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(a) Calculate the electric power required to maintain the interior temperature at 22.0°C if the power is used in electric resistance heaters that convert all the energy transferred in by electrical transmission into internal energy.(b) Calculate the electric power required to maintain the interior temperature at 22.0°C if the power is used to drive an electric motor that operates the compressor of a heat pump that has a coefficient of performance equal to 60.0% of the Carnot-cycle value.
Energy transfers by heat through the exterior walls and roof of a house at a rate of 5.07 x 10°/s - 5.07 kW when the interior temperature is 22.0°C and the outside temperature is -2.50°C. (a) Calculate the electric power required to maintain the interior temperature at 22.0°C if the power is used in electric resistance heaters that convert all the energy transferred in by electrical transmission into internal energy (b) Calculate the electric power required to maintain the interior temperature at 22.0°C if the power is used to drive an electric motor that operates the compressor of a heat pump that has a coefficient of performance equal to 60.0% of the Carnot-cycle value. Part 1 of 4. Conceptualize To maintain constant temperature, the house must take in energy by heat every second in order to replace the energy that the house is losing to the cold environment. The electric heater should be 100% efficient. Part 2 of 4 - Categorien Power is the rate of energy transfer per unit time, so we can find the power in each case by examining the energy input as heat required for the house as a nonisolated system in steady state conditions. Part 3 of 4 . Analyze (a) We know that P Pelectrie-Her/At, where Her stands for energy transmitted electrically. All of the energy transferred into the heater by electrical transmission becomes internal energy, so we have that Her Pelectie Ar 5.02 5.07 kW
Part 4 of 4 . Analyze (6) Now let Th stand for absolute temperature. For a Carnot heat pump, we have (COP) - AT For the actual value of this coefficient, we have COP - (0.600) w 191.10.17 At W / ΔΕ Therefore, to bring the required heat into the house requires input power W10, 1/A Pheat pump Ar COP w w Submit Skip you cannot come back)