An ideal Carnot engine is operated as a heat pump to heat a room in the winter.The heat pump delivers heat to the room at the rate of 47 kJ per second and maintains the room at a temperature of 293 K when the outside temperature is 237 K.The power requirement to run the heat pump under these operating conditions is closest to
A)9000 W.
B)7100 W.
C)20,000 W.
D)15,000 W.
E)11,000 W.

Question

Quizplus · Accepted Answer

The power required to run the heat pump is given by the rate of heat delivery divided by the coefficient of performance (COP) of the heat pump. The COP of a Carnot heat pump is given by the ratio of the temperature of the hot reservoir to the difference in temperature between the hot and cold reservoirs. In this case, the temperature of the hot reservoir is 293 K and the temperature of the cold reservoir is 237 K, so the COP is 293 K / (293 K - 237 K) = 2.44. Therefore, the power required to run the heat pump is 47 kJ/s / 2.44 = 19.3 kJ/s = 19,300 W. The closest choice to this value is A) 9000 W.

An Ideal Carnot Engine Is Operated as a Heat Pump