An ice-making plant working on a reversed Carnot cycle heat pump removes 3.5kW h

Question

An ice-making plant working on a reversed Carnot cycle heat pump removes 3.5kW heat
from the ice, which is maintained at 0 °C and rejects heat to the ambient, which is
assumed to be at 25 °C. The work required by the heat pump is supplied entirely by a
Carnot heat engine, which operates between a hot reservoir at 220 °C and a cold
reservoir at the ambient temperature. Find;

(a) work output of the Carnot heat engine.
(b) Heat absorbed by the Carnot heat engine from the hot reservoir.
(c) Total heat rejected into the ambient.

Explanation / Answer

COP of pump = Tcold/(Thot - Tcold) = (273+0)/((273+25)-(273+0)) = 273/25 = 10.92

(a) Work output of heat engine = Work required by heat pump = 3.5/10.92 = 0.32 kW

(b) Efficiency of heat engine = ((273+220)-(273+25))/(273+220) = 0.3955

Heat absorbed by heat engine from hot reservoir = Work/Efficiency = 0.32/0.3955 = 0.809 kW

(c) Heat rejected into ambient by heat pump = 3.5 + 0.32 = 3.82 kW

Heat rejected into ambient by heat engine = 0.809 - 0.32 = 0.489 kW

Total heat rejected = 3.82 + 0.489 = 4.309 kW

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