Question

The coefficient of performance of a carnot refrigerator is $5/3$. If the refrigerator operating at an intake temperature of $-{23}^{\circ }$C, then what will be the exhaust temperature?

Answer 1

Given:

Coefficient of performance, $\beta =\frac{5}{3}$

Source temperature, $T_1=-23°C=(-23+273)K=250K$

To find:

Exhaust temperature, $T_2=?$

We know the coefficient of performance,

$\beta =\frac{T_2}{T_1-T_2}⟹\frac{5}{3}=\frac{T_2}{250-T_2}⟹1250-5T_2=3T_2⟹8T_2=1250⟹T_2=156.25K=(156.25-273)°C=-116°C$

Hence, the exhaust temperature is -116°C