The temperature inside a Carnot refrigerator placed in a kitchen at 22.0°C is 2.0°C.The heat extracted from the refrigerator is 89 MJ/h.What power is needed to operate this refrigerator?
A) 1.7 kW
B) 1.8 kW
C) 1.5 kW
D) 1.9 kW
E) 1.6 kW

Question

Quizplus · Accepted Answer

The coefficient of performance (COP) of Carnot refrigerator is given by:
COP = (absolute temperature of low temperature reservoir)/(absolute temperature of high temperature reservoir - absolute temperature of low temperature reservoir)

Here, the high temperature reservoir is the temperature of the kitchen (22.0°C = 295.2 K) and the low temperature reservoir is the temperature inside the refrigerator (2.0°C = 275.2 K).

COP = 275.2 K / (295.2 K - 275.2 K) = 13.76

The energy input to the refrigerator is Qh/COP, where Qh is the heat extracted from the refrigerator.

Power = Qh/COP = (89 MJ/h)/(13.76) = 6.47 kW

Therefore, the power needed to operate the refrigerator is 6.47 kW, which is closest to option B (1.8 kW).

The Temperature Inside a Carnot Refrigerator Placed in a Kitchen