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A diatomic gas is used in carnot heat engine having efficiency 80%. Find the ratio of volumes of gas during adiabatic expansion.

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${(\frac{1}{5})}^{\frac{5}{2}}$

${(\frac{1}{3})}^{\frac{5}{2}}$

${(\frac{1}{5})}^{3 / 2}$

${(\frac{1}{5})}^{\frac{2}{5}}$

answer is C.

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Detailed Solution

$η = 1 - \frac{T_{2}}{T_{1}}$

$0.8 = 1 - \frac{T_{2}}{T_{1}}$

$\frac{T_{2}}{T_{1}} = 0.2$

${(\frac{V_{2}}{V_{1}})}^{γ - 1} = \frac{T_{1}}{T_{2}} = 5$

$\frac{V_{1}}{V_{2}} = {(\frac{1}{5})}^{\frac{5}{2}}$

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