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 Tc = temperature outside Oh = heat pumped into building in 1 day Oc = heat taken from outdoors in 1 day W = electrical energy used by heat pump in 1 day (a) Explain why the "coefficient of performance (COP) for a heat pump should be defined as Oh/W. (b) What relation among Oh, Oc and W is implied by energy conservation alone? Will energy conservation permit the COP to be greater than 1?
(c) Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Th and Tc alone.
(d) Explain why a heat pump is better than an electric furnace, which simply converts electrical work directly into heat. (Include some numerical estimates.)