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(D) The given process is $\frac{PT^2}{V} = 	ext{constant}$.For a diatomic gas, the molar heat capacity at constant volume is $C_V = \frac{5}{2}R$.Usi

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$4R$

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(D) The given process is $\frac{PT^2}{V} = 	ext{constant}$.For a diatomic gas, the molar heat capacity at constant volume is $C_V = \frac{5}{2}R$.Using the ideal gas equation $PV = nRT$, we have $T = \frac{PV}{nR}$, which implies $T \propto PV$.Substituting $T$ into the given process equation:$\frac{P(PV)^2}{V} = 	ext{constant} \implies \frac{P^3V^2}{V} = 	ext{constant} \implies P^3V = 	ext{constant}$.Taking the cube root, we get $PV^{1/3} = 	ext{constant}$.This is a polytropic process of the form $PV^x = 	ext{constant}$, where $x = 1/3$.The molar heat capacity $C$ for a polytropic process is given by $C = C_V + \frac{R}{1-x}$.Substituting the values: $C = \frac{5}{2}R + \frac{R}{1 - 1/3} = \frac{5}{2}R + \frac{R}{2/3} = \frac{5}{2}R + \frac{3}{2}R = \frac{8}{2}R = 4R$.

$2$ moles of a diatomic gas undergoes the process: $PT^2/V = \text{constant}$. The molar heat capacity of the gas during the process is:

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