A refrigerator has a coefficient of performance of 4. If the refrigerator absorbs 30 cal of heat from the cold reservoir in each cycle, the heat expelled (in cal) into the heat reservoir is
A) 40.5
B) 37.5
C) 36.5
D) 34.5
E) 22.5

Question

Quizplus · Accepted Answer

Coefficient of performance (COP) = heat removed from the cold reservoir / work done
So, work done = (heat removed from cold reservoir)/COP
Here, COP = 4 and heat removed from cold reservoir = 30 cal
So, work done = (30/4) = 7.5 cal
Now, from the first law of thermodynamics, we know that:
work done = heat removed from cold reservoir - heat added to the hot reservoir
So, heat added to the hot reservoir = heat removed from cold reservoir - work done
Heat added to hot reservoir = 30 - 7.5 = 22.5
Therefore, the heat expelled into the heat reservoir is 22.5 calories. The correct answer choice is B).

A Refrigerator Has a Coefficient of Performance of 4