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+
2
f
.....(i) As each vibrational mode has 2 degrees of freedom, hence total vibrational degrees of freedom =2×24=48 ⇒f=3 (rotational) +3 (translational) +48 (vibrational) ⇒f=3+3+48⇒f=54 Now, put the value of f in Eq. (i), we get γ=1+