Carnot Refrigerator

Theorem: Coefficient of Performance of the Carnot Refrigerator

No refrigerator can have a higher coefficient of performance than that of the Carnot refrigerator, which is given by the temperature $T_{\text{C}}$ of the cold reservoir and the temperature $T_{\text{H}}$ of the hot reservoir.

$$K_{\text{Carnot}}=\frac{T_{\text{C}}}{T_{\text{H}}-T_{\text{C}}}$$

PROOF

TODO