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A polyatomic gas has $f$ vibrational degrees of freedom, then the ratio of the specific heat at constant pressure to that at constant volume will be
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Verified Answer
The correct answer is:
$\frac{4+f}{3+f}$
For a polyatomic atom value of specific heat at constant volume, $C_V=(3+f) R$ where, $f=$ vibration degree of freedom and $R=$ gas constant.
Now,
$$
\begin{aligned}
& C_p=C_V+R \\
& C_p=(3+f) R+R \\
& C_p=(4+f) R
\end{aligned}
$$
Now, ratio of $C_p$ and $C_V$
$$
\frac{C_p}{C_V}=\frac{4+f}{3+f}
$$
Now,
$$
\begin{aligned}
& C_p=C_V+R \\
& C_p=(3+f) R+R \\
& C_p=(4+f) R
\end{aligned}
$$
Now, ratio of $C_p$ and $C_V$
$$
\frac{C_p}{C_V}=\frac{4+f}{3+f}
$$
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