# A heat pump is used to keep a house warm at 22 degrees?

a.) How much work is required of the pump to deliver 2500J of heat into the house if the outdoor temperature is 0 degrees. Assume an ideal (Carnot) coefficient of performance COP= T_H/(T_H-T_L).

b.) How much work is required of the pump to deliver 2500J of heat into the house if the outdoor temperature is -15 degrees. Assume an ideal (Carnot) coefficient of performance COP= T_H/(T_H-T_L).

• For both cases, Work = Energy / COP. You stated the formula for COP that you can calculate, so why can not you do it?

Perhaps, I can see your problem now, in not converting to the temperatures to Kelvin before hand. Add 273 to each temperature reading.

• The heating load is the heat to be rejected into the house being heater, QR.

The Heat Pump Heater COP, is defined by :

COP = QR / WHP

where WHP is the required Heat Pump Heater work.

For a Carnot Heat Pump Heater, you have :

COP = ( TH ) / ( TH - TL )

For part a you have :

QR = 2500 J

COP = ( TH ) / ( TH - TL ) = ( 295.2 K ) / ( 295.2 K - 273.2 K ) = 13.42 COP Units

WHP = QR / COP = 2500 J / 13.42 = 186 J <---------[ a ]-----------------

For Part b, you have :

COP = ( TH ) / (TH - TL ) = ( 295.2 K ) / ( 295.2 K - 258.2 K ) = 7.978 COP Units

WHP = QR / COP = ( 2500 J ) / ( 7.978 COP units ) = 313 J <------[ b ]-------