What is the minimum power required to operate the heat pump?

[swain1]

Homework Statement

It is proposed to heat a house using a heat pump operating between the house (27 degees) and the outside (-13 degrees). The heat loss from the house is 7kW. What is the minimum power required to operate the heat pump?

Homework Equations

The Attempt at a Solution

e=Th/(Th-Tc) =7.5
W=7000/7.5 =933 W

Just checking if this is correct or have I made a mistake. Thanks

 

[OlderDan]

Since you start out with a dimensionless number, a ratio of temperatures, and equate that to some number of Watts, something is surely wrong. Maybe you just need to rewrite things to make it clear

 

[swain1]

I have moved the equation now. If you look at the question you will see that 7000 has units of watts. Is it wrong anyway?

 

[OlderDan]

I have moved the equation now. If you look at the question you will see that 7000 has units of watts. Is it wrong anyway?

That looks better. It would be better still if you had units of W on the 7000.