# Homework Help: Heat pump power input problem

1. Jul 21, 2007

### spazmsfreak

1. A heat pump is being used to keep the temperature inside a house at 23 C, while the tmeperature ouside is -6.0 C. The heat pump is providing heat inot the house at the rate of 8.8 kW with a coefficient of performance of 5.6.
A) What power input (in KW) is needed to run the heat pump?
B) What power input (in KW) would be needed if the heat pump were ideal and still providing 8.8 kW heating power inside the house?

2. Relevant equations
coefficient of performance = (QsubscriptH)/Work
For ideal heat pump:
(QsubscriptC)/(QsubscriptH)=(Temperature subcript C)/(Temperature subscript H)

W=(QsubscriptH)-(QsubscriptC)

3. The attempt at a solution
convert Temperatures to Kelvin
A) coefficient of performance = (QsubscriptH)/Work
5.6=8.8 kW/W
W=1.57 kW

Would power input be work? or would you use the power equation?

B) (QsubscriptC)/(QsubscriptH)=(Temperature subcript C)/(Temperature subscript H)
(QsubscriptC)/8.8 kW=267 K/246 K
(QsubscriptC)=7.94 kW

W=(QsubscriptH)-(QsubscriptC)
=8.8 kW -7.94 kW
=.86 kW
Are my calculations correct?

2. Jul 21, 2007

### Andrew Mason

A) is right. But in B, you are not converting the temperatures correctly. 23 C = 296 K and -0.6 C = 272.4 K.

AM

3. Jul 21, 2007

### spazmsfreak

It should be -6.0 not -0.6. But anyways thanks so much!