A heat pump will be used to heat a building during the winter and will then cool

Question

A heat pump will be used to heat a building during the winter and will then cool the same space during the summer. The rate of heat gain or loss is determined to be 2400 kJ per hour per each degree of temperature difference between the space and the outdoor temoerature. The interioe temperature will be 293 K during the winter, but will be kept at 298 K in the summer.

a) If the outside temperature is 0 deg C, what would be the minimum power to drive the compressor?

b) What would be the coefficient of performance?

c) USing the same power found in the part a above, what would be the maximum outdoor temperature during the summer for this system to operate and maintain the space at 298 K?

d) What would be the coefficient of performance in this mode?

Explanation / Answer

a & b) durin winter Temperature = T2 = 293 K

and exterior temperature = T1 = 0 C = 273 K

so COP = T2/(T2 - T1)

              = 293/(293 - 273) = 14.65

Q1 = 2400 KJ/hr/degrree

temp difference = 293 - 273 = 20 degree

so heat loss = 2400 x 20 KJ/hr = 48000 KJ/hr

now let W = power in

then Q/Win = COP

so 48000/Win =14.65

so Minimum power = Win = 3276.45 KJ/hr = 3276.45/3600 = 0.9101 Kw = 910.1 W

c &d ) nOw power here = 3276.45 KJ/hr

and T2 = 298 K

and heat loss = 2400 KJ/hr x (298 - T1)

where T1 = max outdoor temp

then COP = T2/(T2 - T1) = 298/(298 - T1)

and COP is also = 2400 x (298 - T1)/3276.45

so 298/(298 - T1) = 2400 x (298 - T1)/3276.45

so outdoor temp = T1 = 277.83 K = 4.83 C

and COP = 298/(298 - 277.83) = 14.77

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