A Carnot air conditioner has a coefficient of performance of 17.0 and removes 72.0 MJ of heat from the interior of a house every hour.How much power does it consume?
A)1180 W
B)1320 W
C)520 kW
D)3.14 MW
E)1.25 MW

Question

Quizplus · Accepted Answer

The coefficient of performance (COP) for a Carnot air conditioner is defined as the ratio of the heat removed (Q_c) from the cold reservoir to the work input (W), i.e., COP = Q_c/W. Given COP = 17.0 and Q_c = 72.0 MJ/h = 72000 kJ/h, we can rearrange the formula to solve for W: W = Q_c/COP. Converting 72000 kJ/h to watts (since power is in watts and 1 W = 1 J/s), we first convert hours to seconds (72000 kJ/h * 1000 J/kJ) / (3600 s) = 20000 W = 20 kW. Then, W = 20 kW / 17.0 = 1176.47 W, which rounds to approximately 1180 W.

A Carnot Air Conditioner Has a Coefficient of Performance of 17.0