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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$\mathrm{T}_{1} \mathrm{V}_{1}^{\gamma-1}=\mathrm{T}_{2} \mathrm{V}_{2}^{\gamma-1}$
$\mathrm{T}_{1}(\mathrm{V})^{\frac{7}{5}-1}=\mathrm{T}_{2}(32 \mathrm{V})^{\frac{7}{5}-1}$
$\mathrm{T}_{1}=4 \mathrm{T}_{2}$
$\eta=1-\frac{T_{2}}{4 T_{2}}=0.75$
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