A 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 34 kJ per second and maintains the room at a temperature of 293 K when the outside temperature is 229 K. The power requirement for the heat pump under these operating conditions is closest to
A) 7500 W.
B) 6000 W.
C) 17,000 W.
D) 13,000 W.
E) 9600 W.

Question

Quizplus · Accepted Answer

The power requirement for the heat pump is given by the following equation:$$P = \frac{Q}{COP}$$where:* P is the power requirement in watts* Q is the heat delivered to the room in joules per second* COP is the coefficient of performance of the heat pumpThe COP of a Carnot heat pump is given by the following equation:$$COP = \frac{T_H}{T_H - T_C}$$where:* 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 the following information:* Q = 34 kJ/s* T_H = 293 K* T_C = 229 KSubstituting these values into the equations above, we get:$$COP = \frac{293 K}{293 K - 229 K} = 2.23$$$$P = \frac{34 kJ/s}{2.23} = 15.25 kW$$Therefore, the power requirement for the heat pump is closest to 15,250 W, which is choice A.

A Carnot Engine Is Operated as a Heat Pump to Heat