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 $=48$

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

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

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