An ideal reversible heat pump is used to heat a house in Minnesota in the winter. If the outside air temperature is −15°C and the indoor temperature desired is 20°C, what is the expected coefficient of performance for the heat pump under these conditions?

Question

Quizplus · Accepted Answer

The coefficient of performance (COP) is given by:

COP = Qh/W

where Qh is the heat supplied to the house and W is the work input to the heat pump.

In an ideal reversible heat pump, the COP is given by:

COP = Th/(Th-Tc)

where Th is the temperature of the heat source (the outdoor air in this case) and Tc is the temperature of the cold sink (the indoor air in this case).

Using the given temperatures, we have:

COP = (−15°C + 273.15 K)/(−15°C + 273.15 K − 20°C + 273.15 K)

COP = 288.15 K/46.3 K

COP = 6.22

However, this assumes an ideal reversible heat pump. In reality, there will be losses due to irreversible processes, such as friction and heat transfer to the environment. The actual COP will be lower than this value.

Therefore, the closest option is B) 8.4.

An Ideal Reversible Heat Pump Is Used to Heat a House