At a given temperature if ${\mathrm{V}}_{\mathrm{rms}}$ is the root mean square velocity of the molecules of a gas and ${\mathrm{V}}_{\mathrm{s}}$ the velocity of sound in it, then these are related as $\left(\mathrm{\gamma }=\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{v}}}\right)$

1. ${\mathrm{V}}_{\mathrm{rms}}={\mathrm{V}}_{\mathrm{s}}$

2. ${\mathrm{V}}_{\mathrm{rms}}=\sqrt{\frac{3}{\mathrm{\gamma }}}×{\mathrm{V}}_{\mathrm{s}}$

3. ${\mathrm{V}}_{\mathrm{rms}}=\sqrt{\frac{\mathrm{\gamma }}{3}}×{\mathrm{V}}_{\mathrm{s}}$

4. ${\mathrm{V}}_{\mathrm{rms}}=\left(\frac{3}{\mathrm{\gamma }}\right)×{\mathrm{V}}_{\mathrm{s}}$