Suppose a polyatomic gas molecule has n degree of freedom.
Total energy associated with one gram molecule of the gas, i.e.,
E = n × \(\frac{1}{2}\)RT × 1
=\(\frac{n}{2}\)RT
As,
Cv = \(\frac{d}{dT}\)€
= \(\frac{d}{dT}\)(\(\frac{n}{2}\)RT)
= \(\frac{n}{2}\)R
Cp = Cv + R
Cp = \(\frac{n}{2}\)R + R
= (\(\frac{n}{2}\)+1)R
γ= \(\frac{C_p}{C_V}\)
γ= \(\frac{(\frac{n}{2}+1)R}{\frac{n}{2}R}\)
∴ = \(\frac{2}{n}\)(\(\frac{n}{2}\)+1)
γ= 1+\(\frac{2}{n}\)
