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A refrigerator is a heat engine run in reverse: it absorbs $Q_C$ from a cold reservoir, uses external work $W$, and rejects $Q_H = Q_C + W$ to a hot reservoir. The coefficient of performance: $\text{COP}_{\text{ref}} = Q_C/W = Q_C/(Q_H - Q_C)$. For a Carnot refrigerator: $\text{COP} = T_C/(T_H - T_C)$.

Unlike efficiency, COP can exceed 1 — a good refrigerator removes more heat than the work input. For example, between 250 K and 300 K: $\text{COP} = 250/50 = 5$, meaning 5 J of heat is removed per joule of work.

A heat pump heats a room by extracting heat from cold outdoors: $\text{COP}_{\text{hp}} = Q_H/W = T_H/(T_H - T_C)$. The relation $\text{COP}_{\text{hp}} = \text{COP}_{\text{ref}} + 1$ always holds. A heat pump is always more efficient than direct electrical heating because it "moves" heat rather than "creating" it.

For JEE, remember: efficiency $\eta \leq 1$ always, but COP can be much greater than 1. Both are maximised by minimising the temperature difference $T_H - T_C$.