Question

Calculate the ratio of average velocity of helium atom at ${27}^{o}C$ and methane molecule at ${127}^{o}C$.

Answer 1

We know,

$U_{avg}=\sqrt{\frac{8RT}{\pi M}}$

So,

$\frac{U_{avg}\left(He\right)}{U_{avg}\left(C{H}_4\right)}=\sqrt{\frac{T_{He}\times M_{C{H}_4}}{T_{C{H}_4}\times M_{He}}}$

$M_{He}=4$, $M_{C{H}_4}=16$

Hence,

$\frac{U_{avg}\left(He\right)}{U_{avg}\left(C{H}_4\right)}=\sqrt{3}$