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  4. 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 32V , the efficiency of the engine is :-

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Q. 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 $32V$ , the efficiency of the engine is :-

NTA AbhyasNTA Abhyas 2020

Solution:

$T_{1}V_{1}^{\gamma - 1}=T_{2}V_{2}^{\gamma - 1}\Rightarrow \frac{T_{2}}{ T_{1}}=\frac{1}{4}$
So, $\eta=1-\frac{T_{2}}{ T_{1}}=0.75$