The root mean square (r.m.s.) velocity of a g | vedclass

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(D) The root mean square velocity $(v_{rms})$ of an ideal gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$ or $v_{rms} = \sqrt{\frac{3P}{

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$v$

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(D) The root mean square velocity $(v_{rms})$ of an ideal gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$ or $v_{rms} = \sqrt{\frac{3P}{\rho}}$.From the relation $v_{rms} = \sqrt{\frac{3RT}{M}}$,it is clear that $v_{rms}$ depends only on the temperature $(T)$ and the molar mass $(M)$ of the gas.Since the temperature is kept constant,the $r.m.s.$ velocity remains independent of the pressure $(P)$.Therefore,even if the pressure is increased to $2P$,the $r.m.s.$ velocity remains $v$.

The root mean square $(r.m.s.)$ velocity of a gas particle is $v$ at pressure $P$. If the pressure is increased to $2P$ while keeping the temperature constant,the $r.m.s.$ velocity becomes:

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