Thermodynamics

326 | Thermodynamics°F temperature difference between the indoors and the outdoors.For an outdoor temperature of 35°F, determine (a) thecoefficient of performance and (b) the required power inputto the heat pump. Answers: (a) 13.4, (b) 2.93 hp6–128 A Carnot heat engine receives heat at 750 K andrejects the waste heat to the environment at 300 K. The entirework output of the heat engine is used to drive a Carnotrefrigerator that removes heat from the cooled space at15°C at a rate of 400 kJ/min and rejects it to the same environmentat 300 K. Determine (a) the rate of heat supplied tothe heat engine and (b) the total rate of heat rejection to theenvironment.6–129 Reconsider Prob. 6–128. Using EES (or other)software, investigate the effects of the heatengine source temperature, the environment temperature, andthe cooled space temperature on the required heat supply tothe 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 thecooled space temperature vary from 20 to 0°C. Plot therequired heat supply against the source temperature for thecooled space temperature of 15°C and environment temperaturesof 275, 300, and 325 K, and discuss the results.6–130 A heat engine operates between two reservoirs at 800and 20°C. One-half of the work output of the heat engine isused to drive a Carnot heat pump that removes heat from thecold surroundings at 2°C and transfers it to a house maintainedat 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 enginerequired to keep the house at 22°C.6–131 Consider a Carnot refrigeration cycle executed in aclosed system in the saturated liquid–vapor mixture regionusing 0.8 kg of refrigerant-134a as the working fluid. Themaximum and the minimum temperatures in the cycle are20°C and 8°C, respectively. It is known that the refrigerantis saturated liquid at the end of the heat rejection process, andthe net work input to the cycle is 15 kJ. Determine the fractionof the mass of the refrigerant that vaporizes during theheat addition process, and the pressure at the end of the heatrejection process.6–132 Consider a Carnot heat-pump cycle executed in asteady-flow system in the saturated liquid–vapor mixtureregion using refrigerant-134a flowing at a rate of 0.264 kg/sas the working fluid. It is known that the maximum absolutetemperature in the cycle is 1.25 times the minimum absolutetemperature, and the net power input to the cycle is 7 kW. Ifthe refrigerant changes from saturated vapor to saturated liquidduring the heat rejection process, determine the ratio ofthe maximum to minimum pressures in the cycle.6–133 A Carnot heat engine is operating between a sourceat T H and a sink at T L . If it is desired to double the thermalefficiency of this engine, what should the new source temperaturebe? Assume the sink temperature is held constant.6–134 When discussing Carnot engines, it is assumed thatthe engine is in thermal equilibrium with the source and thesink during the heat addition and heat rejection processes,**respectively. That is, it is assumed that T H T H and T L T Lso that there is no external irreversibility. In that case, the thermalefficiency of the Carnot engine is h C 1 T L /T H .In reality, however, we must maintain a reasonable temperaturedifference between the two heat transfer media in orderto have an acceptable heat transfer rate through a finite heatexchanger surface area. The heat transfer rates in that casecan be expressed aswhere h and A are the heat transfer coefficient and heat transfersurface area, respectively. When the values of h, A, T H ,and T Lare fixed, show that the power output will be a maximum whenAlso, show that the maximum net power output in thiscase isW # C,max Q # H 1hA2 H 1T H T H * 2Q # L 1hA2 L 1T * L T L 2*T LT a T 1>2Lb*H T H1hA2 H T Hc 1 a T 1>2 2Lb d1 1hA2 H >1hA2 L T HHeat sourceT H·Q HT*HHeat engine*T LT LHeat sink·Q LFIGURE P6–1346–135 Replacing incandescent lights with energy-efficientfluorescent lights can reduce the lighting energy consumptionto one-fourth of what it was before. The energy consumed bythe lamps is eventually converted to heat, and thus switchingto energy-efficient lighting also reduces the cooling load insummer but increases the heating load in winter. Consider abuilding that is heated by a natural gas furnace with an efficiencyof 80 percent and cooled by an air conditioner with aCOP of 3.5. If electricity costs $0.08/kWh and natural gascosts $1.40/therm, determine if efficient lighting will increase