Question

1. A food compartment is kept at -12°C by a refrigerator in an environment at 30° C. The total heat transfer to the food compartment is estimated to be 3300 kJ/hr and the heat rejection in the condenser is 4800 kJ/hr. Determine the power input to the compressor, in kW, and the COP of the refrigerator. 30°C 800 kJ/h in 3300 kJ/h -12°C

Answer 1

Let food compartment Temperature as $T_{L}=-12^{\circ}C=-12+273=261K$

Environment Temperature as $T_{H}=30^{\circ}C=30+273=303K$

Heat taken from the food compartment is

$Q_{L}=3300KJ/hr=\frac{3300}{3600}=0.916KW$

Heat rejection in the condenser as

$Q_{H}=4800KJ/hr=\frac{4800}{3600}=1.333KW$

Energy balance

$\dot{W}+Q_{L}=Q_{H}$

$\dot{W}=Q_{H}-Q_{L}=1.33-0.916=0.4173\, KW$

QL 0.916 0.4173 2.195

Power input to the compressor 0.4173 KW

COP=2.195

NOTE

Ideal COP is

$COP=\frac{T_L}{T_H-T_L}=\frac{261}{303-261}=6.214$