Efficiency

$\eta =\frac{\text{output}}{\text{input}}$.

So for an engine, $\eta =\frac{\text{Work}}{\text{Heat In}}$. We can think of the engine receiving heat from a hot source and expelling to a low temperature source and doing work. Carnot efficiency: ${\eta }_c=\frac{W}{Q_H}=\frac{Q_H-Q_C}{Q_H}=1-\frac{Q_C}{Q_H}=1-\frac{T_C}{T_H}$. For a cycle, $\mathrm{\Delta }{S}_H=\mathrm{\Delta }{S}_C$ and $\mathrm{\Delta }S=\int dQ/T$ and so $\mathrm{\Delta }{S}_{H,C}=\frac{Q_{H,C}}{T_{H,C}}$ (negative for cold term).

For a Fridge, the heat comes in from the cold reservoir, we do work on it, and it expells heat to the hot temperature source. Output: $Q_C$. Input: $W$.

For a heat pump, it is very similar, Output: $Q_H$. Input: $W$.