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Degree of Freedom

An ideal gas ...

Question

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by $P V^{n}$ = constant, then n is given by (Here $C_{P}$ and $C_{V}$ are molar specific heat at constant pressure and constant volume, respectively):

A

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B

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C

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D

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Solution

The correct option is A

$C = C_{V} + \frac{R}{1 - n} \Rightarrow C - C_{V} = \frac{R}{1 - n} \to L o r C = C_{P} - R \frac{R}{1 - n} \Rightarrow C - C_{P} = \frac{n R}{1 - n} \Rightarrow \frac{C = C_{P}}{C - C_{V}} = n$

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