For the simple reversible heat pump diagram presented below

For the simple reversible heat pump diagram presented below, calculate the overall coefficient of performance, and the net work supplied to the heat pump.

Solution

>> For Reversible Heat Pump

COP = Q1/W = T1/(T1 - T2)

As, T1 = Temperature of Source (or high temperature body) = 70 C = 273 + 70 = 343 K

and, T2 = Temperature of Sink (or low temperature body) = 20 C = 273 + 20 = 293 K

So, COP = 343/(343-293)

=> COP = 6.86 .......ANSWER.......

As, COP = Q1/W

and, Q1 = Qh = 36000 KJ/hr = 10 KW

So, W = Qh/COP = 10/6.86 = 1.458 kW = 52447.81 KJ/hr .....Required Work Supplied......