# A polyatomic ideal gas has 24 vibrational modes.

Question:

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

1. (1) $1.03$

2. (2) $1.3$

3. (3) $1.37$

4. (4) $10.3$

Correct Option: 1

Solution:

(1)

Since each vibrational mode has 2 degrees of freedom hence total vibrational degrees of

freedom $=48$

$\mathrm{f}=3+3+48=54$

$\gamma=1+\frac{2}{\mathrm{f}}=\frac{28}{27}=1.03$