A perfectly reversible heat pump with a coefficient of performance of 14 supplies energy to a building as heat to maintain its temperature at 27°C.If the pump motor does work at the rate of 1 kW, at what rate does the pump supply energy to the building?
A)15 kW
B)3.9 kW
C)1.4 kW
D)0.26 kW
E)0.067 kW

Question

Quizplus · Accepted Answer

The coefficient of performance (COP) for a heat pump is defined as the ratio of the heat supplied to the work input. Given a COP of 14 and a work input of 1 kW, the heat supplied to the building is COP × work input = 14 × 1 kW = 14 kW. However, since the heat pump is perfectly reversible and supplies energy, the actual rate at which energy is supplied to the building is the sum of the work input and the heat supplied, which equals 1 kW (work input) + 14 kW (heat supplied) = 15 kW.

A Perfectly Reversible Heat Pump with a Coefficient of Performance