Question

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

• A. 1.67
• B. 1.4
• C. 1.29
• D. 1.33

Answer 1

Answer: (B)

Potential energy, $U=\frac{f}{2}nRT$ and $C_V=\frac{f}{2}R$
Where,
$f$ is degree of freedom.
For diatomic gas, $f=5$
$<br/>\begin{array}{l}<br/>C_V=\frac{5}{2}R\\ <br/>C_P=C_V+R=\frac{5}{2}R+R=\frac{7}{2}R<br/>\end{array}<br/>$
Specific heat ratio, $\gamma =\frac{C_p}{C_v}=\frac{7}{5}=1.4$
Hence, specific heat ratio is $1.4$