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JEE Main 2010 (AIEEE) · Heat Engines, Refrigerators & Second Law

Heat Engines, Refrigerators & Second Law question from JEE Main 2010 (AIEEE)

Q78JEE Main 2010 · AIEEEDifficult

Heat Engines, Refrigerators & Second Law

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V$ to $32\ V$ , the efficiency of the engine is

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Answer: (b)

Adiabatic: $TV^{\gamma - 1} =$ constant, $\gamma = \frac{7}{5}$ for a diatomic gas.
$\frac{T_2}{T_1} = \left(\frac{1}{32}\right)^{2/5} = \frac{1}{4}$
$\eta = 1 - \frac{1}{4} = 0.75$
So the answer is (b) $0.75$ .

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