Question

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

• A. $1.03$
• B. $1.30$
• C. $10.3$
• D. $1.37$

Answer 1

The correct option is A $1.03$

From the formula of degree of freedom, we have,

Degree of freedom,
$f=\text{Translational DOF+Rotational DOF+Vibrational DOF}$

$\Rightarrow f=3+3+24\times 2$

Since, each vibrational mode has $2$ degrees of freedom.

$\Rightarrow f=54$

Now, $\gamma$ of the gas is given by,

$\gamma =1+\frac{2}{f}$

$\Rightarrow \gamma =1+\frac{2}{54}\approx 1.03$

Hence, $\left(A\right)$ is the required answer.