The GATE Grind

GATE 2019 ME (ME2) – Question 43

Thermodynamics · Zeroth, first and second laws, work, heat and energy changes · 2 marks · Multiple choice

The shown heat engine operates between two reservoirs and rejects heat $Q_2$, all drawn by a heat pump. The pump receives the engine’s entire work W. With $T_3>T_1>T_2$, find the relationship between engine efficiency η and heat-pump COP.

Diagram for GATE 2019 ME (ME2) question 43
  1. $COP=\eta$
  2. $COP=1+\eta$
  3. $COP=\eta^{-1}$
  4. $COP=\eta^{-1}-1$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $COP=\eta^{-1}$

Explanation

Engine balance is $Q_1=W+Q_2$. Heat-pump balance is $Q_3=W+Q_2$, so $Q_3=Q_1$. Therefore $COP=Q_3/W=1/\eta$. **C**.