A typical heat pump may heat a home at a rate of 40,000 Btu/hr. If a heat pump has a coefficient of performance of 3.6, how much power does it need to run, in hp? According to Delmarva Power, the average cost of electricity is 14 cents per kilowatt hour. How much would it cost to run the heat pump all winter (say, 2000 hours)?

A heat pump is a device that allows to emit heat to an enclosure (Qout), by means of the input of an electric power (W) and the heat input of an external source (Qin), the coefficient of performance COP, allows to know the relationship between the emitted heat (Qout) and the added electrical power (W), the equation for the COP is

[tex]COP=\frac{Qout}{Win} \\Win=\frac{Qout}{COP}\\Win=\frac{40000}{3.6}\\\\Win=11111.1Btu/h[/tex]

For this part we must multiply the time by the power found, then use conversion factors until we find the operating cost value

Win=11111.11Btu/h=3.26Kw

energy consumed in 2000h=3.26kw.2000h=6500Kwh

[tex]cost=6520 Kwh\frac{14cents}{Kwh} =91280cents[/tex]=912.8dollars

cost to run the heat pump all winter is 912.8dollars