The Best COP hp of a Heat Pump for Home Use

A Carnot engine reversed will give the best possible performance as a heat pump. As noted above, ${\text{COP}}_{\text{hp}}=1/\text{Eff}$, so that we need to first calculate the Carnot efficiency to solve this problem.

Carnot efficiency in terms of absolute temperature is given by:

The temperatures in kelvins are $T_{\text{h}}=\text{318 K}$ and $T_{\text{c}}=\text{258 K}$, so that

Thus, from the discussion above,

or

so that

This result means that the heat transfer by the heat pump is 5.30 times as much as the work put into it. It would cost 5.30 times as much for the same heat transfer by an electric room heater as it does for that produced by this heat pump. This is not a violation of conservation of energy. Cold ambient air provides 4.3 J per 1 J of work from the electrical outlet.

Figure 15.30 Heat transfer from the outside to the inside, along with work done to run the pump, takes place in the heat pump of the example above. Note that the cold temperature produced by the heat pump is lower than the outside temperature, so that heat transfer into the working fluid occurs. The pump’s compressor produces a temperature greater than the indoor temperature in order for heat transfer into the house to occur.