A heat pump is an electrical device that heats a building by pumping heat in from the cold outside. In other words, it's the same as a refrigerator, but its purpose is to warm the hot reservoir rather than to cool the cold reservoir (even though it does both). Let us define the following standard symbols, all taken to be positive by convention:Th = temperature inside buildingTe = temperature outsideQh heat pumped into building in 1 day Qe = heat taken from outdoors in 1 dayW = electrical energy used by heat pump in 1 day Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Th and Te alone

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A heat pump is an electrical device that heats a building by pumping heat in from the cold outside. In other words, it's the same as a refrigerator, but its purpose is to warm the hot reservoir rather than to cool the cold reservoir (even though it does both). Let us define the following standard symbols, all taken to be positive by convention:
Th = temperature inside building
Te = temperature outside
Qh heat pumped into building in 1 day Qe = heat taken from outdoors in 1 day
W = electrical energy used by heat pump in 1 day

Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Th and Te alone 

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