Which of the following equations does not rep | vedclass

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

Vedclass · Accepted Answer

$(\frac{3P}{dM_w})^{1/2}$

Vedclass · Answer

(D) The root mean square velocity $(u_{rms})$ of a gas is given by the formula: $u_{rms} = \sqrt{\frac{3RT}{M_w}}$.From the ideal gas equation,$PV = nRT = \frac{m}{M_w}RT$,we have $\frac{RT}{M_w} = \frac{PV}{m} = \frac{P}{\rho}$,where $\rho$ (or $d$) is the density of the gas $(d = \frac{m}{V})$.Substituting this into the $u_{rms}$ formula:$1$. $u_{rms} = \sqrt{\frac{3RT}{M_w}}$ (Option $A$ is correct).$2$. $u_{rms} = \sqrt{\frac{3P}{d}}$ (Option $B$ is correct).$3$. $u_{rms} = \sqrt{\frac{3PV}{M}}$ (Option $C$ is correct,as $PV = nRT$ and $M$ is total mass).Option $D$ is $(\frac{3P}{dM_w})^{1/2}$,which is dimensionally incorrect as it does not represent velocity.

Which of the following equations does not represent the root mean square velocity $(u_{rms})$?

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