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  4. A polyatomic ideal gas has 24 vibrational modes. What is the value of γ ?

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Q. A polyatomic ideal gas has $24$ vibrational modes. What is the value of $\gamma$ ?

JEE MainJEE Main 2021Kinetic Theory

Solution:

Since each vibrational mode has $2$ degrees of freedom hence total vibrational degrees of
freedom $=48$
$f=3+3+48=54$
$\gamma=1+\frac{2}{ f }=\frac{28}{27}=1.03$