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Temperature

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Question

How much would the root mean square speed become when the absolute temperature of a gas is increased by $16$ times ?

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Solution

Root mean square speed
$v_{r m s} \propto \sqrt{T}$
$∴ \frac{v_{r m s_{1}}}{v_{r m s_{2}}} = \sqrt{\frac{T_{1}}{T_{2}}}$
Given, $T_{2} = 16 T_{1}$
$∴ \frac{v_{r m s_{1}}}{v_{r m s_{2}}} = \sqrt{\frac{T_{1}}{16 T_{1}}}$
$\Rightarrow v_{r m s_{2}} = 4 v_{r m s_{1}}$

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