= Carnot refrigerator
{c}
A <Carnot refrigerator> runs a reversible <Carnot cycle> in the direction that removes <heat> $Q_c$ from a cold reservoir at $T_c$ and delivers $Q_h$ to a hot reservoir at $T_h>T_c$. It requires supplied <work> $W=Q_h-Q_c$. Zero total <entropy production> gives $Q_c/T_c=Q_h/T_h$.
Its <coefficient of performance>, defined as useful cooling divided by supplied <work>, is therefore
$$
\mathrm{COP}=\frac{Q_c}{W}=\frac{T_c}{T_h-T_c}.
$$
All <temperatures> here are absolute. The ratio can exceed one because supplied <work> moves <heat> rather than being the only <energy> delivered to the cold-side process. For reservoirs at $250\ \mathrm K$ and $300\ \mathrm K$, the reversible value is five. A real refrigerator produces <entropy> and requires more <work> for the same cooling between those reservoirs. The ideal result is a limit, not a claim of finite cooling power without thermal gradients.
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