Initially,the root mean square (rms) velocity | vedclass

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Question

(A) The formula for $rms$ velocity is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Initially,for $N_2$ molecules at temperature $T$,$u = \sqrt{\frac{3RT}{28 	ime

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$2 \ u$

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(A) The formula for $rms$ velocity is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Initially,for $N_2$ molecules at temperature $T$,$u = \sqrt{\frac{3RT}{28 	imes 10^{-3} \ kg/mol}}$.After the temperature is doubled $(T' = 2T)$ and $N_2$ dissociates into $N$ atoms,the molar mass becomes $M' = 14 	imes 10^{-3} \ kg/mol$.The new $rms$ velocity $v'$ is given by $v' = \sqrt{\frac{3R(2T)}{14 	imes 10^{-3}}} = \sqrt{4 	imes \frac{3RT}{28 	imes 10^{-3}}} = 2 	imes \sqrt{\frac{3RT}{28 	imes 10^{-3}}}$.Therefore,$v' = 2u$.

Initially,the root mean square $(rms)$ velocity of $N_2$ molecules at a certain temperature is $u$. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms,then the new $rms$ velocity will be:

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