At constant pressure,the root mean square vel | vedclass

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

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$1/\sqrt{d}$

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(D) The root mean square velocity $(u_{rms})$ of an ideal gas is given by the formula: $u_{rms} = \sqrt{\frac{3RT}{M}}$.From the ideal gas equation,$PV = nRT = \frac{m}{M}RT$,we can write $P = \frac{m}{MV}RT = \frac{dRT}{M}$,where $d$ is the density $(d = m/V)$.Thus,$\frac{RT}{M} = \frac{P}{d}$.Substituting this into the $u_{rms}$ formula,we get $u_{rms} = \sqrt{\frac{3P}{d}}$.Since pressure $(P)$ is constant,$u_{rms} \propto \frac{1}{\sqrt{d}}$.

At constant pressure,the root mean square velocity of an ideal gas is proportional to the density $(d)$ as:

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