Thermodynamics Part 2

Since we know that, the heat capacity ratio $γ$ for an ideal gas can be related to the degrees of freedom of gas molecules $(f)$ by formula $γ=1+\;\frac{2}{f}$.....(i) As each vibrational mode has 2 degrees of freedom, hence total vibrational degrees of freedom $=2 \times 24=48$ $\Rightarrow f=3$ (rotational) $+3$ (translational) $+48$ (vibrational) $\Rightarrow \;\; f=3+3+48 \Rightarrow f=54$ Now, put the value of $f$ in Eq. (i), we get $γ=1+\;\frac{2}{54} \Rightarrow γ=1+\;\frac{1}{27}$ $\Rightarrow \;\; γ=\;\frac{28}{27}$ or $γ=1.03$