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  Sheet (5) Part (I): Second Law of Thermodynamics and Thermal Energy Reservoirs: 1) Describe an imaginary process that satisfies the first law but violates the second law of thermodynamics. 2) Describe an imaginary process that satisfies the second law but violates the first law of thermodynamics. 3) Describe an imaginary process that violates both the first and the second laws of thermodynamics. 4) 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. 5) What is a thermal energy reservoir? Give some examples. 6) 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. 7) Consider the energy generated by a TV set. What is a suitable choice for a thermal energy reservoir? Part (II): Heat Engines and Thermal Efficiency: 8 ) Is it possible for a heat engine to operate without rejecting any waste heat to a low-temperature reservoir? Explain. 9 ) What are the characteristics of all heat engines?  10) What is the Kelvin-Planck expression of the second law of thermodynamics? 11) Does a heat engine that has a thermal efficiency of 100 % necessarily violate (a) the first law and (&) the second law of thermodynamics? Explain. 12) In the absence of any friction and other irreversibility, can a heat engine have an efficiency of 100 %? Explain.   13) 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 . [Answer: (a)35.3MW, (b) 45%]  14) A steam power plant with a power output of 150 MW consumes coal at a rate of 60 tons/hr. If the heating value of the coal is 30,000 kJ/kg, determine the overall efficiency of this plant. [Answer: 30%] 15) An automobile engine consumes fuel at a rate of 28L/h and delivers 60 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/cm ³  . determine the efficiency of this engine. [Answer: 21.9%] 16) A coal-burning steam power plant produces a net power of 300 MW with an overall thermal efficiency of 32 %. 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. [Answer: (a) 2.89 x 10  6   kg, (b) 402 kg/s] Part (III): Refrigerators and heat Pumps: 17) What is the difference between a refrigerator and a heat pump? 18) What is the difference between a refrigerator and an air conditioner? 19) Define the coefficient of performance of a refrigerator. Can it be greater than unity? 20) Define the coefficient of performance of a heat pump. Can it be greater than unity? 21) What is the Clausius expression of the second law of thermodynamics? 22) Show that the Kelvin-Planck and the Clausius expressions of the second law are equivalent. 23) A household refrigerator with a COP of 1.2 removes heat from the refrigerated space at a rate of 60 kJ/min. Determine (a) the electric power consumed by the refrigerator and (b) the rate of heat transfer to the kitchen air. [Answer: (a) 0.83 KW, (b) 110 KJ/min.] 24) Determine the COP of a heat pump that supplies energy to a house at a rate of 8000 kJ/hr for each kW of electric power it draws. Also, determine the rate of energy absorption from the outdoor air. [Answer: 2.22, 4400 KJ/h.] 25) A heat pump is used to maintain a house at a constant temperature of 23 ˚ C. The house is losing heat to the outside air through the walls and the windows at a rate of 60,000 kJ/hr while the energy generated within the house from people, lights, and appliances amounts to 4000 kJ/tr. For a COP of 2.5, determine the required power input to the heat pump. [Answer: 6.22 KW]  Part (IV): Reversible and Irreversible Processes: 26) 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. 27) Why are engineers interested in reversible processes even though they can never be achieved? 28) What are the four processes that make up the Carnot cycle? 29) What are the two statements known as the Carnot principles? 30) 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 temperatures limits. How do you evaluate this claim? 31) 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? 32) 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. Part (V): Carnot Heat Engines: 33) Is there any way to increase the efficiency of a Carnot heat engine other than by increasing T H , or decreasing ,T L , 34) 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.  Answers: [(a) 70%, (b) 9.33 kW.] 35) An innovative 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. [Answer: 29 1 %]  Part (VI): Carnot Refrigerators and Heat Pumps: 36) How can we increase the COP of a Carnot refrigerator? 37) What is the highest COP that a refrigerator operating between temperature levels T L  and T H  can have? 38) A refrigerator is to remove heat from the cooled space at a rate of 300kJ/min to maintain its temperature at -8 ˚ C.If the air surrounding the refrigerator is at 25 ˚ C, determine the minimum power input required for this refrigerator.  [Answer: 0.623]   39) 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. [Answer: 0.46]   40) A Carnot refrigerator operates in a room in which the temperature is 25 ˚ C. The refrigerator consumes 500 W of power when operating and has a COP of 4.5. Determine (a) the rate of heat removal from the refrigerated space and (b) the temperature of the refrigerated space.  Answers: [(a) 135KJ/min., (b) -29.2 ˚   C]   41) The structure of a house is such that it loses heat at a rate of 5400 kJ/h per ˚ C difference between the indoors and outdoors. A heat pump that requires a power input of 6 kW is used to maintain this house at 2l ˚ C. Determine the lowest outdoor temperature for which the heat pump can meet the heating requirements of this house.  Answers: [ -13.3 ˚   C] 42) A Carnot heat pump is to be used to heat a house and maintain it at 20 ˚ C in winter. On a day when the average outdoor temperature remains at about 2 ˚ C, the house is estimated to lose heat at a rate of 82,000 kJ/h. If the heat pump consumes 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 8.5 ₵ /kWh for electricity; and (c) the heating cost for the same day if resistance heating is used instead of a heat pump.  Answers: [(a) 4.19 h, (b)$ 2.85 kW, (c) $46.47] 43) 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.    Answers: [(a) 4982 KJ/min, (b) 5682 KJ/min]

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