Question

The temperature inside a Carnot refrigerator placed in a kitchen at 22 degree Celcius is 2 degree Celcius. The heat extracted from the refrigerator is 89 MJ/h. What power is needed to operate this refrigerator?

Answer 1

Answer: 1.79 kW

Explanation:

Given

The temperature of the refrigerator is $T_L=2^{\circ}C\approx 275\ K$

The temperature of the kitchen is $T_H=22^{\circ}C$

COP of the refrigerator is

$COP=\dfrac{T_L}{T_H-T_L}=\dfrac{\text{Desired effect}}{\text{Power}}\\\\\Rightarrow COP=\dfrac{275}{22-2}=\dfrac{89}{P}\\\\\Rightarrow P=\dfrac{20}{275}\times 89=6.47\ MJ/h\ \text{or}\ 1.79\ kW$