Problem #1 Heat Pump Used to Heat House in Winter A heat pump is used to heat a

Question

Problem #1 Heat Pump Used to Heat House in Winter A heat pump is used to heat a house during the winter. The house is to be maintained at 27 degree Celsius at all times. The house is losing heat at a rate of 125000 kJ/h when the outside temperature drops to -5 degree Celsius. (15 pts) a. Determine the minimum power required to drive this heat pump in kW. 12 pts) b. A resistance heater converts electric energy to heat at a 1:1 ratio. What is the power in kW requirement for using a resistance heater. Calculate the ratio of the work required to use a resistance heater to the work required to use a heat pump.

Explanation / Answer

a) The  coefficient of performance of the heat pump = Thot / ( Thot - Tcold)

= 27 / ( 27+5)

= 0.84375

Therefore the minimum power required to drive the heat pump = 125000 / (3.6 * 0.84375) watt

=41152.26 watt

= 41.152 kW

b) For the resistance heater the power required = 125000 / 3.6 watt

= 34.722 kW

c)Since the time of operation of the rresistance heater and the heat pump is same

The ratio of thier work is = 34.722 / 41.125 = 0.8443 equivalent to COP

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