GATE ME 2019 Set 2 — Question 43
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Thermodynamics → Laws & Properties → Coefficient of Performance
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Question
The figure shows a heat engine (HE) working between two reservoirs. The amount of heat () rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output () of the heat engine. If temperatures, , then the relation between the efficiency () of the heat engine and the coefficient of performance (COP) of the heat pump is
Correct answer
(C) COP = ⁻¹
Solution
For the Heat Engine (HE):By energy balance: .For the Heat Pump (HP):By energy balance: .Comparing the energy balances, we see that . Substituting this into the COP expression:Thus, option (C) is correct.
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