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Thermodynamics
First Law of Thermodynamics
GATE 2019
Hard

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 T1>T3>T2, then the relation between the efficiency (η) of the heat engine and the coefficient of performance (COP) of the heat pump is

  • ACOP=η
  • BCOP=1+η
  • COP=η⁻¹
  • DCOP=η⁻¹−1

Explanation

η=W/Q1, so Q1=W/η. Q2=Q1−W=W(1/η−1). For the heat pump, COP=Q3/W=(Q2+W)/W=Q2/W+1=(1/η−1)+1=1/η. So COP=η⁻¹.

Source: GATE ME 2019 Session 2 (Set 3) (2019)

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