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+‌

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+‌

2

54

⇒γ=1+‌

1

27

⇒‌‌γ=‌

28

27

or γ=1.03