# What Is The Relation Between Efficiency η Of A Heat Engine And The Co-efficient Of Performance ɑ Of A Refrigerator?

The relation between efficiency η of a heat engine and the coefficient of performance α of a refrigerator is $$\eta = \frac{1}{1 + \alpha}$$

Efficiency if a heat engine is given by$$: \eta = 1 – \frac{T_{2}}{T_{1}}$$ $$\Rightarrow \frac{T_{1} – T_{2}}{T_{1}}$$ $$\Rightarrow \frac{1}{1 + \frac{T_{2}}{T_{1}-T_{2}}}$$ $$\Rightarrow \frac{1}{1 + \alpha}$$

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