We were discussing “Carnot cycle and its efficiency” as well as “Carnot theorem and its explanation” in our previous posts. We have also seen the concept of “corollary of Carnot’s theorem” and simultaneously “efficiency of a reversible heat engine” in our recent posts.

Today we will see here the coefficient of performance of a reversible heat pump or refrigerator.
As we have already discussed the “concept of heat pump in thermodynamics, where we have defined that heat pump is basically defined as a device which will be operated in a thermodynamic cycle and will transfer the heat energy from a lower temperature thermal energy reservoir to higher temperature thermal energy reservoir by securing work energy from surrounding.

Let us see one reversible refrigerator or heat pump, as displayed in following figure, which is receiving heat energy from lower temperature thermal energy reservoir at temperature T2 and transferring heat energy to higher temperature thermal energy reservoir at temperature T1 by securing work energy W from surrounding.

### Let us see the coefficient of performance of reversible refrigerator and reversible heat pump

Performance of refrigerator or heat pump will be given by a term i.e. coefficient of performance and it will be written as C.O.P during writing or solving the problems.

For easy understanding of concept of Coefficient of performance i.e. C.O.P we will use one formula to avoid confusion and formula is as mentioned here

C.O.P = Desired output/Required Input

### For refrigerator:

Desired output term will be the heat flowing from lower temperature or cold thermal energy reservoir and it is also termed cooling effect.

### For heat pump:

Desired output term will be the heat flowing towards higher temperature or hot thermal energy reservoir and it is also termed heating effect.

Required input term will be common for both cases i.e. for heat pump and refrigerator too and it will be work energy secured by system from surrounding.

Required input = W = (Q1-Q2)

### Coefficient of performance for a refrigerator

Coefficient of performance for a refrigerator

### Coefficient of performance for a heat pump

Coefficient of performance for a heat pump

Do you have any suggestions? Please write in comment box.
We will see another topic i.e. "Clausius theorem" in our next post in the category of thermal engineering.

### Reference:

Engineering thermodynamics by P. K. Nag