What is the power input (in kW) needed to run the heat pump?

[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?

Homework Equations

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

W=(QsubscriptH)-(QsubscriptC)

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?

 

[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

 

[spazmsfreak]

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

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