Question

What is the relationship between the COP of a Carnot refrigerator and the COP of a Carnot heat pump when the two cycles are operating between the same two thermal reservoirs?

Answer 1

COP of heat pump = 1 + COP of heat refrigerator

Step-by-step explanation:

As we know that COP is the ratio of desired effect to the work input.

So in refrigerator our desired effect is to cool space and on the other hand in heat pump our desired effect is to heat the space.

`COP_(pump)=(T_H)/(T_H-T_L)`

`COP_(refr)=(T_L)/(T_H-T_L)`

Given that temperature limits for pump as well as refrigerator is same.

So from the above two equations we can say that

COP of heat pump = 1 + COP of heat refrigerator