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The ratio of the specific heats $\frac{C_P}{C_V} = \gamma$ in terms of degrees of freedom (n) is given by
A
$\left(1 + \frac{1}{n}\right)$
B
$\left(1 + \frac{n}{3}\right)$
C
$\left(1 + \frac{2}{n}\right)$
D
$\left(1 + \frac{n}{2}\right)$
Detailed Solution
$C_v = \frac{n}{2}R$ and $C_p = \left(\frac{n}{2} + 1\right)R$
$\gamma = \frac{C_p}{C_v} = \frac{\frac{n}{2} + 1}{\frac{n}{2}} = \frac{n+2}{n}$
$\gamma = 1 + \frac{2}{n}$
$\gamma = \frac{C_p}{C_v} = \frac{\frac{n}{2} + 1}{\frac{n}{2}} = \frac{n+2}{n}$
$\gamma = 1 + \frac{2}{n}$