Helium gas goes through a cycle ABCD (consisting of two isochoric and… | JEE Main 2012 (AIEEE)

Q75JEE Main 2012 · AIEEEDifficult

Heat Engines, Refrigerators & Second Law

Helium gas goes through a cycle $ABCD$ (consisting of two isochoric and isobaric lines) as shown in figure efficiency of this cycle is nearly: (Assume the gas to be close to ideal gas)

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Answer: (a)

Helium is monatomic: $C_V = \frac{3}{2}R$ , $C_P = \frac{5}{2}R$ . Net work = area $= P_0V_0$ .
Heat in A→B (isochoric): $\frac{3}{2}(2P_0V_0 - P_0V_0) = 1.5P_0V_0$
Heat in B→C (isobaric): $\frac{5}{2}\,(2P_0)(2V_0 - V_0) = 5P_0V_0$
$\eta = \frac{P_0V_0}{6.5P_0V_0} \approx 0.154 = 15.4\%$
So the answer is (a) $15.4\%$ .

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