The average speed bar{v} and r.m.s. speed v_{ | vedclass

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Question

(A) The root mean square speed is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.The average speed is given by $\bar{v} = \sqrt{\frac{8RT}{\pi M}}$.Taking

Vedclass · Accepted Answer

$\bar{v} = 0.92\,v_{rms}$

Vedclass · Answer

(A) The root mean square speed is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.The average speed is given by $\bar{v} = \sqrt{\frac{8RT}{\pi M}}$.Taking the ratio of the two speeds:$\frac{\bar{v}}{v_{rms}} = \frac{\sqrt{\frac{8RT}{\pi M}}}{\sqrt{\frac{3RT}{M}}} = \sqrt{\frac{8}{3\pi}}$.Calculating the value:$\sqrt{\frac{8}{3 	imes 3.14}} = \sqrt{\frac{8}{9.42}} \approx \sqrt{0.849} \approx 0.921$.Therefore,$\bar{v} = 0.92\,v_{rms}$.

The average speed $\bar{v}$ and $r.m.s.$ speed $v_{rms}$ of the molecules are related as

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