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(D) For a polytropic process $PV^n = K$, the molar heat capacity is given by $C = C_v + \frac{R}{1-n}$.For a diatomic gas, $C_v = \frac{5}{2}R$. Given

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None of these.

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(D) For a polytropic process $PV^n = K$, the molar heat capacity is given by $C = C_v + \frac{R}{1-n}$.For a diatomic gas, $C_v = \frac{5}{2}R$. Given $n = 1.3$, $C = \frac{5}{2}R + \frac{R}{1-1.3} = 2.5R - 3.33R = -0.83R$.Since $C  0$ for expansion in this process, but here $C$ is negative, implying heat is released or absorbed depending on the sign of $dT$).Actually, for $1 Statement $A$: The gas absorbs heat during expansion. This is correct.Statement $B$: The gas cools down during expansion. This is correct as $T \propto V^{1-n} = V^{-0.3}$.Statement $C$: Work done by the gas is positive during expansion, so work done by the surroundings is negative. This is correct.Since all statements $A$, $B$, and $C$ are correct, the incorrect statement is none of these.

$A$ diatomic gas undergoes a process represented by $PV^{1.3} = \text{constant}$. Choose the incorrect statement.

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