Diatomic gas is used in carnot heat engine. If efficiency of given carnot heat engine is $80\%$ , then find the ratio of initial volume to final volume of gas during adiabatic expansion
Diffcult
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$\eta=1-\frac{T_{2}}{T_{1}}$
$0.8=1-\frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}$
$\frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}=0.2$
$\mathrm{T}_{2} \mathrm{V}_{2}^{\gamma-1}=\mathrm{T}_{1} \mathrm{V}_{1}^{\gamma-1}$
$\left(\frac{\mathrm{V}_{2}}{\mathrm{V}_{1}}\right)^{\gamma-1}=\frac{\mathrm{T}_{1}}{\mathrm{T}_{2}}=5$
$\frac{V_{1}}{V_{2}}=\left(\frac{1}{5}\right)^{\frac{5}{2}}$
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