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Q.
The root mean square velocity of the molecules of a gas is $1260 \,m / s$. The average speed of the molecules is
Kinetic Theory
Solution:
$v_{ av }=\sqrt{\frac{8 k T}{m \pi}}, $
$v_{ rms }=\sqrt{\frac{3 k T}{m}}$
$\therefore \frac{v_{ av }}{v_{ rms }} =\frac{\sqrt{8 / \pi}}{\sqrt{3}} $
or$ \frac{v_{ av }}{1260}=\sqrt{\frac{8}{3 \pi}} $
$ \therefore v_{ av }=1260 \times \sqrt{\frac{8}{3 \pi}}=1161\, m s ^{-1}$