Kinetic theory of ideal gases

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Question

If four molecules of a gas have speed 2, 4, 6, 8 kms^-1 respectively, then root mean square speed (in kms^-1) will be .. and respectively.

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Solution

Here, $c_{1} = 2 {kms}^{- 1}; c_{2} = 4 {kms}^{- 1}$
$c_{3} = 6 {kms}^{- 1} and c_{4} = 8 {kms}^{- 1}$
,

Root mean square speed,
$\begin{matrix} c = \sqrt{\frac{c_{1}^{2} + c_{2}^{2} + c_{3}^{2} + c_{4}^{2}}{4}} = \sqrt{\frac{2^{2} + 4^{2} + 6^{2} + 8^{2}}{4}} \\ = 5 .48 {kms}^{- 1} \end{matrix}$

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