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  4. A diatomic gas molecule has translational, rotational and vibrational degrees of freedom . Then (cp/cv) is

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Q. A diatomic gas molecule has translational, rotational and vibrational degrees of freedom . Then $\frac{c_p}{c_v}$ is

Kinetic Theory

Solution:

Potential energy, $U =\frac{ f }{2} nRT $ and $ C _{ V }=\frac{ f }{2} R$
Where,
$f$ is degree of freedom.
For diatomic gas, $f =5$
$
\begin{array}{l}
C_{V}=\frac{5}{2} R \\
C_{P}=C_{V}+R=\frac{5}{2} R+R=\frac{7}{2} R
\end{array}
$
Specific heat ratio, $\gamma=\frac{ C _{ p }}{ C _{ v }}=\frac{7}{5}=1.4$
Hence, specific heat ratio is $1.4$