Refrigerator And Coefficient Of Performance

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A domestic refrigerator extracts 360 J of heat from the food compartment for every 120 J of electrical work its compressor consumes per cycle. What is its coefficient of performance?

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The coefficient of performance of a refrigerator rates how much heat it removes from the cold space per unit of work input, defined as $	ext{COP} = \dfrac{Q_C}{W}$. Here $Q_C = 360	ext{ J}$ is the heat drawn from the food and $W = 120	ext{ J}$ is the work supplied, so $	ext{COP} = 360/120 = 3$. The value 4 would arise from dividing the heat rejected to the room, $Q_H = Q_C + W = 480	ext{ J}$, by the work, which defines a heat pump's COP rather than a refrigerator's. The value 0.33 inverts the ratio, treating it like engine efficiency. The value 2 has no basis in the given numbers. Unlike efficiency, the COP of a refrigerator can exceed one because the work merely pumps heat rather than creating it. By energy conservation the compressor delivers $Q_H = Q_C + W = 480	ext{ J}$ to the room each cycle, which is why a working refrigerator warms the kitchen overall even as it cools its interior. The theoretical ceiling on COP is set by the Carnot expression $T_C/(T_H - T_C)$, so smaller temperature differences allow far higher performance. As a magnitude check, a good refrigerator moves several joules of heat per joule of electricity, so a COP of 3 is entirely realistic for household appliances.

Refrigerator And Coefficient Of Performance

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