# If one mole of the polyatomic gas is having two vibrational modes

Question:

If one mole of the polyatomic gas is having two vibrational modes and $\beta$ is the ratio of molar specific heats for polyatomic gas $\left(\beta=\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{v}}}\right)$ then the value of $\beta$ is :

1. (1) $1.02$

2. (2) $1.2$

3. (3) $1.25$

4. (4) $1.35$

Correct Option:

Solution:

(2)

$f=4+3+3=10$

assuming non linear

$\beta=\frac{C_{p}}{C_{v}}=1+\frac{2}{f}=\frac{12}{10}=1.2$