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 Carnot efficiency times the heat removed from the house per second. The Carnot efficiency is given by:$$\eta = 1 - \frac{T_c}{T_h}$$where $T_c$ is the inside temperature and $T_h$ is the outside temperature. Plugging in the given values, we get:$$\eta = 1 - \frac{293 \mathrm {~K}}{369 \mathrm {~K}} = 0.203$$The power required is then:$$P = \eta Q_c = (0.203)(14 \mathrm {~kJ/s}) = 2.84 \mathrm {~kW} = 2840 \mathrm {~W}$$The closest answer choice is A) 3600 W.

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 $14 \mathrm {~kJ}$