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.

List-$I$	List-$II$
$(a)$ $U_{rms} / U_{av}$	$(i)$ $1.22$
$(b)$ $U_{av} / U_{mp}$	$(ii)$ $1.13$
$(c)$ $U_{rms} / U_{mp}$	$(iii)$ $1.08$

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

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The ratio of root mean square velocity of $H_2$ at $50 \ K$ to that of $O_2$ at $800 \ K$ is

Match the following (where $U_{rms}$ = root mean square speed,$U_{av}$ = average speed,$U_{mp}$ = most probable speed)
List-$I$ List-$II$
$(a)$ $U_{rms} / U_{av}$ $(i)$ $1.22$
$(b)$ $U_{av} / U_{mp}$ $(ii)$ $1.13$
$(c)$ $U_{rms} / U_{mp}$ $(iii)$ $1.08$

Explain the molecular speed distribution curve.

At $T$ $(K)$,the $P$,$V$ and $u_{rms}$ of $1$ mole of an ideal gas were measured. The following graph is obtained. What is its slope $(m)$? ($x$-axis $= PV$; $y$-axis $= u_{rms}^2$,$M =$ Molar mass)

The rms velocity $u_{rms}$,mean velocity $u_{av}$ and most probable velocity $u_{mp}$ of a gas differ from each other at a given temperature. Which of the following ratios regarding them is correct?

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