A heating system must maintain the interior of a building at TH = 20°C when the outside temperature is TC = 10°C. If the rate of heat transfer from the building through its walls and roof is 15 kW, determine the electrical power required, in kW, to heat the building using: (a) electrical-resistance heating; (b) a heat pump whose coefficient of performance is 4; (c) a reversible heat pump operating between hot and cold reservoirs at 20°C and 10°C, respectively.

A) 150 kW will be required to heat the building using electrical-resistance heating, this is because, electrical-resistance heating is 100% efficient.

B) for a heat pump whose coefficient of performance is 4,

Using COP = Q/W

where,

Q = heat delivered

W = power or work input.

4 = 150/W,

W = 150/4 = 37.5 kW

C) COP for reversible heat pump is given as

COP = T2 / (T2-T1)

Where T2 = hot temperature = 20 + 273 = 293 K

T1 = cold temperatures = 10 + 273 = 283 K

COP = 293 / (293-283) = 29.3

COP = Q/W

29.3 = 150/W

W = 0.195 kW = 195.3 watts