Question

It costs $180 to heat a house with electricity in a typical winter month. (Electric heat simply converts all the incoming electrical energy to heat.)

Part A

What would the monthly heating bill be following conversion to an electrically powered heat-pump system with COP=3.1?

dollars = ?

Answer 1

The COP of a heat pump cycle is the ratio of what we want to what we pay for.

Some people call refrigeration cycles "heat pumps", but I don't like that term. Refrigeration cycles are the same machinery and piping as a heat pump, but the definitions of what we want vary.

When refrigeration is used, heat is considered trash, and we desire to suck it out of the food storage unit and blow it in to the kitchen OR suck it out of the building and blow it out to the atmosphere.

When heat pumps are used, heat is considered treasure. We desire to suck it in from the outdoor cold environment, and blow it in to the building.

So, what we want is heat to heat our house. What we pay for is electricity.

When electric resistance heaters are used, energy we want equals energy we pay for.


When heat pumps are used, the heat we suck in from outside, we don't pay for. We get some energy without paying for it at the expense of paying for some other energy input of a smaller amount.

Q_dot_desired = $180

COP = Q_dot_desired/W_dot_purchased

Solve for W_dot_purchased:
W_dot_purchased = Q_dot_desired/COP

Conclusion:
W_dot_purchased = $58.07