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

(a) 4 (b) 5

Step-by-step explanation:

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

For any power cycle we know that
`\eta =1-(T_L)/(T_H)`

`0.2 =1-(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=(T_L)/(T_H-T_L)` here COP is coefficient of performance

So
`COP=(T_L)/(1.25T_L-T_L)`

`COP=(1)/(0.25)=4`

(b) For heat pump we know that
`COP=(T_H)/(T_H-T_L)` here COP is coefficient of performance

So
`COP=(1.25 T_L)/(1.25T_L-T_L)`

`COP=(1.25 )/(0.25)=5`