A heat pump with a COP of 3.2 is used to heat a perfectly sealed house (no air l

Question

A heat pump with a COP of 3.2 is used to heat a perfectly sealed house (no air leaks). The entire mass within the house (air, furniture, etc.) is equivalent to 1200 kg of air. When running, the heat pump consumes electric power at a rate of 5 kW. The temperature of the house was 7 degree C when the heat pump was turned on. If heat transfer through the envelope of the house (walls, roof, etc.) is negligible, the length of time the heat pump must run to raise the temperature of the entire contents of the house to 22 degree C is 13.5 min 43.1 min 138 min 18.8 min 808 min

Explanation / Answer

Heat required to raise the temperature of the from 7 o C to 22 oC is Q = mC dt

Where C = Specific heat of air = 1005 J /kg K

Substitute values you get Q = 1200(1005)(22-7)

                                         = 18.09x10 6 J

COP = 3.2

We know COP =Q/W

W = Q/COP

    = (18.09 x10 6 ) / (3.2)

    = 5.653125x10 6 J

Power P = 5 kW = 5000 W

Required time t = W / P

                        = 1130.625 s

                        = (1130.625/60) min

                        = 18.84 min

i.e., option(d) is correct.

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