Question

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

• A. $1.67$
• B. $2.14$
• C. $1.29$
• D. $1.33$

Answer 1

The correct option is D $1.33$

The diatomic molecule has total 6 degress of freedom(3 translational, 2 rotational and 1 vibrational)
Now $C_p$ is given as $(1+\frac{f}{2})R=(1+\frac{6}{2})R=4R$
and $C_v$ is given as $\frac{f}{2}R=\frac{6}{2}R=3R$
Thus we get $\frac{C_p}{C_v}=\frac{4}{3}=1.33$