Question
What sets the limits on efficiency of a heat engine?

Answer

The temperature of the cold reservoir sets the limit on the efficiency of a heat engine.
[Notes: (1) $\eta=1-\frac{T_{ C }}{T_{ H }}$
This formula shows that for maximum efficiency, $T_C$ should be as low as possible and $T_H $ should be as high as possible.
(2) For a Carnot engine, efficiency
$\left.\eta=1-\frac{T_{ C }}{T_{ H }} \cdot \eta \rightarrow 1 T _{ C } \rightarrow 0.\right]$

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