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(D) The molar specific heat $C$ for a polytropic process $PV^{n} = 	ext{constant}$ is given by the formula: $C = C_{V} + \frac{R}{1-n}$.Given that th

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$\gamma$

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(D) The molar specific heat $C$ for a polytropic process $PV^{n} = 	ext{constant}$ is given by the formula: $C = C_{V} + \frac{R}{1-n}$.Given that the specific heat $C = 0$, we have: $0 = C_{V} + \frac{R}{1-n}$.Substituting $C_{V} = \frac{R}{\gamma-1}$, we get: $0 = \frac{R}{\gamma-1} + \frac{R}{1-n}$.Rearranging the terms: $\frac{R}{n-1} = \frac{R}{\gamma-1}$.This implies $n-1 = \gamma-1$, which simplifies to $n = \gamma$.Therefore, the process is an adiabatic process, and the value of $n$ is $\gamma$.

$A$ gas undergoes a change in which its pressure $P$ and volume $V$ are related as $PV^{n} = \text{constant}$, where $n$ is a constant. If the specific heat of the gas in this change is zero, then the value of $n$ is $(\gamma = \text{adiabatic ratio})$.

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