Question

How many degrees of freedom have the gas molecules if at S.T.P the gas density is 1.3 kg/m${}^3$ and the velocity of sound in the gas is 330 m/sec?

• A. $5$
• B. $6$
• C. $4$
• D. $3$

Answer 1

The correct option is A $5$

Velocity of sound in the gas is given by
$v=\sqrt{\frac{\gamma P}{\rho }}$ where
P is pressure, $\rho$ is the density of the gas and $\gamma =\frac{C_p}{C_v}$ is the ratio of specific heats at constant pressure to constant volume.
$\therefore \gamma =\frac{{330}^2\times 1.3}{1.013\times {10}^5}=1.4$
But, $\gamma =\frac{2+f}{f}$ where f is the no of degrees of freedom.
Solving $1.4=\frac{2}{f}+1$
$\therefore \frac{2}{f}=0.4$
$\therefore f=5$