Solved: What are the characteristics of all heat engines?

Problem 173P When was the concept of the heat pump conceived and by whom? When was the first heat pump built, and when were the heat pumps first mass-produced?

Problem 2P Describe an imaginary process that satisfies the first law but violates the second law of thermodynamics.

Problem 3P Describe an imaginary process that satisfies the second law but violates the first law of thermodynamics.

Problem 1P Describe an imaginary process that violates both the first and the second laws of thermodynamics.

Problem 4P An experimentalist claims to have raised the temperature of a small amount of water to 150°C by transferring heat from high-pressure steam at 120°C. Is this a reasonable claim? Why? Assume no refrigerator or heat pump is used in the process.

Problem 6P Consider the process of baking potatoes in a conventional oven. Can the hot air in the oven be treated as a thermal energy reservoir? Explain.

Problem 5P What is a thermal energy reservoir? Give some examples.

Problem 7P What are the characteristics of all heat engines?

Problem 8P What is the Kelvin-Planck expression of the second f law of thermodynamics?

Problem 10P Baseboard heaters are basically electric resistance heaters and are frequently used in space heating. A home owner claims that her 5-year-old baseboard heaters have a conversion efficiency of 100 percent. Is this claim in violation of any thermodynamic laws? Explain.

Problem 12P In the absence of any friction and other irreversibility’s, can a heat engine have an efficiency of 100 percent? Explain.

Problem 14P Consider a pan of water being heated (a) by placing it on an electric range and (b) by placing a heating element in the water. Which method is a more efficient way of heating water? Explain.

Problem 13P Are the efficiencies of all the work-producing devices, including the hydroelectric-power plants, limited by the Kelvin-Planck statement of the second law? Explain.

Problem 9P Is it possible for a heat engine to operate without rejecting any waste heat to a low-temperature reservoir? Explain.

Problem 11P Does a heat engine that has a thermal efficiency of 100 percent necessarily violate (a) the first law and (b) the L second law of thermodynamics? Explain.

Problem 16P A car engine with a power output of 110 hp has a thermal efficiency of 28 percent. Determine the rate of fuel consumption if the heating value of the fuel is 19,000 Btu/lbm.

Problem 18P The thermal efficiency of a general heat engine is 35 percent, and it produces 60 hp. At what rate is heat transferred to this engine, in kJ/s?

A heat engine has a heat input of \(3 \times 10^{4} \mathrm{Btu} / \mathrm{h}\) and a thermal efficiency of 40 percent. Calculate the power it will produce, in hp. Equation Transcription: Text Transcription: 3 times 10^4 Btu/h

Problem 15P A steam power plant receives heat from a furnace at a rate of 280 GJ/h. Heat losses to the surrounding air from the steam as it passes through the pipes and other components are estimated to be about 8 GJ/h. If the waste heat is transferred to the cooling water at a rate of 145 GJ/h, determine (a) net power output and (b) the thermal efficiency of this power plant.

Problem 20P A heat engine that pumps water out of an under’ ground mine accepts 700 kJ of heat and produces 250 kJ of work. How much heat does it reject, in kJ?

Problem 19P A 600-MW steam power plant, which is cooled by a nearby river, has a thermal efficiency of 40 percent. Determine the rate of heat transfer to the river water. Will the actual heat transfer rate be higher or lower than this value? Why?

Problem 21P A heat engine with a thermal efficiency of 45 percent rejects 500 kJ/kg of heat. How much heat does it receive?

An Ocean Thermal Energy Conversion (OTEC) power plant built in Hawaii in 1987 was designed to operate between the temperature limits of \(86^{\circ} \mathrm{F}\) at the ocean surface and \(41^{\circ} \mathrm{F}\) at a depth of \(2100 \mathrm{ft}\). About \(13,300 \mathrm{gpm}\0 of cold seawater was to be pumped from deep ocean through a 40 -in diameter pipe to serve as the cooling medium or heat sink. If the cooling water experiences a temperature rise of \(6^{\circ} \mathrm{F}\) and the thermal efficiency is \(2.5\) percent, determine the amount of power generated. Take the density of seawater to be \(64 \mathrm{lbm} / \mathrm{ft}^{3}\). Equation Transcription: 86°F 41°F Text Transcription: 86 degree fahrenheit 41 degree fahrenheit 2100 ft 13,300 gpm

Problem 22P A steam power plant with a power output of 150 MW consumes coal at a rate of 60 tons/h. If the heating value of the coal is 30,000 kJ/kg, determine the overall efficiency of this plant.

Problem 25P Solar energy stored in large bodies of water, called solar pounds, is being used to generate electricity. If such a solar power plant has an efficiency of 3 percent and a net power output of 180 kW, determine the average value of the required solar energy collection rate, in Btu/h.

Problem 26P A coal-burning steam power plant produces a net power of 300 MW with an overall thermal efficiency of 32 percent. The actual gravimetric air-fuel ratio in the furnace is calculated to be 12 kg air/kg fuel. The heating value of the coal is 28,000 kJ/kg. Determine (a) the amount of coal consumed during a 24-hour period and (b) the rate of air flowing through the furnace.

Problem 28P What is the difference between a refrigerator and a heat pump?

Problem 29P What is the difference between a refrigerator and an air conditioner?

Problem 30P In a refrigerator, heat is transferred from a lower-temperature medium (the refrigerated space) to a higher-temperature one (the kitchen air). Is this a violation of the second law of thermodynamics? Explain.

Problem 31P A heat pump is a device that absorbs energy from the cold outdoor air and transfers it to the warmer indoors. Is this a violation of the second law of thermodynamics? Explain.

Problem 34P A heat pump that is used to heat a house has a COP of 2.5. That is, the heat pump delivers 2.5 kWh of energy to the house for each 1 kWh of electricity it consumes. Is this a violation of the first law of thermodynamics? Explain.

Problem 32P Define the coefficient of performance of a refrigerator in words. Can it be greater than unity?

Problem 35P A refrigerator has a COP of 1.5. That is, the refrigerator removes L5 kWh of energy from the refrigerated space for each 1 kWh of electricity it consumes. Is this a violation of the first law of thermodynamics? Explain.

Problem 33P Define the coefficient of performance of a heat pump in words. Can it be greater than unity?

Problem 36P What is the Clausius expression of the second law of thermodynamics?

Problem 39P Determine the COP of a heat pump that supplies energy to a house at a rate of 8000 kJ/h for each kW of electric power it draws. Also, determine the rate of energy absorption from the outdoor air.

Problem 37P Show that the Kelvin-Planck and the Clausius expressions of the second law are equivalent.

Problem 38P Determine the COP of a refrigerator that removes heat from the food compartment at a rate of 5040 kJ/h for each kW of power it consumes. Also, determine the rate of heat rejection to the outside air.

Problem 41P A refrigerator used to cool a computer requires 1.2 kW of electrical power and has a COP of 1.8. Calculate the cooling effect of this refrigerator, in kW.

A residential heat pump has a coefficient of performance of \(2.4\). How much heating effect, in Btu/h, will result when \(5\ hp\) is supplied to this heat pump? Equation Transcription: Text Transcription: 2.4 5 hp

Problem 42P An air conditioner removes heat steadily from a house at a rate of 750 kJ/min while drawing electric power at a rate of 6 kW. Determine (a) the COP of this air conditioner and (b) the rate of heat transfer to the outside air.

Reconsider Prob. 6–45. Using EES (or other) software, determine the power input required by the air conditioner to cool the house as a function for air conditioner EER ratings in the range 5 to 15. Discuss your results and include representative costs of air-conditioning units in the EER rating range.

A food department is kept at \(-12^{\circ} \mathrm{C}\) by a refrigerator in an environment at \(30^{\circ} \mathrm{C}\). The total heat gain to the food department is estimated to be \(3300 \mathrm{~kJ} / \mathrm{h}\) and the heat rejection in the condenser is \(4800 \mathrm{~kJ} / \mathrm{h}\). Determine the power input to the compressor, in \(\mathrm{kW}\) and the COP of the refrigerator. Equation Transcription: -12°C 30°C Text Transcription: -12 degree celsius 30 degree celsius 3300 kJ/h 4800 kJ/h kW

When a man returns to his well-sealed house on a summer day, he finds that the house is at \(35^{\circ} \mathrm{C}\). He turns on the air conditioner, which cools the entire house to \(20^{\circ} \mathrm{C}\) in \(30 \mathrm{~min}\). If the COP of the air-conditioning system is \(2.8\), determine the power drawn by the air conditioner. Assume the entire mass within the house is equivalent to \(800 \mathrm{~kg}\) of air for which \(c_{v}=0.72 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\) and \(c_{p}=1.0 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\). Equation Transcription: 35°C 20°C Text Transcription: 35 degree celsius 20 degree celsius 30 min 800 kg c_v=0.72 kJ/kg dot degree celsius c_p=1.0 kJ/kg dot degree celsius

Problem 48P Bananas are to be cooled from 24 to 13°C at a rate of 215 kg/h by a refrigeration system. The power input to the refrigerator is 1.4 kW. Determine the rate of cooling, in kJ/min, and the COP of the refrigerator. The specific heat of I banana above freezing is 3.35 kJ/kg-°C.

Problem 47P A heat pump with a COP of 2.5 supplies energy to a house at a rate of 60,000 Btu/h. Determine (a) the electric power drawn by the heat pump and (b) the rate of heat absorption from the outside air.

A heat pump is used to maintain a house at a constant temperature of \(23^{\circ} \mathrm{C}). The house is losing heat to the outside air through the walls and the windows at a rate of \(85,000 \mathrm{~kJ} / \mathrm{h}\) while the energy generated within the house from people, lights, and appliances amounts to \(4000 \mathrm{~kJ} / \mathrm{h}\). For a \(\mathrm{COP}\) of \(3.2\), determine the required power input to the heat pump. Equation Transcription: 23 degree celsius Text Transcription: 23°C 85,000 kJ/h 4000 kJ/h

Problem 44P A household refrigerator that has a power input of 450 W and a COP of 1.5 is to cool 5 large watermelons, 10 kg each, to 8°C. If the watermelons are initially at 28°C, determine how long it will take for the refrigerator to cool them. The watermelons can be treated as water whose specific heat is 4.2 kJ/kg·°C. Is your answer realistic or optimistic? Explain.

Problem 50P Water enters an ice machine at 55°F and leaves as ice at 25°F. If the COP of the ice machine is 2.4 during this operation, determine the required power input for an ice production rate of 28 Ibm/h. (169 Btu of energy needs to be removed from each Ibm of water at 55°F to turn it into ice at25°F.)

A household refrigerator runs one-fourth of the time and removes heat from the food compartment at an average rate of \(800\ kJ/h\). If the COP of the refrigerator is \(2.2\), determine the power the refrigerator draws when running. Equation Transcription: Text Transcription: 2.2 800 kJ/h

Problem 52P A heat pump used to heat a house runs about onethird of the time. The house is losing heat at an average rate of 22,000 kJ/h. If the COP of the heat pump is 2.8, determine the power the heat pump draws when running.

Problem 53P Consider an office room that is being cooled adequately by a 12,000 Btu/h window air conditioner. Now it is decided to convert this room into a computer room by installing several computers, terminals, and printers with a total rated power of 8.4 kW. The facility has several 7000 Btu/h air conditioners in storage that can be installed to meet the additional cooling requirements. Assuming a usage factor of 0.4 (i.e., only 40 percent of the rated power will be consumed at any given time) and additional occupancy of seven people, each generating heat at a rate of 100 W, determine how many of these air conditioners need to be installed to the room.

Consider a building whose annual air-conditioning load is estimated to be \(40,000\ kWh\) in an area where the unit cost of electricity is \($0.10/kWh\). Two air conditioners are considered for the building. Air conditioner A has a seasonal average COP of \(2.3\) and costs \($5500\) to purchase and install. Air conditioner B has a seasonal average COP of \(3.6\) and costs \($7000\) to purchase and install. All else being equal, determine which air conditioner is a better buy. Equation Transcription: Text Transcription: $5500 40,000 kWh $0.10/kWh $7000

Problem 56P An inventor claims to have developed a resistance heater that supplies 1.2 kWh of energy to a room for each kWh of electricity it consumes. Is this a reasonable claim, or has the inventor developed a perpetual-motion machine? Explain.

Problem 57P It is common knowledge that the temperature of air rises as it is compressed. An inventor thought about using this high-temperature air to heat buildings. He used a compressor driven by an electric motor. The inventor claims that the compressed hot-air system is 25 percent more efficient than a resistance heating system that provides an equivalent amount of heating. Is this claim valid, or is this just another perpetual-motion machine? Explain.

Problem 58P A cold canned drink is left in a warmer room where its temperature rises as a result of heat transfer. Is this a reversible process? Explain.

Refrigerant-134a enters the condenser of a residential heat pump at \(800 \mathrm{kPa}\) and \(35^{\circ} \mathrm{C}\) at a rate of 0.018 kg/s and leaves at \(800 \mathrm{kPa}\) as a saturated liquid. If the compressor consumes \(1.2 \mathrm{kW}\) of power, determine (a) the COP of the heat pump and (b) the rate of heat absorption from the outside air. Equation Transcription: 35°C Text Transcription: 800 kPa 35 degree celsius 0.018 kg/s 1.2 kW

Problem 59P A block slides down an inclined plane with friction and no restraining force. Is this process reversible or irreversible? Justify your answer.

Problem 60P Show that processes involving rapid chemical reactions are irreversible by considering the combustion of a natural gas (e.g., methane) and air mixture in a rigid container.

Problem 61P Show that processes that use work for mixing are irreversible by considering an adiabatic system whose contents are stirred by turning a paddle wheel inside the system (e.g., stirring a cake mix with an electric mixer).

Problem 64P How do you distinguish between internal and external irreversibilities?

Problem 65P Is a reversible expansion or compression process necessarily quasi-equilibrium? Is a quasi-equilibrium expansion or compression process necessarily reversible? Explain.

Problem 62P Why does a nonquasi-equilibrium compression process require a larger work input than the corresponding quasi-equilibrium one?

Problem 66P Why are engineers interested in reversible processes even though they can never be achieved?

Problem 63P Why does a nonquasi-equilibrium expansion process deliver less work than the corresponding quasi-equilibrium one?

Problem 67P What are the four processes that make up the Carnot cycle?

Problem 68P What are the two statements known as the Carnot principles?

Problem 69P Is it possible to develop (a) an actual and (b) a reversible heat-engine cycle that is more efficient than Carnot cycle operating between the same temperature limits? Explain.

Problem 71P Somebody claims to have developed a new reversible heat-engine cycle that has the same theoretical efficiency as the Carnot cycle operating between the same temperature hmits. Is this a reasonable claim?

Problem 74P From a work-production perspective, which is more m valuable: (a) thermal energy reservoirs at 675 K and 325 K Hi or (b) thermal energy reservoirs at 625 K and 275 K?

Problem 70P Somebody claims to have developed a new reversible heat-engine cycle that has a higher theoretical efficiency than the Carnot cycle operating between the same temperature limits. How do you evaluate this claim?

Problem 72P Is there any way to increase the efficiency of a Carnot heat engine other than by increasing TH or decreasing TL?

Problem 73P Consider two actual power plants operating with h solar energy. Energy is supplied to one plant from a solar pond at 80°C and to the other from concentrating collectors I that raise the water temperature to 600°C. Which of these $ power plants will have a higher efficiency? Explain.

A heat engine is operating on a Carnot cycle and has a thermal efficiency of 55 percent. The waste heat from this engine is rejected to a nearby lake at \(60^{\circ} \mathrm{F}\) at a rate of \(800 Btu/min\). Determine (a) the power output of the engine and (b) the temperature of the source. Equation Transcription: 60°F Text Transcription: 60 degree fahrenheit 800 Btu/min

Problem 76P A Carnot heat engine receives 650 kJ of heat from a source of unknown temperature and rejects 250 kJ of it to a sink at 24°C. Determine (a) the temperature of the source and (b) the thermal efficiency of the heat engine.

A heat engine operates between a source at \(477^{\circ} \mathrm{C}\) and a sink at \(25^{\circ} \mathrm{C}\). If heat is supplied to the heat engine at a steady rate of \(65,000 kJ/min\), determine the maximum power output of this heat engine. Equation Transcription: 477°C 25°C Text Transcription: 477 degree celsius 25 degree celsius 65,000 kJ/min

In tropical climates, the water near the surface of the ocean remains warm throughout the year as a result of solar energy absorption. In the deeper parts of the ocean, however, the water remains at a relatively low temperature since the sun’s rays cannot penetrate very far. It is proposed to take advantage of this temperature difference and construct a power plant that will absorb heat from the warm water near the surface and reject the waste heat to the cold water a few hundred meters below. Determine the maximum thermal efficiency of such a plant if the water temperatures at the two respective locations are 24 and \(3^{\circ} \mathrm{C}\). Equation Transcription: 3°C Text Transcription: 3 degree celsius

Problem 77P A Carnot heat engine operates between a source at 1000 K and a sink at 300 K. If the heat engine is supplied with heat at a rate of 800 kJ/min, determine (a) the thermal efficiency and (b) the power output of this heat engine.

Problem 83P A well-established way of power generation involves the utilization of geothermal energy—the energy of hot water that exists naturally underground—as the heat source. If a supply of hot water at 140°C is discovered at a location where the environmental temperature is 20°C, determine the maximum thermal efficiency a geothermal power plant built at that location can have.

Reconsider Prob. 6–78. Using EES (or other) software, study the effects of the tempera- tures of the heat source and the heat sink on the power produced and the cycle thermal efficiency. Let the source temperature vary from 300 to \(1000^{\circ} \mathrm{C}\), and the sink temperature to vary from 0 to \(50^{\circ} \mathrm{C}\). Plot the power produced and the cycle efficiency against the source temperature for sink temperatures of \(0^{\circ} \mathrm{C}\), \(258^{\circ} \mathrm{C}\), and \(50^{\circ} \mathrm{C}\), and discuss the results. Equation Transcription: 1000°C 50°C 0°C, 258°C Text Transcription: 1000°C 50°C 0°C, 258°C

Problem 84P A homeowner buys a new refrigerator and a new air conditioner. Which one of these devices would you expect to have a higher COP? Why?

Problem 87P In an effort to conserve energy in a heat-engine cycle, somebody suggests incorporating a refrigerator that will absorb some of the waste energy QL and transfer it to the energy source of the heat engine. Is this a smart idea? Explain.

Problem 81P A heat engine receives heat from a heat source at 1200°C and has a thermal efficiency of 40 percent. The heat engine does maximum work equal to 500 kJ. Determine the heat supplied to the heat engine by the heat source, the heat rejected to the. heat sink, and the temperature of the heat sink.

An inventor claims to have devised a cyclical engine for use in space vehicles that operates with a nuclear-fuel-generated energy source whose temperature is \(920\ R\) and a sink at \(490\ R\) that radiates waste heat to deep space. He also claims that this engine produces \(4.5\ hp\) while rejecting heat at a rate of \(15,000\ Btu/h\). Is this claim valid? Equation Transcription: Text Transcription: 920 R 490 R 4.5 hp 15,000 Btu/h

Problem 85P A homeowner buys a new refrigerator with no freezer compartment and a deep freezer for the new kitchen. Which of these devices would you expect to have a lower COP? Why?

Problem 86P How can we increase the COP of a Carnot refrigerator?

Problem 88P It is well established that the thermal efficiency of a heat engine increases as the temperature TL at which heat is rejected from the heat engine decreases. In an effort to increase the efficiency of a power plant, somebody suggests refrigerating the cooling water before it enters the condenser, where heat rejection takes place. Would you be in favor ofthis idea? Why?

Problem 92P An air-conditioning system operating on the reversed Carnot cycle is required to transfer heat from a house at a rate of 750 kJ/min to maintain its temperature at 24°C. If the outdoor air temperature is 35°C, determine the power required to operate this air-conditioning system.

Problem 89P It is well known that the thermal efficiency of heat engines increases as the temperature of the energy source increases. In an attempt to improve the efficiency of a power plant, somebody suggests transferring heat from the available energy source to a higher-temperature medium by a heat pump before energy is supplied to the power plant. What do you think of this suggestion? Explain.

Problem 94P A heat pump operates on a Carnot heat pump cycle with a COP of 8.7. It keeps a space at 24°C by consuming 2.15 kW of power. Determine the temperature of the reservoir from which the heat is absorbed and the heating load provided by the heat pump.

Problem 91P A Carnot refrigerator operates in a room in which the temperature is 22°C and consumes 2 kW of power when operating. If the food compartment of the refrigerator is to be maintained at 3°C, determine the rate of heat removal from the food compartment.

During an experiment conducted in a room at \(50^{\circ} \mathrm{C}\), a laboratory assistant measures that a refrigerator that draws \(2\ kW\) of power has removed \(30,000\ kJ\) of heat from the refrigerated space, which is maintained at \(230^{\circ} \mathrm{C}\). The running time of the refrigerator during the experiment was \(20\ min\). Determine if these measurements are reasonable. Equation Transcription: 25°C 230°C Text Transcription: 25 degree celsius 2 kW 30,000 kJ 230 degree celsius 20 min

Problem 93P An inventor claims to have developed a heat pump that produces a 200-kW heating effect for a 293 K heated zone while only using 75 kW of power and a heat source at 273 K. Justify the validity of this claim.

A refrigerator is to remove heat from the cooled space at a rate of \(300\ kJ/min\) to maintain its temperature at \(28^{\circ} \mathrm{C}\). If the air surrounding the refrigerator is at \(25^{\circ} \mathrm{C}\), determine the minimum power input required for this refrigerator. Equation Transcription: 28°C 25°C Text Transcription: 300 kJ/min 28 degree celsius 25 degree celsius

Problem 96P An inventor claims to have developed a refrigeration system that removes heat from the closed region at ?12°C and transfers it to the surrounding air at 25°C while maintaining a COP of 6.5. Is this claim reasonable? Why?

Problem 100P A refrigerator operating on the reversed Carnot cycle has a measured work input of 200 kW and heat rejection of 2000 kW to a heat reservoir at 27°C. Determine the cooling load supplied to the refrigerator, in kW, and the temperature of the heat source, in °C.

A heat pump is used to maintain a house at \(25^{\circ} \mathrm{C}\) by extracting heat from the outside air on a day when the outside air temperature is \(4^{\circ} \mathrm{C}\). The house is estimated to lose heat at a rate of \(110,000 kJ/h\), and the heat pump consumes \(4.75 kW\) of electric power when running. Is this heat pump powerful enough to do the job? Equation Transcription: 25°C 4°C Text Transcription: 25 degree celsius 4 degree celsius 110,000 kJ/h 4.75 kW

Problem 98P A completely reversible refrigerator operates between thermal energy reservoirs at 450 R and 540 R. How many kilowatts of power are required for this device to produce a 15,000-Btu/h cooling effect?

Problem 102P The performance of a heat pump degrades (i.e., its COP decreases) as the temperature of the heat source decreases. This makes using heat pumps at locations with severe weather conditions unattractive. Consider a house that is heated and maintained at 20°C by a heat pump during the winter. What is the maximum COP for this heat pump if heat is extracted from the outdoor air at (a) 10°C, (b) -5°C, and (c) -30°C?

A Carnot heat pump is to be used to heat a house and maintain it at \(25^{\circ} \mathrm{C}\) in winter. On a day when the average outdoor temperature remains at about \(2^{\circ} \mathrm{C}\), the house is estimated to lose heat at a rate of \(55,000 \mathrm{~kJ} / \mathrm{h}\). If the heat pump consumes \(4.8 \mathrm{~kW}\) of power while operating, determine (a) how long the heat pump ran on that day; (b) the total heating costs, assuming an average price of \(11 \mathrm{c} / \mathrm{kWh}\) for electricity; and (c) the heating cost for the same day if resistance heat-ing is used instead of a heat pump. Equation Transcription: 25°C 2°C 4.8 kW Text Transcription: 25 degree celsius 2 degree celsius 4.8 kW 55,000 kJ/h 11¢/kWh

A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at \(-35^{\circ} \mathrm{C}\) by rejecting waste heat to cooling water that enters the condenser at \(18^{\circ} \mathrm{C}\) at a rate of \(0.25 \mathrm{~kg} / \mathrm{s}\) and leaves at \(26^{\circ} \mathrm{C}\). The refrigerant enters the condenser at \(1.2 \mathrm{MPa}\) and \(50^{\circ} \mathrm{C}\) and leaves at the same pressure subcooled by \(5^{\circ} \mathrm{C}\). If the compressor consumes \(3.3 \mathrm{~kW}\) of power, determine (a) the mass flow rate of the refrigerant, (b) the refrigeration load, (c) the COP, and (d) the minimum power input to the compressor for the same refrigeration load. Equation Transcription: -35°C 18°C 26°C 50°C 5°C Text Transcription: 134a -35 degree celsius 18 degree celsius 26 degree celsius 0.25 kg/s 1.2 MPa 50 degree celsius 5degree celsius 3.3 kW

Problem 105P A Carnot heat engine receives heat from a reservoir at 900°C at a rate of 800 kJ/min and rejects the waste heat to the ambient air at 27°C. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at ?5°C and transfers it to the same ambient air at 27°C. Determine (a) the maximum rate of heat removal from the refrigerated space and (b) the total rate of heat rejection to the ambient air.

Problem 99P An air-conditioning system is used to maintain a house at 72°F when the temperature outside is 90°F. If this air-conditioning system draws 5 hp of power when operating, determine the maximum rate of heat removal from the house that it can accomplish.

Problem 103P A heat pump is to be used for heating a house in winter. The house is to be maintained at 78°F at all times. When the temperature outdoors drops to 25°F, the heat losses from the house are estimated to be 70,000 Btu/h. Determine the minimum power required to run this heat pump if heat is extracted from (a) the outdoor air at 25°F and (b) the well water at 50°F.

Problem 106P A Carnot heat engine receives heat from a reservoir at 1700°F at a rate of 700 Btu/min and rejects the waste heat to the ambient air at 80°F. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at 20°F and transfers it to the same ambient air at 80°F. Determine (a) the maximum rate of heat removal from the refrigerated space and (b) the total rate of heat rejection to the ambient air.

An air-conditioner with refrigerant-\(134a\) as the working fluid is used to keep a room at \(23^{\circ} \mathrm{C}\) by rejecting the waste heat to the outdoor air at \(34^{\circ} \mathrm{C}\). The room gains heat through the walls and the windows at a rate of \(250\ kJ/min\) while the heat generated by the computer, TV, and lights amounts to 900 W. The refrigerant enters the compressor at \(400\ kPa\) as a saturated vapor at a rate of \(8\0 L/min\) and leaves at \(1200\ kPa\) and \(70^{\circ} \mathrm{C}\). Determine (a) the actual COP, (b) the maximum COP, and (c) the minimum volume flow rate of the refrigerant at the compressor inlet for the same compressor inlet and exit conditions. Equation Transcription: 34°C 23°C 70°C Text Transcription: 134a 34 degree celsius 23 degree celsius 250 kJ/min 900 W 1200 kPa 70 degree celsius

Problem 107P The structure of a house is such that it loses heat at a rate of 3800 kJ/h per °C difference between the indoors and outdoors. A heat pump that requires a power input of 4 kW is used to maintain this house at 24°C. Determine the lowest outdoor temperature for which the heat pump can meet the heating requirements of this house.

Problem 111P Explain how you can reduce the energy consumption of your household refrigerator.

Problem 109P Derive an expression for the COP of a completely reversible refrigerator in terms of the thermal energy reservoir temperatures, TL and TH.

Problem 110P Why are today’s refrigerators much more efficient than those built in the past?

Problem 114P Someone proposes that the entire refrigerator/ freezer requirements of a store be met using a large freezer that supplies sufficient cold air at ?20°C instead of installing separate refrigerators and freezers. What do you think of this proposal?

Problem 112P Why is it important to clean the condenser coils of a household refrigerator a few times a year? Also, why is it important not to block airflow through the condenser coils?

Problem 113P Someone proposes that the refrigeration system of a supermarket be overdesigned so that the entire air-conditioning needs of the store can be met by refrigerated air without installing any air-conditioning system. What do you think of this proposal?

Problem 115P The “Energy Guide” label of a refrigerator states that the refrigerator will consume $170 worth of electricity per year under normal use if the cost of electricity is $0.125/kWh. If the electricity consumed by the lightbulb is negligible and the refrigerator consumes 400 W when running, determine the fraction of the time the refrigerator will run.

Problem 116P The interior lighting of refrigerators is usually provided by incandescent lamps whose switches are actuated by the opening of the refrigerator door. Consider a refrigerator whose 40-W light bulb remains on about 60 h per year. It is proposed to replace the light bulb by an energy-efficient bulb that consumes only 18 W but costs $25 to purchase and install. If the refrigerator has a coefficient of performance of 1.3 and the cost of electricity is 8 cents per kWh, determine if the energy savings of the proposed light bulb justify its cost.

Problem 119P An air-conditioning system is used to maintain a house at a constant temperature of 20°C. The house is gaining heat from outdoors at a rate of 20,000 kJ/h, and the heat generated in the house from the people, lights, and appliances amounts to 8000 kJ/h. For a COP of 2.5, determine the required power input to this air-conditioning system.

Problem 120P A Carnot heat pump is used to heat and maintain a residential building at 75°F. An energy analysis of the house reveals that it loses heat at a rate of 2500 Btu/h per °F temperature difference between the indoors and the outdoors. For an outdoor temperature of 35°F, determine (a) the coefficient of performance and (b) the required power input to the heat pump.

It is often stated that the refrigerator door should be opened as few times as possible for the shortest duration of time to save energy. Consider a household refrigerator whose interior volume is \(0.9 \mathrm{~m}^{3}\) and average internal temperature is \(4^{\circ} \mathrm{C}\). At any given time, one-third of the refrigerated space is occupied by food items, and the remaining \(0.6 \mathrm{~m}^{3}\) is filled with air. The average temperature and pressure in the kitchen are \(20^{\circ} \mathrm{C}\) and \(95 \mathrm{kPa}\), respectively. Also, the moisture contents of the air in the kitchen and the refrigerator are \(0.010\) and \(0.004 \mathrm{~kg}\) per \(\mathrm{kg}\) of air, respectively, and thus \(0.006 \mathrm{~kg}\) of water vapor is condensed and removed for each \(\mathrm{kg}\) of air that enters. The refrigerator door is opened an average of 20 times a day, and each time half of the air volume in the refrigerator is replaced by the warmer kitchen air. If the refrigerator has a coefficient of performance of \(1.4\) and the cost of electricity is \(11.5\) cents per \(\mathrm{kWh}\), determine the cost of the energy wasted per year as a result of opening the refrigerator door. What would your answer be if the kitchen air were very dry and thus a negligible amount of water vapor condensed in the refrigerator? Equation Transcription: 4°C 20°C Text Transcription: 4 degree celsius 0.9 m^3 20 degree celsius 95 kPa 0.004 kg 0.006 kg

6-117 It is commonly recommended that hot foods be cooled first to room temperature by simply waiting a while before they are put into the refrigerator to save energy. Despite this commonsense recommendation, a person keeps cooking a large pan of stew three times a week and putting the pan into the refrigerator while it is still hot, thinking that the money saved is probably too little. But he says he can be convinced if you can show that the money saved is significant. The average mass of the pan and its contents is \(5 \mathrm{~kg}\). The average temperature of the kitchen is \(23^{\circ} \mathrm{C}\), and the average temperature of the food is \(95^{\circ} \mathrm{C}\) when it is taken off the stove. The refrigerated space is maintained at \(3^{\circ} \mathrm{C}\), and the average specific heat of the food and the pan can be taken to be \(3.9 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\). If the refrigerator has a coefficient of performance of \(1.5\) and the cost of electricity is 10 cents per \(\mathrm{kWh}\), determine how much this person will save a year by waiting for the food to cool to room temperature before putting it into the refrigerator. Equation Transcription: 23°C 95°C 3°C °C Text Transcription: 5 kg 23 degree celsius 95 degree celsius 3 degree celsius 3.9 kJ/kg dot degree celsius

Problem 121P A heat engine receives heat from a heat source at 1200°C and rejects heat to a heat sink at 50°C. The heat K engine does maximum work equal to 500 kJ. Determine the H. heat supplied to the heat engine by the heat source and the heat rejected to the heat sink.

Problem 122P A heat pump creates a heating effect of 32, 000 Btu/h for a space maintained at 530 R while using 1.8 kW of electrical power. What is the minimum temperature of the source that’ satisfies the second law of thermodynamics?

Problem 123P A refrigeration system uses water-cooled condenser for rejecting the waste heat. The system absorbs heat from a space at 25°F at a rate of 24,000 Btu/h. Water enters the condenser at 65°F at a rate of 1.45 lbm/s. The COP of the system is estimated to be 1.9. Determine (a) the power input to the system, in kW, (b) the temperature of the water at the exit of the condenser, in °F and (c) the maximum possible COP of the system. The specific heat of water is 1.0 Btu/bm·°F.

Problem 124P A heat pump with a COP of 2.8 is used to heat an air-tight house. When running, the heat pump consumes 5 kW of power. If the temperature in the house is 7°C when the heat pump is turned on, how long will it take for the heat pump to raise the temperature of the house to 22°C? Is this answer realistic or optimistic? Explain. Assume the entire mass within the house (air, furniture, etc.) is equivalent to 1500 kg of air.

A promising method of power generation involves collecting and storing solar energy in large artificial lakes a few meters deep, called solar ponds. Solar energy is absorbed by all parts of the pond, and the water temperature rises everywhere. The top part of the pond, however, loses to the atmosphere much of the heat it absorbs, and as a result, its temperature drops. This cool water serves as insulation for the bottom part of the pond and helps trap the energy there. Usually, salt is planted at the bottom of the pond to prevent the rise of this hot water to the top. A power plant that uses an organic fluid, such as alcohol, as the working fluid can be operated between the top and the bottom portions of the pond. If the water temperature is \(35^{\circ}near the surface and \(80^{\circ} \mathrm{C}\) near the bottom of the pond, determine the maximum thermal efficiency that this power plant can have. Is it realistic to use 35 and \(80^{\circ} for temperatures in the calculations? Explain. Equation Transcription: 80°C 35°C Text Transcription: 80 degree celsius 35 degree celsius

Reconsider Prob. 6–126. Using EES (or other) software, investigate the effect of the net work input on the minimum pressure. Let the work input vary from 10 to \(30\ kJ\). Plot the minimum pressure in the refrigeration cycle as a function of net work input, and discuss the results. Equation Transcription: Text Transcription: 30 kJ

Problem 126P Consider a Carnot refrigeration cycle executed in a closed system in the saturated liquid–vapor mixture region using 0.96,kg of refrigerant-134a as the working fluid. It is known that the maximum absolute temperature in the cycle is 1.2 times the minimum absolute temperature, and the net work input to the cycle is 22 kJ. If the refrigerant changes from saturated vapor to saturated liquid during the heat rejection process, determine the minimum pressure in the cycle.

Problem 128P Consider two Carnot heat engines operating in series. The first engine receives heat from the reservoir at 1400 K and rejects the waste heat to another reservoir at temperature T. The second engine receives this energy rejected by the first one, converts some of it to work, and rejects the rest to a reservoir at 300 K. If the thermal efficiencies of both engines are the same, determine the temperature T.

Reconsider Prob. 6–129. Using EES (or other) software, investigate the effects of the heat engine source temperature, the environment temperature, and the cooled space temperature on the required heat supply to the heat engine and the total rate of heat rejection to the environment. Let the source temperature vary from 500 to \(1000\ K\), the environment temperature vary from 275 to \(325\ K\), and the cooled space temperature vary from ?20 to \(0^{\circ} \mathrm{C}\). Plot the required heat supply against the source temperature for the cooled space temperature of \(-15^{\circ} \mathrm{C}\) and environment temperatures of 275, 300, and \(325\ K\), and discuss the results. Equation Transcription: 0°C - 15°C Text Transcription: 1000 K 325 K 0 degree celsius - 15 degree celsius 325 K

Problem 129P A Carnot heat engine receives heat at 900 K and rejects the waste heat to the environment at 300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at ?15°C at a rate of 250 kJ/min and rejects it to the same environment at 300 K. Determine (a) the rate of heat supplied to the heat engine and (b) the total rate of heat rejection to the environment.

Problem 132P An inventor claims to have developed a refrigerator that maintains the refrigerated space at 408F while operating in a room where the temperature is 858F and that has a COP of 13.5. I this claim reasonable?

Problem 131P A heat engine operates between two reservoirs at 800 and 20°C. One-half of the work output of the heat engine is used to drive a Carnot heat pump that removes heat from the cold surroundings at 2°C and transfers it to a house maintained at 22°C. If the house is losing heat at a rate of 62,000 kJ/h, determine the minimum rate of heat supply to the heat engine required to keep the house at 22°C.

Problem 134P The COP of a refrigerator decreases as the temperature of the refrigerated space is decreased. That is, removing heat from a medium at a very low temperature will require a large work input. Determine the minimum work input required to remove 1 kJ of heat from liquid helium at 3 K when the outside temperature is 300 K.

An old gas turbine has an efficiency of 21 percent and develops a power output of \(6000 kW\). Determine the fuel consumption rate of this gas turbine, in L/min, if the fuel has a heating value of \(42,000 kJ/kg\) and a density of \(0.8\ g/cm^{3}\) Equation Transcription: Text Transcription: 6000 kW 42,000 kJ/kg 0.8 g/cm^3

Problem 135P Consider a Carnot heat-pump cycle executed in a steady-flow system in the saturated liquid–vapor mixture region using refrigerant-134a flowing at a rate of 0.22 kg/s as the working fluid. It is known that the maximum absolute temperature in the cycle is 1.2 times the minimum absolute temperature, and the net power input to the cycle is 5 kW. If the refrigerant changes from saturated vapor to saturated liquid during the heat rejection process, determine the ratio of the maximum to minimum pressures in the cycle.

Problem 136P Replacing incandescent lights with energy-efficient fluorescent lights can reduce the lighting energy consumption to one-fourth of what it was before. The energy consumed by the lamps is eventually converted to heat, and thus switching to energy-efficient lighting also reduces the cooling load in summer but increases the heating load in winter. Consider a building that is heated by a natural gas furnace with an efficiency of 80 percent and cooled by an air conditioner with a COP of 3.5. If electricity costs $0.12/kWh and natural gas costs $1.40/therm (1 therm =105,500 kJ), determine if efficient lighting will increase or decrease the total energy cost of the building (a) in summer and (b) in winter.

Problem 137P A heat pump supplies heat energy to a house at the rate of 140,000 kJ/h when the house is maintained at 25°C. Over a period of one month, the heat pump operates for 100 hours to transfer energy from a heat source outside the house to inside the house. Consider a heat pump receiving heat from two different outside energy sources. In one application the heat pump receives heat from the outside air at 0°C. In a second application the heat pump receives heat from a lake having a water temperature of 10°C. If electricity costs $0.105/kWh, determine the maximum money saved by using the lake water rather than the outside air as the outside energy source.

The cargo space of a refrigerated truck whose inner dimensions are \(12 \mathrm{~m} \times 2.3 \mathrm{~m} \times 3.5 \mathrm{~m}\) is to be pre cooled from \(25^{\circ} \mathrm{C}\) to an average temperature of \(5^{\circ} \mathrm{C}\). The construction of the truck is such that a transmission heat gain occurs at a rate of \(120 \mathrm{~W} /{ }^{\circ} \mathrm{C}\). If the ambient temperature is \(25^{\circ} \mathrm{C}\), determine how long it will take for a system with a refrigeration capacity of \(11 \mathrm{~kW}\) to precool this truck. Equation Transcription: 25°C 5°C °C Text Transcription: 12 m times 2.3 m times 3.5 m 25 degree celsius 5 degree celsius 120 W/ degree celsius 11 kW

Problem 139P The maximum flow rate of a standard shower head is about 3.5 gpm (13.3 L/min) and can be reduced to 2.75 gpm (10.5 L/min) by switching to a low-flow shower head that is equipped with flow controllers. Consider a family of four, with each person taking a 6-minute shower every morning. City water at 15°C is heated to 55°C in an oil water heater whose efficiency is 65 percent and then tempered to 42°C by cold water at the T-elbow of the shower before being routed to the shower head. The price of heating oil is $2.80/gal and its heating value is 146,300 kJ/gal. Assuming a constant specific heat of 4.18 kJ/kg · °C for water, determine the amount of oil and money saved per year by replacing the standard shower heads by the low-flow ones.

Problem 141P A refrigeration system is to cool bread loaves with an average mass of 350 g from 30 to - 10°C at a rate of 1200 loaves per hour by refrigerated air at ?30°C. Taking the average specific and latent heats of bread to be 2.93 U/kg-°C and 109.3 kJ/kg, respectively, determine (a) the rate of heat removal from the breads, in kJ/h; (b) the required volume flow rate of air, in m3/h, if the temperature rise of air is not to exceed 8°C; and (c) the size of the compressor of the refrigeration system, in kW, for a COP of 1.2 for the refrigeration system.

The drinking water needs of a production facility with 20 employees is to be met by a bubbler type water fountain. The refrigerated water fountain is to cool water from 22 to \(8^{\circ} \mathrm{C}\) and supply cold water at a rate of \(0.4 L\) per hour per person. Heat is transferred to the reservoir from the surroundings at \(25^{\circ} \mathrm{C}\) at a rate of \(45 W\). If the COP of the refrigeration system is \(2.9\), determine the size of the compressor, in \(W\), that will be suitable for the refrigeration system of this water cooler. Equation Transcription: 8°C 25°C Text Transcription: 8 degree celsius 0.4 L 25 degree celsius 45 W 2.9

A typical electric water heater has an efficiency of 95 percent and costs \($350\) a year to operate a unit cost of electricity of \($0.11/kWh\). A typical heat pump–powered water heater has a COP of 3.3 but costs about \($800\) more to install. Determine how many years it will take for the heat pump water heater to pay for its cost differential from the energy it saves. Equation Transcription: Text Transcription: $800

Problem 147P The kitchen, bath, and other ventilation fans in a house should be used sparingly since these fans can discharge a houseful of warmed or cooled air in just one hour. Consider a 200-m2 house whose ceiling height is 2.8 m. The house is heated by a 96 percent efficient gas heater and is maintained at 22°C and 92 kPa. If the unit cost of natural gas is $1.20/therm (1 therm = 105,500 kJ), determine the cost of energy “vented out” by the fans in 1 h. Assume the average outdoor temperature during the heating season to be 5°C.

Problem 145P A homeowner is trying to decide between a high efficiency natural gas furnace with an efficiency of 97 percent and a ground-source heat pump with a COP of 3.5. The unit costs of electricity and natural gas are $0.115/kWh and $1.42/therm (1 therm = 105,500 kJ). Determine which system will have a lower energy cost.

Problem 146P The “Energy Guide” label on a washing machine indicates that the washer will use $85 worth of hot water per year if the water is heated by an electric water heater at an electricity rate of $0.113/kWh. If the water is heated from 12 to 55°C, determine how many liters of hot water an average family uses per week. Disregard the electricity consumed by the washer, and take the efficiency of the electric water heater to be 91 percent.

Problem 148P Repeat Prob. 6–147 for the air-conditioning cost in a dry climate for an outdoor temperature of 33°C. Assume the COP of the air-conditioning system to be 2.1, and the unit cost of electricity to be $0.12/kWh. (Reference Prob. 6–147) The kitchen, bath, and other ventilation fans in a house should be used sparingly since these fans can discharge a houseful of warmed or cooled air in just one hour. Consider a 200-m2 house whose ceiling height is 2.8 m. The house is heated by a 96 percent efficient gas heater and is maintained at 22°C and 92 kPa. If the unit cost of natural gas is $1.20/therm (1 therm = 105,500 kJ), determine the cost of energy “vented out” by the fans in 1 h. Assume the average outdoor temperature during the heating season to be 5°C.

A heat pump with refrigerant-\(134a\) as the working fluid is used to keep a space at \(25^{\circ} \mathrm{C}\) by absorbing heat from geothermal water that enters the evaporator at \(60^{\circ} \mathrm{C}\) at a rate of \(0.065 kg/s\) and leaves at \(408^{\circ} \mathrm{C}\). Refrigerant enters the evaporator at \(12^{\circ} \mathrm{C}\) with a quality of 15 percent and leaves at the same pressure as saturated vapor. If the compressor consumes \(1.6 kW\) of power, determine (a) the mass flow rate of the refrigerant, (b) the rate of heat supply, (c) the COP, and (d) the minimum power input to the compressor for the same rate of heat supply. Equation Transcription: 25°C 12°C 408°C 60°C Text Transcription: 0.065 kg/s 1.6 kW 25 degree celsius 12 degree celsius 408 degree celsius 60 degree celsius

Problem 152P Prove that the COP of all completely reversible refrigerators must be the same when the reservoir temperatures are the same.

Cold water at \(10^{\circ} \mathrm{C}\) enters a water heater at the rate of \(0.02 \mathrm{~m}^{3} / \mathrm{min}\) and leaves the water heater at \(50^{\circ} \mathrm{C}\). The water heater receives heat from a heat pump that receives heat from a heat source at \(0^{\circ} \mathrm{C}\). (a) Assuming the water to be an incompressible liquid that does not change phase during heat addition, determine the rate of heat supplied to the water, in \(kJ/s\). (b) Assuming the water heater acts as a heat sink having an average temperature of \(30^{\circ} \mathrm{C}\), determine the minimum power supplied to the heat pump, in \(kW\). Equation Transcription: 10°C 0°C 30°C Text Transcription: 10 degree celsius 0.02 m3/min 0 degree celsius 30 degree celsius kJ/s W

When discussing Carnot engines, it is assumed that the engine is in thermal equilibrium with the source and the sink during the heat addition and heat rejection processes, respectively. That is, it is assumed that \(T_{H}^{*}=T_{H}\) and \(T_{L}^{*}=T_{L}\) so that there is no external irreversibility. In that case, the thermal efficiency of the Carnot engine is \(\eta_{C}=1-T_{L} / T_{H}\). In reality, however, we must maintain a reasonable temperature difference between the two heat transfer media in order to have an acceptable heat transfer rate through a finite heat exchanger surface area. The heat transfer rates in that case can be expressed as \(\dot{Q}_{H}=\left(h_{A}\right)_{H}\left(T_{H}-T_{H}^{*}\right) \dot{Q}_{L}=(h A)_{L}\left(T_{L}^{*}-T_{L}\right)\) where \(h\) and \(A\) are the heat transfer coefficient and heat transfer surface area, respectively. When the values of \(h, A, T_{H}\) and \(T_{L}\) are fixed, show that the power output will be a maximum when \(\frac{T_{L}^{*}}{T_{H}^{*}}=\left(\frac{T_{L}}{T_{H}}\right)^{1 / 2}\) Also, show that the maximum net power output in this case is \(\dot{W}_{C, \max }=\frac{(h A)_{H} T_{H}}{1+(h A)_{H} /(h A)_{L}}\left[1-\left(\frac{T_{L}}{T_{H}}\right)^{1 / 2}\right]^{2}\) Equation Transcription: Text Transcription: T_H^*=T_H T_L^*=T_L \eta_{C}=1-T_{L} / T_{H} \dot{Q}_{H}=\left(h_{A}\right)_{H}\left(T_{H}-T_{H}^{*}\right) \dot{Q}_{L}=(h A)_{L}\left(T_{L}^{*}-T_{L}\right) h,A,T_H \frac{T_{L}^{*}}{T_{H}^{*}}=\left(\frac{T_{L}}{T_{H}}\right)^{1 / 2} \dot{W}_{C, \max }=\frac{(h A)_{H} T_{H}}{1+(h A)_{H} /(h A)_{L}}\left[1-\left(\frac{T_{L}}{T_{H}}\right)^{1 / 2}\right]^{2}

Show that \(\mathrm{COP}_{\mathrm{HP}}=\mathrm{COP}_{\mathrm{R}}+1\) when both the heat pump and the refrigerator have the same \(Q_{L}\) and \(Q_{H}\) values. Equation Transcription: Text Transcription: COP_HP=COP_R+1 Q_L Q_H

Problem 156P A 2.4-m high 200-m2 house is maintained at 22°C by an air-conditioning system whose COP, is 3.2. It is estimated that the kitchen, bath, and other ventilating fans of the house discharge a houseful of conditioned air once every hour. If the average outdoor temperature is 32°C, the density of air is 1.20 kg/m3, and the unit cost of electricity is $0.10/kWh, the amount of money “vented out” by the fans in 10 hours is (a) $0.50 ________________ (b) $1.60 ________________ (c)$5.00 ________________ (d) $11.00 ________________ (e) $16.00

A heat pump receives heat from a lake that has an average wintertime temperature of \(6^{\circ} \mathrm{C}\) and supplies heat into a house having an average temperature of \(23^{\circ} \mathrm{C}\). (a) If the house loses heat to the atmosphere at the rate of \(52,000\ kJ/h\), determine the minimum power supplied to the heat pump, in \(kW\). (b) A heat exchanger is used to transfer the energy from the lake water to the heat pump. If the lake water temperature decreases by \(5^{\circ} \mathrm{C}\) as it flows through the lake water-to-heat pump heat exchanger, determine the minimum mass flow rate of lake water, in \(kg/s\). Neglect the effect of the lake water pump. Equation Transcription: 6°C 23°C 5°C Text Transcription: 6 degree celsius 23 degree celsius 5 degree celsius 52,000 kJ/h kg/s

Problem 157P The drinking water needs of an office are met by cooling tab water in a refrigerated water fountain from 23 to 6°C at an average rate of 10 kg/h. If the COP of this refrigerator is 3.1, the required power input to this refrigerator is (a) 197W ________________ (b) 612W ________________ (c) 64W ________________ (d) 109W ________________ (e) 403W

Problem 153P A Carnot heat engine is operating between a source at TH and a sink at TL. If it is desired to double the thermal efficiency of this engine,- what should the new source temperature be? Assume the sink temperature is held constant.

Problem 159P A heat pump is absorbing heat from the cold outdoors at 5°C and supplying heat to a house at 25°C at a rate of 18,000 kJ/h. If the power consumed by the heat pump is 1.9 kW, the coefficient of performance of the heat pump is (a) 1.3 ________________ (b) 2.6 ________________ (c) 3 ________________ (d) 3.8 ________________ (e) 13.9

Problem 158P The label on a washing machine indicates that the washer will use $85 worth of hot water if the water is heated by a 90 percent efficient electric heater at an electricity rate of $0.09/kWh. If the water is heated from 18 to 45°C, the amount of hot water an average family uses per year is (a) 11.6 tons ________________ (b) 15.8 tons ________________ (c) 27.1 tons ________________ (d) 30.1 tons ________________ (e) 33.5 tons

Problem 160P A heat engine cycle is executed with steam in the saturation dome. The pressure of steam is 1 MPa during heat addition, and 0.4 MPa during heat rejection. The highest possible efficiency of this heat engine is (a) 8.0% ________________ (b) 15.6% ________________ (c) 20.2% ________________ (d) 79.8% ________________ (e) 100%

Problem 162P A heat pump cycle is executed with R-134a under the saturation dome between the pressure limits of 1.4 and 0.16 MPa. The maximum coefficient of performance of this heat pump is t (a) 1.1 ________________ (b) 3.8 ________________ (c) 4.8 ________________ (d) 5.3 ________________ (e) 2.9

Problem 161P A heat engine receives heat from a source at 1000°C and rejects the waste heat to a sink at 50°C. If heat is supplied to this engine at a rate of 100 kJ/s, the maximum power this heat engine can produce is (a) 25.4kW ________________ (b) 55.4kW ________________ (c) 74.6kW ________________ (d) 95.0kW ________________ (e) 100kW

Problem 163P A refrigeration cycle is executed with R-134a under the saturation dome between the pressure limits of 1.6 and 0.2 MPa. If the power consumption of the refrigerator is 3 kW, the maximum rate of heat removal from the cooled space)f this refrigerator is (a) 0.45kJ/s. ________________ (b) 0.78 kJ/s ________________ (c) 3.0 kJ/s ________________ (d) 11.6kJ/s ________________ (e) 14.6 kJ/s

Problem 164P A heat pump with a COP of 3.2 is used to heat a perfectly sealed house (no air leaks). The entire mass within the house (air, furniture, etc.) is equivalent to 1200 kg of air. When running, the heat pump consumes electric power at a rate of 5 kW. The temperature of the house was 7°C when the heat pump was turned on. If heat transfer through the envelope of the house (walls, roof, etc.) is negligible, the length of time the heat pump must run to raise the temperature of the entire contents of the house to 22°C is (a) 13.5 min ________________ (b) 43.1 min ________________ (c) 138min ________________ (d) 18.8 min ________________ (e) 808 min

Problem 166P An air-conditioning system operating on the reversed Carnot cycle is required to remove heat from the house at a rate of 32 kJ/s to maintain its temperature constant at 20°C. If the temperature of the outdoors is 35°C, the power required to operate this air-conditioning system is (a) 0.58kW ________________ (b) 3.20kW ________________ (c) 1.56kW ________________ (d) 2.26kW ________________ (e) 1.64kW

Problem 165P A heat engine cycle is executed with steam in the saturation dome between the pressure limits of 7 and 2 MPa. If heat is supplied to the heat engine at a rate of 150 kJ/s, the maximum power output of this heat engine is (a) 8.1kW ________________ (b) 19.7kW ________________ (c) 38.6kW ________________ (d) 107 kW ________________ (e) 130 kW

Problem 168P Two Carnot heat engines are operating in series such that the heat sink of the first engine serves as the heat source of the second one. If the source temperature of the first engine is 1300 K and the sink temperature of the second engine is 300 K and the thermal efficiencies of both engines are the same, the temperature of the intermediate reservoir is (a) 625 K ________________ (b) 800K ________________ (c) 860K ________________ (d) 453 K ________________ (e) 758 K

Problem 169P Consider a Carnot refrigerator and a Carnot heat pump operating between the same two thermal energy reservoirs. If the COP of the refrigerator is 3.4, the COP of the heat pump is (a) 1. 7 ________________ (b) 2.4 ________________ (c) 3.4 ________________ (d) 4.4 ________________ (e) 5. 0

Problem 167P A refrigerator is removing heat from a cold medium at 3°C at a rate of 7200 kJ/h and rejecting the waste heat to a medium at 3°C.(If the coefficient of performance of the refrigerator is 2, the power consumed by the refrigerator is (a) 0.1kW ________________ (b) 0.5kW ________________ (c) 1.0kW ________________ (d) 2.0kW ________________ (e) 5.0kW

Problem 171P A window air conditioner that consumes 1 kW of electricity when running and has a coefficient of performance of 3 is placed in the middle of a room, and is plugged in. The rate of cooling or heating this air conditioner will provide to the air in the room when running is (a) 3 kJ/s, cooling ________________ (b) 1 kJ/s, cooling ________________ (c) 0.33 kJ/s, heating ________________ (d) 1 kJ/s, heating ________________ (e) 3 kJ/s, heating

Problem 172P Devise a Carnot heat engine using steady-flow components, and describe how the Carnot cycle is executed in that engine. What happens when the directions of heat and work interactions are reversed?

Problem 170P A typical new household refrigerator consumes about 680 kWh of electricity per year and has a coefficient of performance of 1.4. The amount of heat removed by this refrigerator from the refrigerated space per year is (a) 952 MJ/yr ________________ (b) 1749 MJ/yr ________________ (c) 2448 MJ/yr ________________ (d) 3427 MJ/yr ________________ (e) 4048 MJ/yr

Problem 23P An automobile engine consumes fuel at a rate of 22 L/h and delivers 55 kW of power to the wheels. If the fuel has a heating value of 44,000 kJ/kg and a density of 0.8 g/cm3, determine the efficiency of this engine.

Problem 24P In 2001, the United States produced 51 percent of its electricity in the amount of 1.878 X 1012 kWh from coal-fired power plants. Taking the average thermal efficiency to be 34 percent, determine the amount of thermal energy rejected by the coal-fired power plants in»the United States that year.

Problem 6.61 C Show that the processes that use work for mixing are irreversible by considering an adiabatic system whose contents are stirred by turning a paddle wheel inside the system (e.g, stirring a cake mix with an electric mixer).

Problem 6.62C Why does a non quasi-equilibrium compression process require a larger work input than the corresponding quasi equilibrium one?

Problem 6.63 Why does a nonquasi-equilibrium expansion process deliver less work than the corresponding quasi-equilibrium one

How do you distinguish between internal and external irreversibilities?

Is a reversible expansion or compression process necessarily quasi-equilibrium? Is a quasi-equilibrium expansion or compression process necessarily reversible? Explain.

Why are engineers interested in reversible processes even though they can never be achieved?

What are the four processes that make up the carnot cycle?

What are the two statements known as the carnot principles?

Is it possible to develop (a) an actual and (b) a reversible heat-engine cycle that is more efficient than a Carnot cycle operating between the same temperature limits? Explain

Baseboard heaters are basically electric resistance heaters and are frequently used in space heating. A home owner claims that her 5-year-old baseboard heaters have a conversion efficiency of 100 percent. Is this claim in violation of any thermodynamic laws? Explain.

Does a heat engine that has a thermal efficiency of 100 percent necessarily violate (a) the first law and (b) the second law of thermodynamics? Explain.

In the absence of any friction and other irreversibilities, can a heat engine have an efficiency of 100 percent? Explain.

Are the efficiencies of all the work-producing devices, including the hydroelectric power plants, limited by the KelvinPlanck statement of the second law? Explain.

Consider a pan of water being heated (a) by placing it on an electric range and (b) by placing a heating element in the water. Which method is a more efficient way of heating water? Explain.

A steam power plant receives heat from a furnace at a rate of . Heat losses to the surrounding air from the steam as it passes through the pipes and other components are estimated to be about . If the waste heat is transferred to the cooling water at a rate of , determine (a) net power output and (b) the thermal efficiency of this power plant.

A car engine with a power output of has a thermal efficiency of 28 percent. Determine the rate of fuel consumption if the heating value of the fuel is .

A heat engine has a heat input of and a thermal efficiency of 40 percent. Calculate the power it will produce, in hp.

The thermal efficiency of a general heat engine is 35 percent, and it produces 60 hp. At what rate is heat transferred to this engine, in ?

A a steam power plant, which is cooled by a nearby river, has a thermal efficiency of 40 percent. Determine the rate of heat transfer to the river water. Will the actual heat transfer rate be higher or lower than this value? Why?

A heat engine that pumps water out of an underground mine accepts of heat and produces of work. How much heat does it reject, in ?

A heat engine with a thermal efficiency of 45 percent rejects of heat. How much heat does it receive?

A steam power plant with a power output of consumes coal at a rate of . If the heating value of the coal is , determine the overall efficiency of this plant.

An automobile engine consumes fuel at a rate of 22 L/h and delivers 55 kW of power to the wheels. If the fuel has a heating value of 44,000 kJ/kg and a density of 0.8 g/cm3 , determine the efficiency of this engine.

In 2001, the United States produced 51 percent of its electricity in the amount of 1.878 3 1012 kWh from coalfired power plants. Taking the average thermal efficiency to be 34 percent, determine the amount of thermal energy rejected by the coal-fired power plants in the United States that year.

Solar energy stored in large bodies of water, called solar pounds, is being used to generate electricity. If such a solar power plant has an efficiency of 3 percent and a net power output of 180 kW, determine the average value of the required solar energy collection rate, in Btu/h.

A coal-burning steam power plant produces a net power of 300 MW with an overall thermal efficiency of 32 percent. The actual gravimetric airfuel ratio in the furnace is calculated to be 12 kg air/kg fuel. The heating value of the coal is 28,000 kJ/kg. Determine (a) the amount of coal consumed during a 24-hour period and (b) the rate of air flowing through the furnace.

An Ocean Thermal Energy Conversion (OTEC) power plant built in Hawaii in 1987 was designed to operate between the temperature limits of 868F at the ocean surface and 418F at a depth of 2100 ft. About 13,300 gpm of cold seawater was to be pumped from deep ocean through a 40-indiameter pipe to serve as the cooling medium or heat sink. If the cooling water experiences a temperature rise of 68F and the thermal efficiency is 2.5 percent, determine the amount of power generated. Take the density of seawater to be 64 lbm/ft3 .

What is the difference between a refrigerator and a heat pump?

What is the difference between a refrigerator and an air conditioner?

In a refrigerator, heat is transferred from a lowertemperature medium (the refrigerated space) to a highertemperature one (the kitchen air). Is this a violation of the second law of thermodynamics? Explain.

A heat pump is a device that absorbs energy from the cold outdoor air and transfers it to the warmer indoors. Is this a violation of the second law of thermodynamics? Explain.

Define the coefficient of performance of a refrigerator in words. Can it be greater than unity?

Define the coefficient of performance of a heat pump in words. Can it be greater than unity?

A heat pump that is used to heat a house has a COP of 2.5. That is, the heat pump delivers 2.5 kWh of energy to the house for each 1 kWh of electricity it consumes. Is this a violation of the first law of thermodynamics? Explain.

A refrigerator has a COP of 1.5. That is, the refrigerator removes 1.5 kWh of energy from the refrigerated space for each 1 kWh of electricity it consumes. Is this a violation of the first law of thermodynamics? Explain.

What is the Clausius expression of the second law of thermodynamics?

Show that the KelvinPlanck and the Clausius expressions of the second law are equivalent.

Determine the COP of a refrigerator that removes heat from the food compartment at a rate of 5040 kJ/h for each kW of power it consumes. Also, determine the rate of heat rejection to the outside air.

Determine the COP of a heat pump that supplies energy to a house at a rate of 8000 kJ/h for each kW of electric power it draws. Also, determine the rate of energy absorption from the outdoor air.

A residential heat pump has a coefficient of performance of 2.4. How much heating effect, in Btu/h, will result when 5 hp is supplied to this heat pump?

A refrigerator used to cool a computer requires 1.2 kW of electrical power and has a COP of 1.8. Calculate the cooling effect of this refrigerator, in kW.

An air conditioner removes heat steadily from a house at a rate of 750 kJ/min while drawing electric power at a rate of 6 kW. Determine (a) the COP of this air conditioner and (b) the rate of heat transfer to the outside air.

A food department is kept at 2128C by a refrigerator in an environment at 308C. The total heat gain to the food department is estimated to be 3300 kJ/h and the heat rejection in the condenser is 4800 kJ/h. Determine the power input to the compressor, in kW and the COP of the refrigerator.

A household refrigerator that has a power input of 450 W and a COP of 1.5 is to cool 5 large watermelons, 10 kg each, to 88C. If the watermelons are initially at 288C, determine how long it will take for the refrigerator to cool them. The watermelons can be treated as water whose specific heat is 4.2 kJ/kg8C. Is your answer realistic or optimistic? Explain.

When a man returns to his well-sealed house on a summer day, he finds that the house is at 358C. He turns on the air conditioner, which cools the entire house to 208C in 30 min. If the COP of the air-conditioning system is 2.8, determine the power drawn by the air conditioner. Assume the entire mass within the house is equivalent to 800 kg of air for which cv 5 0.72 kJ/kg8C and cp 5 1.0 kJ/kg8C.

Reconsider Prob. 645. Using EES (or other) software, determine the power input required by the air conditioner to cool the house as a function for airconditioner EER ratings in the range 5 to 15. Discuss your results and include representative costs of air-conditioning units in the EER rating range.

A heat pump with a COP of 2.5 supplies ener gy to a house at a rate of 60,000 Btu/h. Determine (a) the electric power drawn by the heat pump and (b) the rate of heat absorption from the outside air.

Bananas are to be cooled from 24 to 138C at a rate of 215 kg/h by a refrigeration system. The power input to the refrigerator is 1.4 kW. Determine the rate of cooling, in kJ/ min, and the COP of the refrigerator. The specific heat of banana above freezing is 3.35 kJ/kg8C.

A heat pump is used to maintain a house at a constant temperature of 238C. The house is losing heat to the outside air through the walls and the windows at a rate of 85,000 kJ/h while the energy generated within the house from people, lights, and appliances amounts to 4000 kJ/h. For a COP of 3.2, determine the required power input to the heat pump.

Water enters an ice machine at 558F and leaves as ice at 258F. If the COP of the ice machine is 2.4 during this operation, determine the required power input for an ice production rate of 28 lbm/h. (169 Btu of energy needs to be removed from each lbm of water at 558F to turn it into ice at 258F.)

A household refrigerator runs one-fourth of the time and removes heat from the food compartment at an average rate of 800 kJ/h. If the COP of the refrigerator is 2.2, determine the power the refrigerator draws when running.

A heat pump used to heat a house runs about onethird of the time. The house is losing heat at an average rate of 22,000 kJ/h. If the COP of the heat pump is 2.8, determine the power the heat pump draws when running.

Consider an office room that is being cooled adequately by a 12,000 Btu/h window air conditioner. Now it is decided to convert this room into a computer room by installing several computers, terminals, and printers with a total rated power of 8.4 kW. The facility has several 7000 Btu/h air conditioners in storage that can be installed to meet the additional cooling requirements. Assuming a usage factor of 0.4 (i.e., only 40 percent of the rated power will be consumed at any given time) and additional occupancy of seven people, each generating heat at a rate of 100 W, determine how many of these air conditioners need to be installed to the room.

Consider a building whose annual air-conditioning load is estimated to be 40,000 kWh in an area where the unit cost of electricity is $0.10/kWh. Two air conditioners are considered for the building. Air conditioner A has a seasonal average COP of 2.3 and costs $5500 to purchase and install. Air conditioner B has a seasonal average COP of 3.6 and costs $7000 to purchase and install. All else being equal, determine which air conditioner is a better buy.

Refrigerant-134a enters the condenser of a residential heat pump at 800 kPa and 358C at a rate of 0.018 kg/s and leaves at 800 kPa as a saturated liquid. If the compressor consumes 1.2 kW of power, determine (a) the COP of the heat pump and (b) the rate of heat absorption from the outside air.

An inventor claims to have developed a resistance heater that supplies 1.2 kWh of energy to a room for each kWh of electricity it consumes. Is this a reasonable claim, or has the inventor developed a perpetual-motion machine? Explain.

It is common knowledge that the temperature of air rises as it is compressed. An inventor thought about using this high-temperature air to heat buildings. He used a compressor driven by an electric motor. The inventor claims that the compressed hot-air system is 25 percent more efficient than a resistance heating system that provides an equivalent amount of heating. Is this claim valid, or is this just another perpetual-motion machine? Explain.

A cold canned drink is left in a warmer room where its temperature rises as a result of heat transfer. Is this a reversible process? Explain.

A block slides down an inclined plane with friction and no restraining force. Is this process reversible or irreversible? Justify your answer.

Show that processes involving rapid chemical reactions are irreversible by considering the combustion of a natural gas (e.g., methane) and air mixture in a rigid container.

Show that processes that use work for mixing are irreversible by considering an adiabatic system whose contents are stirred by turning a paddle wheel inside the system (e.g., stirring a cake mix with an electric mixer).

Why does a nonquasi-equilibrium compression process require a larger work input than the corresponding quasiequilibrium one?

Why does a nonquasi-equilibrium expansion process deliver less work than the corresponding quasi-equilibrium one?

How do you distinguish between internal and external irreversibilities?

Is a reversible expansion or compression process necessarily quasi-equilibrium? Is a quasi-equilibrium expansion or compression process necessarily reversible? Explain.

Why are engineers interested in reversible processes even though they can never be achieved?

What are the four processes that make up the Carnot cycle?

What are the two statements known as the Carnot principles?

Is it possible to develop (a) an actual and (b) a reversible heat-engine cycle that is more efficient than a Carnot cycle operating between the same temperature limits? Explain.

Somebody claims to have developed a new reversible heat-engine cycle that has a higher theoretical efficiency than the Carnot cycle operating between the same temperature limits. How do you evaluate this claim?

Somebody claims to have developed a new reversible heat-engine cycle that has the same theoretical efficiency as the Carnot cycle operating between the same temperature limits. Is this a reasonable claim?

Is there any way to increase the efficiency of a Carnot heat engine other than by increasing TH or decreasing TL?

Consider two actual power plants operating with solar energy. Energy is supplied to one plant from a solar pond at 808C and to the other from concentrating collectors that raise the water temperature to 6008C. Which of these power plants will have a higher efficiency? Explain.

From a work-production perspective, which is more valuable: (a) thermal energy reservoirs at 675 K and 325 K or (b) thermal energy reservoirs at 625 K and 275 K?

A heat engine is operating on a Carnot cycle and has a thermal efficiency of 55 percent. The waste heat from this engine is rejected to a nearby lake at 608F at a rate of 800 Btu/min. Determine (a) the power output of the engine and (b) the temperature of the source.

A Carnot heat engine receives 650 kJ of heat from a source of unknown temperature and rejects 250 kJ of it to a sink at 248C. Determine (a) the temperature of the source and (b) the thermal efficiency of the heat engine.

A Carnot heat engine operates between a source at 1000 K and a sink at 300 K. If the heat engine is supplied with heat at a rate of 800 kJ/min, determine (a) the thermal efficiency and (b) the power output of this heat engine.

A heat engine operates between a source at 4778C and a sink at 258C. If heat is supplied to the heat engine at a steady rate of 65,000 kJ/min, determine the maximum power output of this heat engine.

Reconsider Prob. 678. Using EES (or other) software, study the effects of the temperatures of the heat source and the heat sink on the power produced and the cycle thermal efficiency. Let the source temperature vary from 300 to 10008C, and the sink temperature to vary from 0 to 508C. Plot the power produced and the cycle efficiency against the source temperature for sink temperatures of 08C, 258C, and 508C, and discuss the results.

An inventor claims to have devised a cyclical engine for use in space vehicles that operates with a nuclear-fuel-generated energy source whose temperature is 920 R and a sink at 490 R that radiates waste heat to deep space. He also claims that this engine produces 4.5 hp while rejecting heat at a rate of 15,000 Btu/h. Is this claim valid?

A heat engine receives heat from a heat source at 12008C and has a thermal efficiency of 40 percent. The heat engine does maximum work equal to 500 kJ. Determine the heat supplied to the heat engine by the heat source, the heat rejected to the heat sink, and the temperature of the heat sink.

In tropical climates, the water near the surface of the ocean remains warm throughout the year as a result of solar energy absorption. In the deeper parts of the ocean, however, the water remains at a relatively low temperature since the suns rays cannot penetrate very far. It is proposed to take advantage of this temperature difference and construct a power plant that will absorb heat from the warm water near the surface and reject the waste heat to the cold water a few hundred meters below. Determine the maximum thermal efficiency of such a plant if the water temperatures at the two respective locations are 24 and 38C.

A well-established way of power generation involves the utilization of geothermal energythe energy of hot water that exists naturally undergroundas the heat source. If a supply of hot water at 1408C is discovered at a location where the environmental temperature is 208C, determine the maximum thermal efficiency a geothermal power plant built at that location can have.

A homeowner buys a new refrigerator and a new air conditioner. Which one of these devices would you expect to have a higher COP? Why?

A homeowner buys a new refrigerator with no freezer compartment and a deep freezer for the new kitchen. Which of these devices would you expect to have a lower COP? Why?

How can we increase the COP of a Carnot refrigerator?

In an effort to conserve energy in a heat-engine cycle, somebody suggests incorporating a refrigerator that will absorb some of the waste energy QL and transfer it to the energy source of the heat engine. Is this a smart idea? Explain

It is well established that the thermal efficiency of a heat engine increases as the temperature TL at which heat is rejected from the heat engine decreases. In an effort to increase the efficiency of a power plant, somebody suggests refrigerating the cooling water before it enters the condenser, where heat rejection takes place. Would you be in favor of this idea? Why?

It is well known that the thermal efficiency of heat engines increases as the temperature of the energy source increases. In an attempt to improve the efficiency of a power plant, somebody suggests transferring heat from the available energy source to a higher-temperature medium by a heat pump before energy is supplied to the power plant. What do you think of this suggestion? Explain.

During an experiment conducted in a room at 258C, a laboratory assistant measures that a refrigerator that draws 2 kW of power has removed 30,000 kJ of heat from the refrigerated space, which is maintained at 2308C. The running time of the refrigerator during the experiment was 20 min. Determine if these measurements are reasonable.

A Carnot refrigerator operates in a room in which the temperature is 228C and consumes 2 kW of power when operating. If the food compartment of the refrigerator is to be maintained at 38C, determine the rate of heat removal from the food compartment.

An air-conditioning system operating on the reversed Carnot cycle is required to transfer heat from a house at a rate of 750 kJ/min to maintain its temperature at 248C. If the outdoor air temperature is 358C, determine the power required to operate this air-conditioning system.

An inventor claims to have developed a heat pump that produces a 200-kW heating effect for a 293 K heated zone while only using 75 kW of power and a heat source at 273 K. Justify the validity of this claim.

A heat pump operates on a Carnot heat pump cycle with a COP of 8.7. It keeps a space at 248C by consuming 2.15 kW of power. Determine the temperature of the reservoir from which the heat is absorbed and the heating load provided by the heat pump.

A refrigerator is to remove heat from the cooled space at a rate of 300 kJ/min to maintain its temperature at 288C. If the air surrounding the refrigerator is at 258C, determine the minimum power input required for this refrigerator.

An inventor claims to have developed a refrigeration system that removes heat from the closed region at 2128C and transfers it to the surrounding air at 258C while maintaining a COP of 6.5. Is this claim reasonable? Why?

A heat pump is used to maintain a house at 258C by extracting heat from the outside air on a day when the outside air temperature is 48C. The house is estimated to lose heat at a rate of 110,000 kJ/h, and the heat pump consumes 4.75 kW of electric power when running. Is this heat pump powerful enough to do the job?

A completely reversible refrigerator operates between thermal energy reservoirs at 450 R and 540 R. How many kilowatts of power are required for this device to produce a 15,000-Btu/h cooling effect?

An air-conditioning system is used to maintain a house at 728F when the temperature outside is 908F. If this air-conditioning system draws 5 hp of power when operating, determine the maximum rate of heat removal from the house that it can accomplish.

A refrigerator operating on the reversed Carnot cycle has a measured work input of 200 kW and heat rejection of 2000 kW to a heat reservoir at 278C. Determine the cooling load supplied to the refrigerator, in kW, and the temperature of the heat source, in 8C.

A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at 2358C by rejecting waste heat to cooling water that enters the condenser at 188C at a rate of 0.25 kg/s and leaves at 268C. The refrigerant enters the condenser at 1.2 MPa and 508C and leaves at the same pressure subcooled by 58C. If the compressor consumes 3.3 kW of power, determine (a) the mass flow rate of the refrigerant, (b) the refrigeration load, (c) the COP, and (d) the minimum power input to the compressor for the same refrigeration load.

The performance of a heat pump degrades (i.e., its COP decreases) as the temperature of the heat source decreases. This makes using heat pumps at locations with severe weather conditions unattractive. Consider a house that is heated and maintained at 208C by a heat pump during the winter. What is the maximum COP for this heat pump if heat is extracted from the outdoor air at (a) 108C, (b) 258C, and (c) 2308C?

A heat pump is to be used for heating a house in winter. The house is to be maintained at 788F at all times. When the temperature outdoors drops to 258F, the heat losses from the house are estimated to be 70,000 Btu/h. Determine the minimum power required to run this heat pump if heat is extracted from (a) the outdoor air at 258F and (b) the well water at 508F.

A Carnot heat pump is to be used to heat a house and maintain it at 258C in winter. On a day when the average outdoor temperature remains at about 28C, the house is estimated to lose heat at a rate of 55,000 kJ/h. If the heat pump consumes 4.8 kW of power while operating, determine (a) how long the heat pump ran on that day; (b) the total heating costs, assuming an average price of 11/kWh for electricity; and (c) the heating cost for the same day if resistance heating is used instead of a heat pump.

A Carnot heat engine receives heat from a reservoir at 9008C at a rate of 800 kJ/min and rejects the waste heat to the ambient air at 278C. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at 258C and transfers it to the same ambient air at 278C. Determine (a) the maximum rate of heat removal from the refrigerated space and (b) the total rate of heat rejection to the ambient air.

A Carnot heat engine receives heat from a reservoir at 17008F at a rate of 700 Btu/min and rejects the waste heat to the ambient air at 808F. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at 208F and transfers it to the same ambient air at 808F. Determine (a) the maximum rate of heat removal from the refrigerated space and (b) the total rate of heat rejection to the ambient air.

The structure of a house is such that it loses heat at a rate of 3800 kJ/h per 8C difference between the indoors and outdoors. A heat pump that requires a power input of 4 kW is used to maintain this house at 248C. Determine the lowest outdoor temperature for which the heat pump can meet the heating requirements of this house.

An air-conditioner with refrigerant-134a as the working fluid is used to keep a room at 238C by rejecting the waste heat to the outdoor air at 348C. The room gains heat through the walls and the windows at a rate of 250 kJ/min while the heat generated by the computer, TV, and lights amounts to 900 W. The refrigerant enters the compressor at 400 kPa as a saturated vapor at a rate of 80 L/min and leaves at 1200 kPa and 708C. Determine (a) the actual COP, (b) the maximum COP, and (c) the minimum volume flow rate of the refrigerant at the compressor inlet for the same compressor inlet and exit conditions.

Derive an expression for the COP of a completely reversible refrigerator in terms of the thermal energy reservoir temperatures, TL and TH.

Why are todays refrigerators much more efficient than those built in the past?

Explain how you can reduce the energy consumption of your household refrigerator.

Why is it important to clean the condenser coils of a household refrigerator a few times a year? Also, why is it important not to block airflow through the condenser coils?

Someone proposes that the refrigeration system of a supermarket be overdesigned so that the entire air-conditioning needs of the store can be met by refrigerated air without installing any air-conditioning system. What do you think of this proposal?

Someone proposes that the entire refrigerator/freezer requirements of a store be met using a large freezer that supplies sufficient cold air at 2208C instead of installing separate refrigerators and freezers. What do you think of this proposal?

The Energy Guide label of a refrigerator states that the refrigerator will consume $170 worth of electricity per year under normal use if the cost of electricity is $0.125/kWh. If the electricity consumed by the lightbulb is negligible and the refrigerator consumes 400 W when running, determine the fraction of the time the refrigerator will run

The interior lighting of refrigerators is usually provided by incandescent lamps whose switches are actuated by the opening of the refrigerator door. Consider a refrigerator whose 40-W lightbulb remains on about 60 h per year. It is proposed to replace the lightbulb by an energy-efficient bulb that consumes only 18 W but costs $25 to purchase and install. If the refrigerator has a coefficient of performance of 1.3 and the cost of electricity is 8 cents per kWh, determine if the energy savings of the proposed lightbulb justify its cost.

It is commonly recommended that hot foods be cooled first to room temperature by simply waiting a while before they are put into the refrigerator to save energy. Despite this commonsense recommendation, a person keeps cooking a large pan of stew three times a week and putting the pan into the refrigerator while it is still hot, thinking that the money saved is probably too little. But he says he can be convinced if you can show that the money saved is significant. The average mass of the pan and its contents is 5 kg. The average temperature of the kitchen is 238C, and the average temperature of the food is 958C when it is taken off the stove. The refrigerated space is maintained at 38C, and the average specific heat of the food and the pan can be taken to be 3.9 kJ/kg8C. If the refrigerator has a coefficient of performance of 1.5 and the cost of electricity is 10 cents per kWh, determine how much this person will save a year by waiting for the food to cool to room temperature before putting it into the refrigerator.

It is often stated that the refrigerator door should be opened as few times as possible for the shortest duration of time to save energy. Consider a household refrigerator whose interior volume is 0.9 m3 and average internal temperature is 48C. At any given time, one-third of the refrigerated space is occupied by food items, and the remaining 0.6 m3 is filled with air. The average temperature and pressure in the kitchen are 208C and 95 kPa, respectively. Also, the moisture contents of the air in the kitchen and the refrigerator are 0.010 and 0.004 kg per kg of air, respectively, and thus 0.006 kg of water vapor is condensed and removed for each kg of air that enters. The refrigerator door is opened an average of 20 times a day, and each time half of the air volume in the refrigerator is replaced by the warmer kitchen air. If the refrigerator has a coefficient of performance of 1.4 and the cost of electricity is 11.5 cents per kWh, determine the cost of the energy wasted per year as a result of opening the refrigerator door. What would your answer be if the kitchen air were very dry and thus a negligible amount of water vapor condensed in the refrigerator?

An air-conditioning system is used to maintain a house at a constant temperature of 208C. The house is gaining heat from outdoors at a rate of 20,000 kJ/h, and the heat generated in the house from the people, lights, and appliances amounts to 8000 kJ/h. For a COP of 2.5, determine the required power input to this air-conditioning system.

A Carnot heat pump is used to heat and maintain a residential building at 758F. An energy analysis of the house reveals that it loses heat at a rate of 2500 Btu/h per 8F temperature difference between the indoors and the outdoors. For an outdoor temperature of 358F, determine (a) the coefficient of performance and (b) the required power input to the heat pump.

A heat engine receives heat from a heat source at 12008C and rejects heat to a heat sink at 508C. The heat engine does maximum work equal to 500 kJ. Determine the heat supplied to the heat engine by the heat source and the heat rejected to the heat sink.

A heat pump creates a heating effect of 32,000 Btu/h for a space maintained at 530 R while using 1.8 kW of electrical power. What is the minimum temperature of the source that satisfies the second law of thermodynamics?

A refrigeration system uses water-cooled condenser for rejecting the waste heat. The system absorbs heat from a space at 258F at a rate of 24,000 Btu/h. Water enters the condenser at 658F at a rate of 1.45 lbm/s. The COP of the system is estimated to be 1.9. Determine (a) the power input to the system, in kW, (b) the temperature of the water at the exit of the condenser, in 8F and (c) the maximum possible COP of the system. The specific heat of water is 1.0 Btu/bm8F.

A heat pump with a COP of 2.8 is used to heat an air-tight house. When running, the heat pump consumes 5 kW of power. If the temperature in the house is 78C when the heat pump is turned on, how long will it take for the heat pump to raise the temperature of the house to 228C? Is this answer realistic or optimistic? Explain. Assume the entire mass within the house (air, furniture, etc.) is equivalent to 1500 kg of air.

A promising method of power generation involves collecting and storing solar energy in large artificial lakes a few meters deep, called solar ponds. Solar energy is absorbed by all parts of the pond, and the water temperature rises everywhere. The top part of the pond, however, loses to the atmosphere much of the heat it absorbs, and as a result, its temperature drops. This cool water serves as insulation for the bottom part of the pond and helps trap the energy there. Usually, salt is planted at the bottom of the pond to prevent the rise of this hot water to the top. A power plant that uses an organic fluid, such as alcohol, as the working fluid can be operated between the top and the bottom portions of the pond. If the water temperature is 358C near the surface and 808C near the bottom of the pond, determine the maximum thermal efficiency that this power plant can have. Is it realistic to use 35 and 808C for temperatures in the calculations? Explain.

Consider a Carnot refrigeration cycle executed in a closed system in the saturated liquidvapor mixture region using 0.96 kg of refrigerant-134a as the working fluid. It is known that the maximum absolute temperature in the cycle is 1.2 times the minimum absolute temperature, and the net work input to the cycle is 22 kJ. If the refrigerant changes from saturated vapor to saturated liquid during the heat rejection process, determine the minimum pressure in the cycle.

Reconsider Prob. 6126. Using EES (or other) software, investigate the effect of the net work input on the minimum pressure. Let the work input vary from 10 to 30 kJ. Plot the minimum pressure in the refrigeration cycle as a function of net work input, and discuss the results.

Consider two Carnot heat engines operating in series. The first engine receives heat from the reservoir at 1400 K and rejects the waste heat to another reservoir at temperature T. The second engine receives this energy rejected by the first one, converts some of it to work, and rejects the rest to a reservoir at 300 K. If the thermal efficiencies of both engines are the same, determine the temperature T.

A Carnot heat engine receives heat at 900 K and rejects the waste heat to the environment at 300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at 2158C at a rate of 250 kJ/min and rejects it to the same environment at 300 K. Determine (a) the rate of heat supplied to the heat engine and (b) the total rate of heat rejection to the environment.

Reconsider Prob. 6129. Using EES (or other) software, investigate the effects of the heat engine source temperature, the environment temperature, and the cooled space temperature on the required heat supply to the heat engine and the total rate of heat rejection to the environment. Let the source temperature vary from 500 to 1000 K, the environment temperature vary from 275 to 325 K, and the cooled space temperature vary from 220 to 08C. Plot the required heat supply against the source temperature for the cooled space temperature of 2158C and environment temperatures of 275, 300, and 325 K, and discuss the results.

A heat engine operates between two reservoirs at 800 and 208C. One-half of the work output of the heat engine is used to drive a Carnot heat pump that removes heat from the cold surroundings at 28C and transfers it to a house maintained at 228C. If the house is losing heat at a rate of 62,000 kJ/h, determine the minimum rate of heat supply to the heat engine required to keep the house at 228C.

An inventor claims to have developed a refrigerator that maintains the refrigerated space at 408F while operating in a room where the temperature is 858F and that has a COP of 13.5. Is this claim reasonable?

An old gas turbine has an efficiency of 21 percent and develops a power output of 6000 kW. Determine the fuel consumption rate of this gas turbine, in L/min, if the fuel has a heating value of 42,000 kJ/kg and a density of 0.8 g/cm3

The COP of a refrigerator decreases as the temperature of the refrigerated space is decreased. That is, removing heat from a medium at a very low temperature will require a large work input. Determine the minimum work input required to remove 1 kJ of heat from liquid helium at 3 K when the outside temperature is 300 K.

Consider a Carnot heat-pump cycle executed in a steady-flow system in the saturated liquidvapor mixture region using refrigerant-134a flowing at a rate of 0.22 kg/s as the working fluid. It is known that the maximum absolute temperature in the cycle is 1.2 times the minimum absolute temperature, and the net power input to the cycle is 5 kW. If the refrigerant changes from saturated vapor to saturated liquid during the heat rejection process, determine the ratio of the maximum to minimum pressures in the cycle.

Replacing incandescent lights with energy-efficient fluorescent lights can reduce the lighting energy consumption to one-fourth of what it was before. The energy consumed by the lamps is eventually converted to heat, and thus switching to energy-efficient lighting also reduces the cooling load in summer but increases the heating load in winter. Consider a building that is heated by a natural gas furnace with an efficiency of 80 percent and cooled by an air conditioner with a COP of 3.5. If electricity costs $0.12/kWh and natural gas costs $1.40/therm (1 therm 5 105,500 kJ), determine if efficient lighting will increase or decrease the total energy cost of the building (a) in summer and (b) in winter.

A heat pump supplies heat energy to a house at the rate of 140,000 kJ/h when the house is maintained at 258C. Over a period of one month, the heat pump operates for 100 hours to transfer energy from a heat source outside the house to inside the house. Consider a heat pump receiving heat from two different outside energy sources. In one application the heat pump receives heat from the outside air at 08C. In a second application the heat pump receives heat from a lake having a water temperature of 108C. If electricity costs $0.105/kWh, determine the maximum money saved by using the lake water rather than the outside air as the outside energy source.

The cargo space of a refrigerated truck whose inner dimensions are 12 m 3 2.3 m 3 3.5 m is to be precooled from 258C to an average temperature of 58C. The construction of the truck is such that a transmission heat gain occurs at a rate of 120 W/8C. If the ambient temperature is 258C, determine how long it will take for a system with a refrigeration capacity of 11 kW to precool this truck.

The maximum flow rate of a standard shower head is about 3.5 gpm (13.3 L/min) and can be reduced to 2.75 gpm (10.5 L/min) by switching to a low-flow shower head that is equipped with flow controllers. Consider a family of four, with each person taking a 6-minute shower every morning. City water at 158C is heated to 558C in an oil water heater whose efficiency is 65 percent and then tempered to 428C by cold water at the T-elbow of the shower before being routed to the shower head. The price of heating oil is $2.80/gal and its heating value is 146,300 kJ/gal. Assuming a constant specific heat of 4.18 kJ/kg 8C for water, determine the amount of oil and money saved per year by replacing the standard shower heads by the low-flow ones.

Using EES (or other) software, determine the maximum work that can be extracted from a pond containing 105 kg of water at 350 K when the temperature of the surroundings is 300 K. Notice that the temperature of water in the pond will be gradually decreasing as energy is extracted from it; therefore, the efficiency of the engine will be decreasing. Use temperature intervals of (a) 5 K, (b) 2 K, and (c) 1 K until the pond temperature drops to 300 K. Also solve this problem exactly by integration and compare the results.

A refrigeration system is to cool bread loaves with an average mass of 350 g from 30 to 2108C at a rate of 1200 loaves per hour by refrigerated air at 2308C. Taking the average specific and latent heats of bread to be 2.93 kJ/kg8C and 109.3 kJ/kg, respectively, determine (a) the rate of heat removal from the breads, in kJ/h; (b) the required volume flow rate of air, in m3 /h, if the temperature rise of air is not to exceed 88C; and (c) the size of the compressor of the refrigeration system, in kW, for a COP of 1.2 for the refrigeration system.

The drinking water needs of a production facility with 20 employees is to be met by a bubbler type water fountain. The refrigerated water fountain is to cool water from 22 to 88C and supply cold water at a rate of 0.4 L per hour per person. Heat is transferred to the reservoir from the surroundings at 258C at a rate of 45 W. If the COP of the refrigeration system is 2.9, determine the size of the compressor, in W, that will be suitable for the refrigeration system of this water cooler.

A typical electric water heater has an efficiency of 95 percent and costs $350 a year to operate at a unit cost of electricity of $0.11/kWh. A typical heat pumppowered water heater has a COP of 3.3 but costs about $800 more to install. Determine how many years it will take for the heat pump water heater to pay for its cost differential from the energy it saves

Reconsider Prob. 6143. Using EES (or other) software, investigate the effect of the heat pump COP on the yearly operation costs and the number of years required to break even. Let the COP vary from 2 to 5. Plot the payback period against the COP and discuss the results.

A homeowner is trying to decide between a highefficiency natural gas furnace with an efficiency of 97 percent and a ground-source heat pump with a COP of 3.5. The unit costs of electricity and natural gas are $0.115/kWh and $1.42/therm (1 therm 5 105,500 kJ). Determine which system will have a lower energy cost.

The Energy Guide label on a washing machine indicates that the washer will use $85 worth of hot water per year if the water is heated by an electric water heater at an electricity rate of $0.113/kWh. If the water is heated from 12 to 558C, determine how many liters of hot water an average family uses per week. Disregard the electricity consumed by the washer, and take the efficiency of the electric water heater to be 91 percent.

The kitchen, bath, and other ventilation fans in a house should be used sparingly since these fans can discharge a houseful of warmed or cooled air in just one hour. Consider a 200-m2 house whose ceiling height is 2.8 m. The house is heated by a 96 percent efficient gas heater and is maintained at 228C and 92 kPa. If the unit cost of natural gas is $1.20/therm (1 therm 5 105,500 kJ), determine the cost of energy vented out by the fans in 1 h. Assume the average outdoor temperature during the heating season to be 58C.

Repeat Prob. 6147 for the air-conditioning cost in a dry climate for an outdoor temperature of 338C. Assume the COP of the air-conditioning system to be 2.1, and the unit cost of electricity to be $0.12/kWh.

A heat pump with refrigerant-134a as the working fluid is used to keep a space at 258C by absorbing heat from geothermal water that enters the evaporator at 608C at a rate of 0.065 kg/s and leaves at 408C. Refrigerant enters the evaporator at 128C with a quality of 15 percent and leaves at the same pressure as saturated vapor. If the compressor consumes 1.6 kW of power, determine (a) the mass flow rate of the refrigerant, (b) the rate of heat supply, (c) the COP, and (d) the minimum power input to the compressor for the same rate of heat supply.

Cold water at 108C enters a water heater at the rate of 0.02 m3 /min and leaves the water heater at 508C. The water heater receives heat from a heat pump that receives heat from a heat source at 08C. (a) Assuming the water to be an incompressible liquid that does not change phase during heat addition, determine the rate of heat supplied to the water, in kJ/s. (b) Assuming the water heater acts as a heat sink having an average temperature of 308C, determine the minimum power supplied to the heat pump, in kW.

A heat pump receives heat from a lake that has an average winter time temperature of 68C and supplies heat into a house having an average temperature of 238C. (a) If the house loses heat to the atmosphere at the rate of 52,000 kJ/h, determine the minimum power supplied to the heat pump, in kW. (b) A heat exchanger is used to transfer the energy from the lake water to the heat pump. If the lake water temperature decreases by 58C as it flows through the lake water-to-heat pump heat exchanger, determine the minimum mass flow rate of lake water, in kg/s. Neglect the effect of the lake water pump.

Prove that the COP of all completely reversible refrigerators must be the same when the reservoir temperatures are the same.

A Carnot heat engine is operating between a source at TH and a sink at TL. If it is desired to double the thermal efficiency of this engine, what should the new source temperature be? Assume the sink temperature is held constant.

When discussing Carnot engines, it is assumed that the engine is in thermal equilibrium with the source and the sink during the heat addition and heat rejection processes, respectively. That is, it is assumed that T* H 5 TH and T* L 5 TL so that there is no external irreversibility. In that case, the thermal efficiency of the Carnot engine is hC 5 1 2 TL/TH. In reality, however, we must maintain a reasonable temperature difference between the two heat transfer media in order to have an acceptable heat transfer rate through a finite heat exchanger surface area. The heat transfer rates in that case can be expressed as Q # H 5 (hA)H(TH 2 T * H) Q # L 5 (hA)L(T * L 2 TL) where h and A are the heat transfer coefficient and heat transfer surface area, respectively. When the values of h, A, TH, and TL are fixed, show that the power output will be a maximum when T * L T * H 5 a TL TH b 1/2 Also, show that the maximum net power output in this case is W # C,max 5 (hA)HTH 1 1 (hA)H/(hA)L c1 2 a TL TH b 1/2 d

Show that COPHP 5 COPR 1 1 when both the heat pump and the refrigerator have the same QL and QH values.

2.4-m high 200-m2 house is maintained at 228C by an air-conditioning system whose COP is 3.2. It is estimated that the kitchen, bath, and other ventilating fans of the house discharge a houseful of conditioned air once every hour. If the average outdoor temperature is 328C, the density of air is 1.20 kg/m3 , and the unit cost of electricity is $0.10/kWh, the amount of money vented out by the fans in 10 hours is (a) $0.50 (b) $1.60 (c) $5.00 (d) $11.00 (e) $16.00

The drinking water needs of an office are met by cooling tab water in a refrigerated water fountain from 23 to 68C at an average rate of 10 kg/h. If the COP of this refrigerator is 3.1, the required power input to this refrigerator is (a) 197 W (b) 612 W (c) 64 W (d) 109 W (e) 403 W

The label on a washing machine indicates that the washer will use $85 worth of hot water if the water is heated by a 90 percent efficient electric heater at an electricity rate of $0.09/kWh. If the water is heated from 18 to 458C, the amount of hot water an average family uses per year is (a) 11.6 tons (b) 15.8 tons (c) 27.1 tons (d) 30.1 tons (e) 33.5 tons

A heat pump is absorbing heat from the cold outdoors at 58C and supplying heat to a house at 258C at a rate of 18,000 kJ/h. If the power consumed by the heat pump is 1.9 kW, the coefficient of performance of the heat pump is (a) 1.3 (b) 2.6 (c) 3.0 (d) 3.8 (e) 13.9

A heat engine cycle is executed with steam in the saturation dome. The pressure of steam is 1 MPa during heat addition, and 0.4 MPa during heat rejection. The highest possible efficiency of this heat engine is (a) 8.0% (b) 15.6% (c) 20.2% (d) 79.8% (e) 100%

A heat engine receives heat from a source at 10008C and rejects the waste heat to a sink at 508C. If heat is supplied to this engine at a rate of 100 kJ/s, the maximum power this heat engine can produce is (a) 25.4 kW (b) 55.4 kW (c) 74.6 kW (d) 95.0 kW (e) 100 kW

A heat pump cycle is executed with R134a under the saturation dome between the pressure limits of 1.4 and 0.16 MPa. The maximum coefficient of performance of this heat pump is (a) 1.1 (b) 3.8 (c) 4.8 (d) 5.3 (e) 2.9

A refrigeration cycle is executed with R-134a under the saturation dome between the pressure limits of 1.6 and 0.2 MPa. If the power consumption of the refrigerator is 3 kW, the maximum rate of heat removal from the cooled space of this refrigerator is (a) 0.45 kJ/s (b) 0.78 kJ/s (c) 3.0 kJ/s (d) 11.6 kJ/s (e) 14.6 kJ/s

A heat pump with a COP of 3.2 is used to heat a perfectly sealed house (no air leaks). The entire mass within the house (air, furniture, etc.) is equivalent to 1200 kg of air. When running, the heat pump consumes electric power at a rate of 5 kW. The temperature of the house was 78C when the heat pump was turned on. If heat transfer through the envelope of the house (walls, roof, etc.) is negligible, the length of time the heat pump must run to raise the temperature of the entire contents of the house to 228C is (a) 13.5 min (b) 43.1 min (c) 138 min (d) 18.8 min (e) 808 min

A heat engine cycle is executed with steam in the saturation dome between the pressure limits of 7 and 2 MPa. If heat is supplied to the heat engine at a rate of 150 kJ/s, the maximum power output of this heat engine is (a) 8.1 kW (b) 19.7 kW (c) 38.6 kW (d) 107 kW (e) 130 kW

An air-conditioning system operating on the reversed Carnot cycle is required to remove heat from the house at a rate of 32 kJ/s to maintain its temperature constant at 208C. If the temperature of the outdoors is 358C, the power required to operate this air-conditioning system is (a) 0.58 kW (b) 3.20 kW (c) 1.56 kW (d) 2.26 kW (e) 1.64 kW

A refrigerator is removing heat from a cold medium at 38C at a rate of 7200 kJ/h and rejecting the waste heat to a medium at 308C. If the coefficient of performance of the refrigerator is 2, the power consumed by the refrigerator is (a) 0.1 kW (b) 0.5 kW (c) 1.0 kW (d) 2.0 kW (e) 5.0 kW

Two Carnot heat engines are operating in series such that the heat sink of the first engine serves as the heat source of the second one. If the source temperature of the first engine is 1300 K and the sink temperature of the second engine is 300 K and the thermal efficiencies of both engines are the same, the temperature of the intermediate reservoir is (a) 625 K (b) 800 K (c) 860 K (d) 453 K (e) 758 K

Consider a Carnot refrigerator and a Carnot heat pump operating between the same two thermal energy reservoirs. If the COP of the refrigerator is 3.4, the COP of the heat pump is (a) 1.7 (b) 2.4 (c) 3.4 (d) 4.4 (e) 5.0

A typical new household refrigerator consumes about 680 kWh of electricity per year and has a coefficient of performance of 1.4. The amount of heat removed by this refrigerator from the refrigerated space per year is (a) 952 MJ/yr (b) 1749 MJ/yr (c) 2448 MJ/yr (d) 3427 MJ/yr (e) 4048 MJ/yr

A window air conditioner that consumes 1 kW of electricity when running and has a coefficient of performance of 3 is placed in the middle of a room, and is plugged in. The rate of cooling or heating this air conditioner will provide to the air in the room when running is (a) 3 kJ/s, cooling (b) 1 kJ/s, cooling (c) 0.33 kJ/s, heating (d) 1 kJ/s, heating (e) 3 kJ/s, heating

Devise a Carnot heat engine using steady-flow components, and describe how the Carnot cycle is executed in that engine. What happens when the directions of heat and work interactions are reversed?

When was the concept of the heat pump conceived and by whom? When was the first heat pump built, and when were the heat pumps first mass-produced?

The sun supplies electromagnetic energy to the earth. It appears to have an effective temperature of approximately 5800 K. On a clear summer day in North America, the energy incident on a surface facing the sun is approximately 0.95 kW/m2 . The electromagnetic solar energy can be converted into thermal energy by being absorbed on a darkened surface. How might you characterize the work potential of the suns energy when it is to be used to produce work?

In the search to reduce thermal pollution and take advantage of renewable energy sources, some people have proposed that we take advantage of such sources as discharges from electrical power plants, geothermal energy, and ocean thermal energy. Although many of these sources contain an enormous amount of energy, the amount of work they are capable of producing is limited. How might you use the work potential to assign an energy quality to these proposed sources? Test your proposed energy quality measure by applying it to the ocean thermal source, where the temperature 30 m below the surface is perhaps 58C lower than at the surface. Apply it also to the geothermal water source, where the temperature 2 to 3 km below the surface is perhaps 1508C hotter than at the surface.

Using a thermometer, measure the temperature of the main food compartment of your refrigerator, and check if it is between 1 and 48C. Also, measure the temperature of the freezer compartment, and check if it is at the recommended value of 2188C.

Using a timer (or watch) and a thermometer, conduct the following experiment to determine the rate of heat gain of your refrigerator. First make sure that the door of the refrigerator is not opened for at least a few hours so that steady operating conditions are established. Start the timer when the refrigerator stops running and measure the time Dt1 it stays off before it kicks in. Then, measure the time Dt2 it stays on. Noting that the heat removed during Dt2 is equal to the heat gain of the refrigerator during Dt1 1 Dt2 and using the power consumed by the refrigerator when it is running, determine the average rate of heat gain for your refrigerator, in W. Take the COP (coefficient of performance) of your refrigerator to be 1.3 if it is not available.

Design a hydrocooling unit that can cool fruits and vegetables from 30 to 58C at a rate of 20,000 kg/h under the following conditions: The unit will be of flood type, which will cool the products as they are conveyed into the channel filled with water. The products will be dropped into the channel filled with water at one end and be picked up at the other end. The channel can be as wide as 3 m and as high as 90 cm. The water is to be circulated and cooled by the evaporator section of a refrigeration system. The refrigerant temperature inside the coils is to be 228C, and the water temperature is not to drop below 18C and not to exceed 68C. Assuming reasonable values for the average product density, specific heat, and porosity (the fraction of air volume in a box), recommend reasonable values for (a) the water velocity through the channel and (b) the refrigeration capacity of the refrigeration system.