For polyatomic gas molecule has 3 rotational degrees of freedom, 3 translational degrees of freedom, and 2 vibrational modes.
So, number of vibrational degrees of freedom
=2(2)=4 ∴ Total number of degrees of freedom,
f=3+3+4=10 Here, ratio of molar specific heats is given as
β= In terms of degrees of freedom,
β=1+ Substituting the value of
f in above equation, we get
β=1+⇒β=1.2