An engine operates by taking a monoatomic ideal gas through the cycle… | JEE Main 2020 (6 Sep, Shift 2)

Q55JEE Main 2020 · 6 SEP · SHIFT 2Difficult

Heat Engines, Refrigerators & Second Law

An engine operates by taking a monoatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 19

Monatomic gas: $C_V = \frac{3}{2}R$ , $C_P = \frac{5}{2}R$ . Net work $= (3P_0 - P_0)(2V_0 - V_0) = 2P_0V_0$ .
Heat in A→B (isochoric): $\frac{3}{2}(3P_0 - P_0)V_0 = 3P_0V_0$
Heat in B→C (isobaric): $\frac{5}{2}\,(3P_0)(V_0) = 7.5P_0V_0$
$\eta = \frac{2P_0V_0}{10.5P_0V_0} \approx 0.19$
So the efficiency is about $19\%$ .

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