Question

A heat pump is used to keep a house warm at 22∘C. How much work is...

A heat pump is used to keep a house warm at 22∘C.

How much work is required of the pump to deliver 3000 J of heat into the house if the outdoor temperature is 0∘C. Assume a COP of 3.0

How much work is required of the pump to deliver 3000 J of heat into the house if the outdoor temperature is -15∘C? Assume a COP of 3.0

How much work is required of the pump to deliver 3000 J of heat into the house if the outdoor temperature is 0∘C. Assume an ideal (Carnot) coefficient of performance COP = TH/(TH−TL).

How much work is required of the pump to deliver 3000 J of heat into the house if the outdoor temperature is -15∘C. Assume an ideal (Carnot) coefficient of performance COP = TH/(TH−TL)

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Homework Answers

Answer #1

a )

given

Q = 3000 J , COP = 3

then W = Q / COP

W = 3000 / 3 = 1000 J

b )

given

Q = 3000 J , COP = 3

then W = Q / COP

W = 3000 / 3 = 1000 J

c )

given

Q = 3000 J ,

COP = TH / ( TH - TL )

= Q / W

TH = 273 + 22 = 295 K ,

TL = 273 + 0 = 273 K

TH - TL = 22 K

so COP = TH / ( TH - TL )

COP = 295 / 22 = 13.4

so W = Q / COP

W = 3000 / 13.4

W = 223.88 J

d )

given

Q = 3000 J ,

COP = TH / ( TH - TL )

= Q / W

TH = 273 + 22 = 295 K ,

TL = 273 - 15 = 258 K

TH - TL = 37 K

so COP = TH / ( TH - TL )

COP = 295 / 37 = 8

so W = Q / COP

W = 3000 / 8

W = 375 J

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