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(B) For a polytropic process,the relation between pressure $P$ and volume $V$ is given by $PV^n = 	ext{constant}$.Given that the process is parabolic

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$\frac{17 R}{6}$

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(B) For a polytropic process,the relation between pressure $P$ and volume $V$ is given by $PV^n = 	ext{constant}$.Given that the process is parabolic,$P \propto V^2$,which implies $P = aV^2$. However,looking at the standard form $PV^n = K$,we rewrite this as $P V^{-2} = K$,so $n = -2$.For an ideal diatomic gas,the adiabatic index $\gamma = 1.4 = \frac{7}{5}$.The molar specific heat $C$ for a polytropic process is given by $C = \frac{R}{\gamma - 1} + \frac{R}{1 - n}$.Substituting the values: $C = \frac{R}{\frac{7}{5} - 1} + \frac{R}{1 - (-2)} = \frac{R}{\frac{2}{5}} + \frac{R}{3} = \frac{5R}{2} + \frac{R}{3}$.Calculating the sum: $C = \frac{15R + 2R}{6} = \frac{17R}{6}$.

The variation of pressure $P$ with volume $V$ for an ideal diatomic gas is parabolic as shown in the figure. The molar specific heat of the gas during this process is

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