Carnot refrigerator

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 thereforeAll 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.