A 52lb sample of helium goes through a 3process refrigeratio

A 5.2lb sample of helium goes through a 3-process refrigeration cycle. The first process experiences 78kJ of heat rejection and consumes 42kJ of work in a polytropic process (n=1.1). The second process rejects 150kJ of heat at a constant volume. The final process is at a constant pressure and requires 22kJ of heat addition. This cyclic device is used to cool a chamber to 18C in a room maintained at 40C.

What is the coefficient of performance of this refrigeration cycle?

Solution

From the problem,

net workput=42 kJ

heat addition=net refrigeration effect=22 kJ

COP=(net refrigeration effect)/(net workput)

=22/42=0.523