# Efficiency, redefined

The efficiency of a machine is in general defined as the ratio between useful (released) energy and the input energy. Therefore, the exact formulas for efficiency depend on the purpose of the machine. What's the difference in the maximal efficiency of a heat pump and a heat engine? Both the engine and the pump have the cold reservoir set at $$T_c = 10^\circ \mbox{C}$$ and the hot reservoir at $$T_h = 70^\circ \mbox{C}$$.

Details and assumptions

• Mechanism of the heat engine: we add heat to make it do more work.
• Mechanism of the heat pump: move heat towards the hot reservoir.
• The efficiency of a heat pump is also called the "coefficient of performance".
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