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(D) For a polytropic process $p V^x = C$,the molar heat capacity $C_{process}$ is given by the formula $C_{process} = C_V + \frac{R}{1 - x}$.Here,the

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$R$

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(D) For a polytropic process $p V^x = C$,the molar heat capacity $C_{process}$ is given by the formula $C_{process} = C_V + \frac{R}{1 - x}$.Here,the given process is $p V^3 = C$,so $x = 3$.For a monoatomic ideal gas,the molar heat capacity at constant volume is $C_V = \frac{3}{2} R$.Substituting these values into the formula:$C_{process} = \frac{3}{2} R + \frac{R}{1 - 3}$$C_{process} = \frac{3}{2} R + \frac{R}{-2}$$C_{process} = \frac{3}{2} R - \frac{1}{2} R = R$.Thus,the heat capacity of the gas during the process is $R$.

One mole of a monoatomic ideal gas is expanded by a process described by $p V^3 = C$,where $C$ is a constant. The heat capacity of the gas during the process is given by ($R$ is the gas constant).

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