A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air temperature is 280 K. Heat loss from the auditorium is 15 kW. The power consumption of the heat pump is ____ kW (rounded off to 2 decimal places).

The correct answer is 1 kW (or 1).

To find the power consumption of the heat pump, we can analyze the Carnot heat pump system using its temperatures and the heat transfer requirements. Let us define the given parameters:

Inside temperature of the auditorium (high temperature reservoir),
T H = 300 K

Ambient air temperature (low temperature reservoir),
T L = 280 K

Heat loss from the auditorium, which is the rate at which heat must be supplied to the auditorium to maintain its temperature,
Q H = 15 kW

For a heat pump operating on a reversed Carnot cycle, the Coefficient of Performance (COP) is given by the relation:
COP HP = T H T H - T L

Substituting the values of the temperatures into the COP equation:
COP HP = 300 300 - 280 = 300 20 = 15

The COP of a heat pump is also defined as the ratio of the desired heating effect to the net work or power input:
COP HP = Q H W

Where W is the power consumption of the heat pump. Rearranging the formula to solve for W:
W = Q H COP HP

Substituting the known values:
W = 15 kW 15 = 1 kW

Thus, the power consumption of the heat pump is 1 kW.