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The figure shows a heat engine (HE) working between two reservoirs. The amount of heat (Q2) rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output (W) of the heat engine. If temperatures, T T T 1 3 2 , then the relation between the efficiency ( ) of the heat engine and the coefficient of performance (COP) of the heat pump is
For Heat engine,
Energy balance for Heat engine gives Q2=Q1−W
And energy balance for Heat pump gives Q3=Q2+W=Q1−W+W=Q1
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