How is the coefficient of performance ($\beta$) of a refrigerator related to the efficiency ($\eta$) of a Carnot heat

Question

How is the coefficient of performance ($\beta$) of a refrigerator related to the efficiency ($\eta$) of a Carnot heat engine operating between the same temperature limits?

Accepted Answer

The coefficient of performance is given by $\beta = \frac{Q2}{W} = \frac{T2}{T1 - T2}$. Expressing in terms of efficiency $\eta = 1 - \frac{T2}{T1}$, we get $\beta = \frac{1 - \eta}{\eta}$.

Thermodynamics

❓ Sibling Questions in this Chapter