A heat engine with a thermal efficiency of 40% receives heat from a reservoir at

Question

A heat engine with a thermal efficiency of 40% receives heat from a reservoir at a temperature of 300 ?F and rejects heat to a reservoir at a temperature of 40 ?F. The heat engine is connected to a heat pump which receives energy from the 40 ?F reservoir and must reject 36,000 Btu/hr of heat to a house at a constant temperature of 80 ?F. If the coefficient of performance of the heat pump is 9 and the heat engine only produces enough work to drive the heat pump, then find: a).the rate of heat transfer to the heat pump from the 40 ?F reservoir (Btu/hr) b).the power required to drive the heat pump (Btu/hr) c).the rate of heat transfer to the heat engine from the 300 ?F reservoir (Btu/hr) d).the rate of heat transfer rejected by the heat engine to the 40 ?F reservoir (Btu/hr).

Explanation / Answer

COP of pump = 9

Q1 = heat rejected = 36000 Btu / hr

So, heat rejected / work = 9

So,W = work input for pump = 36000 / 9 = 4000 Btu / hr

a) So, Q2 = rate of heat transfer to heat pump = Q1 - W = 32000 Btu/hr

b) Power reqd = W = 4000 Btu / hr

c) Q'1 = W / efficiency = 4000 / 0.40 = 10000 Btu/hr

d) Heat Rejeced , Q2' = Q1' - W = 6000 Btu/hr

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