Calculating the Cost of Heating with a Less Efficient Heat Pump

[maxador]

Homework Statement

Assume that you heat your home with a heat pump whose heat exchanger is at Tc=2∘C, and which maintains the baseboard radiators at Th=47∘C. If it would cost $1000 to heat the house for one winter with ideal electric heaters (which have a coefficient of performance of 1), how much would it cost if the actual coefficient of performance of the heat pump were 75% of that allowed by thermodynamics?

Homework Equations

Th/(Th-Tc)=K
U=W+Q
K=Qh/Win

The Attempt at a Solution

i converted to kelvin and then plugged the temperatures into the equation and set it equal to Qh/Win but i am unsure how to proceed. any help is greatly appreciated.

 

[billy_joule]

It's best to type out your working so we can see exactly what you've done.

I assume 'K' is COP (Coefficient of performance), did you account for the given inefficiency here?

What does Qh represent? what are it's units? Is it the same for both the heater and the heat pump? How can you use that information?

What does W_in represent? what are it's units? Is it the same for both the heater and the heat pump? How can you use that information?