Question

The average velocity of gas molecules is $400\text{m/sec}$. Calculate its rms velocity at the same temperature.

Answer 1

$C_{\text{rms}}=\sqrt{\frac{3RT}{M}},C_{\text{av}}=\sqrt{\frac{8RT}{\pi M}}$
$\frac{C_{\text{rms}}}{C_{\text{av}}}=\sqrt{\frac{3RT}{M}}\times \sqrt{\frac{\pi M}{8RT}}=\sqrt{\frac{3\pi }{8}}=1.085$
$C_{\text{rms}}=1.085\times C_{\text{av}}=1.085\times 400=434{\text{ms}}^{-1}$