An ideal Carnot engine is operated as an air conditioner to cool a house in the summer.The air conditioner removes $14 \text { kJ }$ of thermal energy per second from the house,and maintains the inside temperature at $293 \mathrm {~K} \text {, }$ while the outside temperature is $369 \mathrm {~K} .$ The power required to run the air conditioner under these operating conditions is closest to

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The power required to run the air conditioner is given by the formula:$$P = \frac{Q}{t} \left( \frac{T_H}{T_H - T_C} \right)$$where:* $P$ is the power in watts* $Q$ is the thermal energy removed from the house in joules per second* $t$ is the time in seconds* $T_H$ is the temperature of the hot reservoir in kelvins* $T_C$ is the temperature of the cold reservoir in kelvinsIn this problem, we are given that $Q = 14 \text { kJ/s} = 14000 \text { J/s}$, $T_C = 293 \text { K}$, and $T_H = 369 \text { K}$. Substituting these values into the formula, we get:$$P = \frac{14000 \text { J/s}}{1 \text { s}} \left( \frac{369 \text { K}}{369 \text { K} - 293 \text { K}} \right) = 3600 \text { W}$$Therefore, the power required to run the air conditioner is closest to 3600 W, which is choice A.

An Ideal Carnot Engine Is Operated as an Air Conditioner 14 kJ 14 \text { kJ }14 kJ

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