Heating a House by a Heat Pump A heat pump is used to meet t

Heating a House by a Heat Pump A heat pump is used to meet the heating requirements of a house and maintain it at 20 C. On a day when the outdoor air temperature drops to -2 C, the house is estimated to lose heat at rate of 80,000 kJ/h. If the heat pump under these conditions has a COP of 2.5, determine (a) the power consumed by the heat pump and (b) the rate at which heat is absorbed from the cold outdoor air.

Solution

Given : Temperature to be maintained =20^oC= 20+273= 293 K

             Outdoor air Temp. = -2^oC= -2+273= 271 K

           Estimated Heat loss rate= 80000KJ/h

          COP of Heat pump= 2.5

Solution: Heat Loss (Q₂) = 80000KJ/h=22.22KJ/s

COP of heat pump= Q₁ / (Q₁-Q₂)

2.5= Q₁/ (Q₁-80000) or 2.5= Q₁/(Q₁-22.22)

2.5Q₁-200000= Q₁ or 2.5Q₁-55.55= Q₁

1.5 Q₁ = 200000 or 1.5 Q₁ = 55.55

Q1 = 133333.33KJ/h or 37.04KJ/s

(Q₁-Q₂)= 133333.33-80000= 53333.33KJ/h or 14.8KJ/s