transfers (q) in the cycle and the overall cycle efficiency.

Chapter 5: Problem 100 Fundamentals of Thermodynamcs 8

Problem 100HP Air in a piston/cylinder goes through a Carnot cycle with the P–v diagram shown in Fig. 5.24. The high and low temperatures are 600 K and 300 K, respectively. The heat added at the high temperature is 250 kJ/kg, and the lowest pressure in the cycle is 75 kPa. Find the specific volume and pressure after heat rejection and the net work per unit mass. FIGURE 5.24 The ideal-gas Carnot cycle.

Chapter 5: Problem 101 Fundamentals of Thermodynamcs 8

Problem 101HP A 4L jug of milk at 25°C is placed in your refrigerator, where it is cooled down to 5°C. The high temperature in the Carnot refrigeration cycle is 45°C, the low temperature is ?5°C, and the properties of milk are the same as those of liquid water. Find the amount of energy that must be removed from the milk and the additional work needed to drive the refrigerator.

Chapter 5: Problem 102 Fundamentals of Thermodynamcs 8

Problem 102HP Consider the combination of the two heat engines, as in Fig. P5.4. How should the intermediate temperature be selected so that the two heat engines have the same efficiency, assuming Carnot cycle heat engines. FIGURE P5.4

Chapter 5: Problem 104 Fundamentals of Thermodynamcs 8

Problem 104HP We wish to produce refrigeration at?30°C. Areservoir, shown in Fig. P5.104, is available at 200°Cand the ambient temperature is 30°C.Thus, work can be done by a cyclic heat engine operating between the 200°C reservoir and the ambient. This work is used to drive the refrigerator. Determine the ratio of the heat transferred from the 200°Creservoir to the heat transferred from the ?30°C reservoir, assuming all processes are reversible. FIGURE P5.104

Chapter 5: Problem 105 Fundamentals of Thermodynamcs 8

Problem 105HP Redo the previous problem, assuming the actual devices both have a performance that is 60% of the theoretical maximum.

Chapter 5: Problem 103 Fundamentals of Thermodynamcs 8

Problem 103HP Consider a combination of a gas turbine power plant and a steam power plant, as shown in Fig. P5.4. The gas turbine operates at higher temperatures (thus called a topping cycle) than the steam power plant (thus called a bottom cycle). Assume both cycles have a thermal efficiency of 32%. What is the efficiency of the overall combination, assuming QL in the gas turbine equals QH to the steam power plant? FIGURE P5.4

Chapter 5: Problem 108 Fundamentals of Thermodynamcs 8

Problem 108HP A farmer runs a heat pump with a motor of 2 kW. It should keep a chicken hatchery at 30°C; the hatchery loses energy at a rate of 0.5 kW per degree difference to the colder ambient. The heat pump has a COP that is 50% that of a Carnot heat pump. What is the minimum ambient temperature for which the heat pump is sufficient?

Chapter 5: Problem 106 Fundamentals of Thermodynamcs 8

Problem 106HP A house should be heated by a heat pump, ?? =2.2, and maintained at 20°C at all times. It is estimated that it loses 0.8 kW for each degree that the ambient is lower than the inside. Assume an outside temperature of ?10°C and find the needed power to drive the heat pump.

Chapter 5: Problem 107 Fundamentals of Thermodynamcs 8

Problem 107HP Give an estimate for the COP in the previous problem and the power needed to drive the heat pump when the outside temperature drops to?15°C.

Chapter 5: Problem 110 Fundamentals of Thermodynamcs 8

Problem 110HP An air conditioner on a hot summer day removes 8 kW of energy from a house at 21°C and pushes energy to the outside, which is at 31°C. The house has a mass of 15 000 kg with an average specific heat of 0.95 kJ/kgK. In order to do this, the cold side of the air conditioner is at 5°C and the hot side is at 40°C. The air conditioner (refrigerator) has a COP that is 60% that of a corresponding Carnot refrigerator. Find the actual COP of the air conditioner and the power required to run it.

Chapter 5: Problem 109 Fundamentals of Thermodynamcs 8

Problem 109HP An air conditioner with a power input of 1.2 kW is working as a refrigerator (? = 3) or as a heat pump (?? = 4). It maintains an office at 20°C year round that exchanges 0.5 kW per degree temperature difference with the atmosphere. Find the maximum and minimum outside temperatures for which this unit is sufficient.

Chapter 5: Problem 111 Fundamentals of Thermodynamcs 8

Problem 111HP The air conditioner in the previous problem is turned off. How quickly does the house heat up in degrees per second (°C/s)?

Chapter 5: Problem 113 Fundamentals of Thermodynamcs 8

Problem 113HP A Carnot heat engine, shown in Fig. P5.113, receives energy from a reservoir at Tres through a heat exchanger where the heat transferred is proportional to the temperature difference as ?Q H = K(Tres ? TH). It rejects heat at a given low temperature TL. To design the heat engine for maximum work output, show that the high temperature, TH, in the cycle should be selected as TH = ?TresTL FIGURE P5.113

Chapter 5: Problem 112 Fundamentals of Thermodynamcs 8

Problem 112HP Air in a rigid 1-m3 box is at 300 K, 200 kPa. It is heated to 600 K by heat transfer from a reversible heat pump that receives energy from the ambient at 300 K besides the work input. Use constant specific heat at 300 K. Since the COP changes, write dQ=mair Cv dT and finddW. IntegratedW with the temperature to find the required heat pump work.

Chapter 5: Problem 114 Fundamentals of Thermodynamcs 8

Problem 114HP Acombination of a heat engine driving a heat pump (see Fig. P5.114) takes waste energy at 50°C as a source Qw1 to the heat engine, rejecting heat at 30°C. The remainder, Qw2, goes into the heat pump that delivers a QH at 150°C. If the total waste energy is 5 MW, find the rate of energy delivered at the high temperature. FIGURE P5.114

Chapter 5: Problem 115 Fundamentals of Thermodynamcs 8

Problem 115HP A furnace, shown in Fig.P5.115, can deliver heat, QH1, at TH1, and it is proposed to use this to drive a heat engine with a rejection at Tatm instead of direct room heating. The heat engine drives a heat pump that delivers QH2 at Troom using the atmosphere as the cold reservoir. Find the ratioQH2/QH1 as a function of the temperatures. Is this a better set up than direct room heating from the furnace? FIGURE P5.115

Chapter 5: Problem 118 Fundamentals of Thermodynamcs 8

Problem 118HP A Carnot heat engine operating between a high TH and lowTL energy reservoirs has an efficiency given by the temperatures. Compare this to two combined heat engines, one operating between TH and an intermediate temperature TM giving outworkWA and the other operating between TM and TL giving out work WB. The combination must have the same efficiency as the single heat engine, so the heat transfer ratio QH/QL =?(TH, TL)=[QH/QM] [QM/QL]. The last two heat transfer ratios can be expressed by the same function ?() also involving the temperature TM. Use this to show a condition that the function ?() must satisfy.

Chapter 5: Problem 116 Fundamentals of Thermodynamcs 8

Problem 116HP Consider the rock bed thermal storage in Problem 5.60. Use the specific heat so that you can write dQH in terms of dTrock and find the expression for dW out of the heat engine. Integrate this expression over temperature and find the total heat engine work output. Problem 5.60 Thermal storage is made with a rock (granite) bed of 2 m3 that is heated to 400 K using solar energy. A heat engine receives a QH from the bed and rejects heat to the ambient at 290 K. The rock bed therefore cools down, and as it reaches 290 K the process stops. Find the energy the rock bed can give out. What is the heat engine efficiency at the beginning of the process and what is it at the end of the process?

Chapter 5: Problem 119 Fundamentals of Thermodynamcs 8

Problem 119HP Ona cold (?10°C) winter day, a heatpump provides 20kWto heat a house maintained at 20°C and it has a COPHP of 4 using the maximum power available. The next day a storm brings the outside temperature to ?15°C, assuming that the COPHP changes by the same percentage as a Carnot unit and that the house loses heat to the outside air. How cold is the house then?

Chapter 5: Problem 117 Fundamentals of Thermodynamcs 8

Problem 117HP Consider a Carnot cycle heat engine operating in outer space. Heat can be rejected from this engine only by thermal radiation, which is proportional to the radiator area and the fourth power of absolute temperature, ?Qrad ? KAT4. Show that for a given engine work output and given TH, the radiator area will be minimum when the ratio TL/TH = 3/4.

Chapter 5: Problem 120 Fundamentals of Thermodynamcs 8

Problem 120HP A 10-m3 tank of air at 500 kPa, 600 K acts as the high-temperature reservoir for a Carnot heat engine that rejects heat at 300 K. A temperature difference of 25°C between the air tank and the Carnot cycle high temperature is needed to transfer the heat. The heat engine runs until the air temperature has dropped to 400 K and then stops. Assume constant specific heat for air and find how much work is given out by the heat engine.

Chapter 5: Problem 121 Fundamentals of Thermodynamcs 8

Problem 121EUP A window-mounted air conditioner removes 3.5 Btu from the inside of a home using 1.75 Btu work input. Howmuch energy is released outside, and what is its COP?

Chapter 5: Problem 123 Fundamentals of Thermodynamcs 8

Problem 123EUP Calculate the thermal efficiency of the steam power plant cycle described in Problem 4.198E. Problem 4.198E The following data are for a simple steam power plant as shown in Fig. P4.118: State 1 2 3 4 5 6 7 P lbf/in.2 900 890 860 830 800 1.5 1.4 T F 115 350 920 900 110 h, Btu/lbm 85.3 323 1468 1456 1029 78 State 6 has x6 = 0.92 and a velocity of 600 ft/s. The rate of steam flow is 200 000 lbm/h, with 400-hp input to the pump. Piping diameters are 8 in. from the steam generator to the turbine and 3 in. from the condenser to the steam generator. Determine the power output of the turbine and the heat transfer rate in the condenser. FIGURE P4.118

Chapter 5: Problem 122 Fundamentals of Thermodynamcs 8

Problem 122EUP A lawnmower tractor engine produces 18 hp using 40 Btu/s of heat transfer from burning fuel. Find the thermal efficiency and the rate of heat transfer rejected to the ambient.

Chapter 5: Problem 125 Fundamentals of Thermodynamcs 8

Problem 125EUP An industrial machine is being cooled by 0.8 lbm/s water at 60 F that is chilled from 95 F by a refrigeration unit with a COP of 3. Find the rate of cooling required and the power input to the unit.

Chapter 5: Problem 124 Fundamentals of Thermodynamcs 8

Problem 124EUP A large coal-fired power plant has an efficiency of 45% and produces net 1500MWof electricity. Coal releases 12 500 Btu/lbm as it burns, so how much coal is used per hour?

Chapter 5: Problem 126 Fundamentals of Thermodynamcs 8

Problem 126EUP A water cooler for drinking water should cool 10 gal/h water from 65 F to 50 F using a small refrigeration unit with a COP of 2.5. Find the rate of cooling required and the power input to the unit.

Chapter 5: Problem 127 Fundamentals of Thermodynamcs 8

Problem 127EUP A window air-conditioner unit is place on a laboratory bench and tested in cooling mode using 0.75 Btu/s of electric power with a COP of 1.75. What is the cooling power capacity, and what is the net effect on the laboratory?

Chapter 5: Problem 128 Fundamentals of Thermodynamcs 8

Problem 128EUP A farmer runs a heat pump with a 2-kW motor. It should keep a chicken hatchery at 90 F; the hatchery loses energy at a rate of 10 Btu/s to the colder ambient Tamb. What is the minimum COP that will be acceptable for the heat pump?

Chapter 5: Problem 129 Fundamentals of Thermodynamcs 8

Problem 129EUP R-410a enters the evaporator (the cold heat exchanger) in an air-conditioner unit at 0 F, x = 28% and leaves at 0 F, x = 1. The COP of the refrigerator is 1.5 and the mass flow rate is 0.006 lbm/s. Find the net work input to the cycle.

Chapter 5: Problem 130 Fundamentals of Thermodynamcs 8

Problem 130EUP A large stationary diesel engine produces 2000 hp with a thermal efficiency of 40%. The exhaust gas, which we assume is air, flows out at 1400 R and the intake is 520 R. How large a mass flow rate is that if it accounts for half of the ?QL? Can the exhaust flow energy be used?

Chapter 5: Problem 131 Fundamentals of Thermodynamcs 8

Problem 131EUP Calculate the amount of work input a refrigerator needs to make ice cubes out of a tray of 0.5 lbm liquid water at 50 F. Assume the refrigerator has ? = 3.5 and a motor-compressor of 750 W. How much time does it take if this is the only cooling load?

Chapter 5: Problem 132 Fundamentals of Thermodynamcs 8

Problem 132EUP Calculate the thermal efficiency of a Carnot-cycle heat engine operating between reservoirs at 920 F and 110 F. Compare the result with that of Problem 5.123. Problem 5.123 Calculate the thermal efficiency of the steam power plant cycle described in Problem 4.198E. Problem 4.198E The following data are for a simple steam power plant as shown in Fig: State 1 2 3 4 5 6 7 P lbf/in.2 900 890 860 830 800 1.5 1.4 T F 115 350 920 900 110 h, Btu/lbm 85.3 323 1468 1456 1029 78 State 6 has x6 = 0.92 and a velocity of 600 ft/s. The rate of steam flow is 200 000 lbm/h, with 400-hp input to the pump. Piping diameters are 8 in. from the steam generator to the turbine and 3 in. from the condenser to the steam generator. Determine the power output of the turbine and the heat transfer rate in the condenser. FIGURE P4.118

Chapter 5: Problem 133 Fundamentals of Thermodynamcs 8

Problem 133EUP A steam power plant has 1200 F in the boiler, 630 Btu/s work out of the turbine, 900 Btu/s is taken out at 100 F in the condenser, and the pump work is 30 Btu/s. Find the plant’s thermal efficiency. Assuming the same pump work and heat transfer to the boiler, what is the turbine power if the plant is running in a Carnot cycle?

Chapter 5: Problem 137 Fundamentals of Thermodynamcs 8

Problem 137EUP An air conditioner provides 1 lbm/s of air at 60 F cooled from outside atmospheric air at 95 F. Estimate the amount of power needed to operate the air conditioner. Clearly state all assumptions made.

Chapter 5: Problem 135 Fundamentals of Thermodynamcs 8

Problem 135EUP A car engine burns 10 lbm of fuel (equivalent to the addition of QH) at 2600 R and rejects energy to the radiator and the exhaust at an average temperature of 1300 R. If the fuel provides 17 200 Btu/lbm, what is the maximum amount of work the engine can provide?

Chapter 5: Problem 136 Fundamentals of Thermodynamcs 8

Problem 136EUP Consider the combination of a heat engine and a heat pump, as given in Problem 5.41, with a low temperature of 720 R. What should the high temperature be so that the heat engine is reversible? For that temperature, what is the COP for a reversible heat pump? Problem 5.41 Consider a heat engine and heat pump connected as shown in Fig. P5.41. Assume that TH1 = TH2 > Tamb and determine for each of the three cases if the setup satisfies the first law and/or violates the second law. FIGURE P5.41

Chapter 5: Problem 134 Fundamentals of Thermodynamcs 8

Problem 134EUP A large heat pump should upgrade 4000 Btu/s of heat at 175 F to be delivered as heat at 280 F. What is the minimum amount of work (power) input that will drive this?

Chapter 5: Problem 138 Fundamentals of Thermodynamcs 8

Problem 138EUP We propose to heat a house in the winter with a heat pump. The house is to be maintained at 68 F at all times. When the ambient temperature outside drops to 15 F, the rate at which heat is lost from the house is estimated to be 80 000 Btu/h. What is the minimum electrical power required to drive the heat pump?

Chapter 5: Problem 139 Fundamentals of Thermodynamcs 8

Problem 139EUP Consider the setup with two stacked (temperature-wise) heat engines, as in Fig. P5.4. Let TH = 1500 R, TM = 1000 R, and TL = 650 R. Find the two heat engine efficiencies and the combined overall efficiency assuming Carnot cycles. FIGURE P5.4

Chapter 5: Problem 144 Fundamentals of Thermodynamcs 8

Problem 144EUP Anuclear reactor provides a flowof liquid sodium at 1500 F, which is used as the energy source in a steam power plant. The condenser cooling water comes from a cooling tower at 60 F. Determine the maximum thermal efficiency of the power plant. Is it misleading to use the temperatures given to calculate this value?

Chapter 5: Problem 140 Fundamentals of Thermodynamcs 8

Problem 140EUP Thermal storage is provided with a rock (granite) bed of 70 ft3 that is heated to 720 R using solar energy. A heat engine receives QH from the bed and rejects heat to the ambient at 520 R. The rock bed therefore cools down, and as it reaches 520 R, the process stops. Find the energy the rock bed can give out. What is the heat engine efficiency at the beginning of the process, and what is it at the end of the process?

Chapter 5: Problem 141 Fundamentals of Thermodynamcs 8

Problem 141EUP A heat engine has a solar collector receiving 600 Btu/h per square foot, inside which a transfer medium is heated to 800 R. The collected energy powers a heat engine that rejects heat at 100 F. If the heat engine should deliver 8500 Btu/h, what is the minimum size (area) of the solar collector?

Chapter 5: Problem 142 Fundamentals of Thermodynamcs 8

Problem 142EUP Six hundred pound-mass per hour of water runs through a heat exchanger, entering as saturated liquid at 250 F and leaving as saturated vapor. The heat is supplied by a Carnot heat pump operating from a low-temperature reservoir at 60 F with a COP half that of a similar Carnot unit. Find the rate of work into the heat pump.

Chapter 5: Problem 145 Fundamentals of Thermodynamcs 8

Problem 145EUP An inventor has developed a refrigeration unit that maintains the cold space at 14 F while operating in a 77 F room. A COP of 8.5 is claimed. How do you evaluate this?

Chapter 5: Problem 143 Fundamentals of Thermodynamcs 8

Problem 143EUP A power plant with a thermal efficiency of 40% is located on a river similar to the setup in Fig. P5.61. With a total river mass flow rate of 2 × 105 lbm/s at 60 F, find the maximum power production allowed if the river water should not be heated more than 2 F. FIGURE P5.6

Chapter 5: Problem 147 Fundamentals of Thermodynamcs 8

Problem 147EUP In a remote location, you run a heat engine to provide the power to run a refrigerator. The input to the heat engine is 1450 R and the low T is 700 R; it has an actual efficiency equal to half that of the corresponding Carnot unit. The refrigerator has TL = 15 F and TH = 95 F with a COP that is one-third that of the corresponding Carnot unit. Assume a cooling capacity of 7000 Btu/h is needed and find the rate of heat input to the heat engine.

Chapter 5: Problem 146 Fundamentals of Thermodynamcs 8

Problem 146EUP A car engine operates with a thermal efficiency of 35%. Assume the air conditioner has aCOPthat is one-third that of the theoretical maximum, and it is mechanically pulled by the engine. How much extra fuel energy should you spend to remove 1 Btu at 60 F when the ambient is 95 F?

Chapter 5: Problem 149 Fundamentals of Thermodynamcs 8

Problem 149EUP A small house kept at 77 F inside loses 12 Btu/s to the outside ambient at 32 F.A heat pump is used to help heat the house together with possible electric heat. The heat pump is driven by a 2.5-kW motor, and it has a COP that is one-fourth that of a Carnot heat pump unit. Find the actual COP for the heat pump and the amount of electric heat that must be used (if any) to maintain the house temperature.

Chapter 5: Problem 148 Fundamentals of Thermodynamcs 8

Problem 148EUP A heat pump cools a house at 70 F with a maximum of 4000 Btu/h power input. The house gains 2000 Btu/h per degree temperature difference from the ambient, and the heat pump’s COP is 60% of the theoretical maximum. Find the maximum outside temperature for which the heat pump provides sufficient cooling.

Chapter 5: Problem 150 Fundamentals of Thermodynamcs 8

Problem 150EUP A house is cooled by an electric heat pump using the outside as the high-temperature reservoir. For several different summer outdoor temperatures, estimate the percentage savings in electricity if the house is kept at 77 F instead of 68 F. Assume that the house is gaining energy from the outside in direct proportion to the temperature difference.

Chapter 5: Problem 151 Fundamentals of Thermodynamcs 8

Problem 151EUP Arctic explorers are unsure if they can use a 5-kW motor-driven heat pump to stay warm. It should keep their shelter at 60 F; the shelter loses energy at a rate of 0.3 Btu/s per degree difference from the colder ambient. The heat pump has a COP that is 50% that of a Carnot heat pump. If the ambient temperature can fall to ?10 F at night, would you recommend this heat pump to the explorers?

Chapter 5: Problem 152 Fundamentals of Thermodynamcs 8

Problem 152EUP Using the given heat pump in the previous problem, how warm could it make the shelter in the arctic night?

Chapter 5: Problem 154 Fundamentals of Thermodynamcs 8

Problem 154EUP Air in a piston/cylinder goes through a Carnot cycle with the P–v diagram shown in Fig. 5.24. The high and low temperatures are 1200 R and 600 R, respectively. The heat added at the high temperature is 100 Btu/lbm, and the lowest pressure in the cycle is 10 lbf/in.2. Find the specific volume and pressure at all four states in the cycle, assuming constant specific heat at 80 F. FIGURE 5.24

Chapter 5: Problem 155 Fundamentals of Thermodynamcs 8

Problem 155EUP We wish to produce refrigeration at ?20 F. A reservoir is available at 400 F and the ambient temperature is 80 F, as shownin Fig. P5.104 Thus, work can be done by a cyclic heat engine operating between the 400 F reservoir and the ambient. This work is used to drive the refrigerator. Determine the ratio of the heat transferred from the 400 F reservoir to the heat transferred from the ?20 F reservoir, assuming all processes are reversible. FIGURE P5.104

Chapter 5: Problem 153 Fundamentals of Thermodynamcs 8

Problem 153EUP Carbon dioxide is used in an ideal gas refrigeration cycle, the reverse of Fig. 5.24. Heat absorption is at 450 R and heat rejection is at 585 R where the pressure changes from 180 psia to 360 psia. Find the refrigeration COP and the specific heat transfer at the low temperature. FIGURE 5.24

Chapter 5: Problem 157 Fundamentals of Thermodynamcs 8

Problem 157EUP The air conditioner in the previous problem is turned off. How quickly does the house heat up in degrees per second (F/s)?

Chapter 5: Problem 156 Fundamentals of Thermodynamcs 8

Problem 156EUP An air conditioner on a hot summer day removes 8 Btu/s of energy from a house at 70 F and pushes energy to the outside, which is at 88 F. The house has 30 000 lbm mass with an average specific heat of 0.23 Btu/lbm°R. In order to do this, the cold side of the air conditioner is at 40 F and the hot side is at 100 F. The air conditioner (refrigerator) has a COP that is 60% that of a corresponding Carnot refrigerator. Find the actual COP of the air conditioner and the power required to run it.

Chapter 5: Problem 158 Fundamentals of Thermodynamcs 8

Problem 158EUP A window air conditioner cools a room at TL = 68 F with a maximum of 1.2 kW power input. The room gains 0.33 Btu/s per degree temperature difference from the ambient, and the refrigeration COP is ? = 0.6 ?Carnot. Find the maximum outside temperature, TH, for which the air conditioner provides sufficient cooling.

Chapter 5: Problem 159 Fundamentals of Thermodynamcs 8

Problem 159EUP The room in Problem 5.158E has a combined thermal mass of 4000 lbm wood, 500 lbm steel, and 1000 lbm plaster board. Estimate how quickly the room heats up if the air conditioner is turned off on a day when it is 95 F outside. Problem 5.158E A window air conditioner cools a room at TL = 68 F with a maximum of 1.2 kW power input. The room gains 0.33 Btu/s per degree temperature difference from the ambient, and the refrigeration COP is ? = 0.6 ?Carnot. Find the maximum outside temperature, TH, for which the air conditioner provides sufficient cooling.

Chapter 5: Problem 160 Fundamentals of Thermodynamcs 8

Problem 160EUP A 350-ft3 tank of air at 80 lbf/in.2, 1080 R acts as the high-temperature reservoir for a Carnot heat engine that rejects heat at 540 R. A temperature difference of 45 F between the air tank and the Carnot cycle high temperature is needed to transfer the heat. The heat engine runs until the air temperature has dropped to 700 R and then stops. Assume constant specific heat capacities for air and find how much work is given out by the heat engine.

Table of Contents

Textbook Solutions for Fundamentals of Thermodynamcs

Question

Solution

Solved: Using the given heat pump in the previous problem,

Chapter 5 textbook questions

Register

Table of Contents

Textbook Solutions for Fundamentals of Thermodynamcs

Question

Solution

Solved: Using the given heat pump in the previous problem,

Chapter 5 textbook questions

Login

Register

Reset password