An ideal Carnot engine is operated as an air conditioner to cool a house in the summer. The air conditioner removes $14 \mathrm {~kJ}$ of heat per second from the house, and maintains the inside temperature at $293 \mathrm {~K}$ while the outside temperature is $369 \mathrm {~K}$ The power required to run the air conditioner under these operating conditions is closest to
A) 3600 W.
B) 4400 W.
C) 5100 W.
D) 5800 W.
E) 6600 W.

Question

Quizplus · Accepted Answer

The power required to run the air conditioner is given by the equation:$$P = \frac{Q}{C}$$where:* P is the power in watts* Q is the heat removed from the house in joules per second* C is the coefficient of performance of the air conditionerThe coefficient of performance of a Carnot engine is given by the equation:$$C = \frac{T_c}{T_h - T_c}$$where:* $T_c$ is the temperature of the cold reservoir in kelvins* $T_h$ is the temperature of the hot reservoir in kelvinsIn this problem, $T_c = 293 \mathrm {~K}$ and $T_h = 369 \mathrm {~K}$. Therefore, the coefficient of performance is:$$C = \frac{293 \mathrm {~K}}{369 \mathrm {~K} - 293 \mathrm {~K}} = 2.06$$The power required to run the air conditioner is:$$P = \frac{14 \mathrm {~kJ/s}}{2.06} = 3600 \mathrm {~W}$$Therefore, the correct answer is A.

An Ideal Carnot Engine Is Operated as an Air Conditioner 14 kJ14 \mathrm {~kJ}14 kJ

An Ideal Carnot Engine Is Operated as an Air Conditioner $14 \mathrm {~kJ}$