Question

The thermal efficiency of a reversible power cycle operating between hot and cold reservoirs is 20%. Evaluate the coefficient of performance of (a) a reversible refrigeration cycle operating between the same two reservoirs. (b) a reversible heat pump cycle operating between the same two reservoirs.

Answer 1

Answer:

(a) 4 (b) 5

Explanation:

We have given the thermal efficiency is 20% that is efficiency $\eta$ =0.2

For any power cycle we know that $\eta =1-\frac{T_L}{T_H}$

$0.2 =1-\frac{T_L}{T_H}$

So $T_H=1.25T_L$

Here $T_H$ is higher temperature and $T_L$  is lower temperature of reservoirs

(a) For refrigeration cycle we know that $COP=\frac{T_L}{T_H-T_L}$ here COP is coefficient of performance

So $COP=\frac{T_L}{1.25T_L-T_L}$

$COP=\frac{1}{0.25}=4$

(b)   For heat pump we know that $COP=\frac{T_H}{T_H-T_L}$ here COP is coefficient of performance

So $COP=\frac{1.25 T_L}{1.25T_L-T_L}$

$COP=\frac{1.25 }{0.25}=5$