A Carnot heat pump supplies heat to a house at a rate of 480

A Carnot heat pump supplies heat to a house at a rate of 48,000 kJ/hour to maintain its temperature constant at 20 degree C. If the temperature of the outdoors is 5 degree C, what is the power required to operate this heat pump?

Solution

>> Carnot Heat Pump

Q1 = Heat supplied to a house = 48000 kJ/hr = 13.333 KW

T1 = Temperature of Home = 20 C = 293 K

T2 = Temperature of Surroundings = 5 C = 278 K

As, COP of Carnot Heat Pump = Q1/W = T1/(T1 - T2)

=> 13.333/W = 293/(293 - 278)

=> W = 0.683 KW = 2457.338 KJ/hr .........REQUIRED POWER TO OPERATE THIS HEAT PUMP.......