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) 7100 W.
B) 11,000 W.
C) 15,000 W.
D) 20,000 W.
E) 9000 W.

Question

Quizplus · Accepted Answer

The efficiency of a Carnot heat pump is given by the formula: $$COP = \frac{T_{hot}}{T_{hot} - T_{cold}}$$, where $T_{hot}$ and $T_{cold}$ are the temperatures of the hot and cold reservoirs, respectively, in Kelvin. Here, $T_{hot} = 293K$ and $T_{cold} = 237K$. Thus, $$COP = \frac{293}{293 - 237} = \frac{293}{56}$$.The power requirement $P$ can be calculated using the formula: $$P = \frac{Q}{COP}$$, where $Q$ is the heat delivered per second (47 kJ/s or 47000 W). Substituting the values, we get: $$P = \frac{47000}{\frac{293}{56}} = \frac{47000 \times 56}{293}$$.Calculating this gives $P \approx 9000 W$, which is closest to option E.

An Ideal Carnot Engine Is Operated as a Heat Pump