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

Question

A heat pump is used to maintain a house temperature of 22 degrees Celsius. 
a.) How much work is required from the pump to deliver 2500 J of heat into the house when the outdoor temperature is 0 degrees Celsius? Assume an ideal Carnot coefficient of performance (COP) given by the formula COP = T_H / (T_H - T_L).
b.) How much work is required from the pump to deliver 2500 J of heat into the house when the outdoor temperature is -15 degrees Celsius? Again, assume an ideal Carnot coefficient of performance with the same formula COP = T_H / (T_H - T_L).

Otto Hills · Accepted Answer

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.

Anonymous · Answer

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 ]-------

Anonymous

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

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