Heat pumps and refrigerators are heat engines running in reverse; a work input w causes the system to absorb heat qcfrom a cold reservoir at Tc and emit heat −qH into a hot reservoir at Th. The coefficient of performance K of a refrigerator is qc/w, and the coefficient of performance ε of a heat pump is −qH/w. (a) For reversible Carnot-cycle refrigerators and heat pumps, express K and ε in terms of Tc and TH.(b) Show that εrev is always greater than 1. (c) Suppose a reversible heat pump transfers heat from the outdoors at 0°C to a room at 20°C. For each joule of work input to the heat pump, how much heat will be deposited in the room? (d) What happens to Krey as TC goes to 0 K?
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