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  4. The root mean square velocity of the molecules of a gas is 1260 m s-1. The average speed of the molecules is

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Q. The root mean square velocity of the molecules of a gas is $1260\, m \,s^{-1}$. The average speed of the molecules is

Kinetic Theory

Solution:

$\upsilon_{av} = \sqrt{\frac{8kT}{m\pi}}, \upsilon_{rms} = \sqrt{\frac{3kT}{m }}$
$\therefore \quad \frac{\upsilon _{av} }{\upsilon _{rms}} = \frac{\sqrt{8/\pi}}{\sqrt{3}} \quad$ or $\quad \frac{\upsilon _{av}}{1260} = \sqrt{\frac{8}{3\pi }}$
$\therefore \quad \upsilon _{av} = 1260\times \sqrt{\frac{8}{3\pi }} = 1161\,m\,s^{-1}$