(A) The root mean square speed of a gas molecule is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$. Since $T$ is constant,$v_{rms} \propto \frac{1}{\sqrt{M

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$(v_{rms})_1 < (v_{rms})_2 < (v_{rms})_3$ and $(\bar{K})_1 = (\bar{K})_2 = (\bar{K})_3$

(A) The root mean square speed of a gas molecule is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$. Since $T$ is constant,$v_{rms} \propto \frac{1}{\sqrt{M}}$.Given $m_1 > m_2 > m_3$,it follows that $(v_{rms})_1 The average kinetic energy of a gas molecule is given by $\bar{K} = \frac{3}{2}kT$. Since the temperature $T$ is the same for all gases in the mixture,the average kinetic energy depends only on the temperature and is independent of the molecular mass.Therefore,$(\bar{K})_1 = (\bar{K})_2 = (\bar{K})_3$.

Class 11 Physics Kinetic Theory of Gases Speed (velocity) of Gas (rms, mean and Most probable speed)

Easy

For a mixture of three different gases with molecular masses $m_1 > m_2 > m_3$ at the same temperature,what is the relationship between their root mean square speeds $(v_{rms})$ and average kinetic energies $(\bar{K})$?

A
$(v_{rms})_1 < (v_{rms})_2 < (v_{rms})_3$ and $(\bar{K})_1 = (\bar{K})_2 = (\bar{K})_3$
B
$(v_{rms})_1 = (v_{rms})_2 = (v_{rms})_3$ and $(\bar{K})_1 = (\bar{K})_2 > (\bar{K})_3$
C
$(v_{rms})_1 > (v_{rms})_2 > (v_{rms})_3$ and $(\bar{K})_1 < (\bar{K})_2 > (\bar{K})_3$
D
$(v_{rms})_1 > (v_{rms})_2 > (v_{rms})_3$ and $(\bar{K})_1 < (\bar{K})_2 < (\bar{K})_3$

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Kinetic Theory of Gases

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Speed (velocity) of Gas (rms, mean and Most probable speed)

An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by $2$ times the initial rms speed. If the initial gas temperature is $27^{\circ} C$, then the final temperature of the ideal gas is : (in $^{\circ} C$)

EasyTS EAMCET 2019

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Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic),the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement among the following is:

EasyNEET 2022

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At $T$ $K$ temperature,the average speed of $O_2$ will be $\left( \frac{7}{4} \right)$ of the $rms$ speed of $N_2$ at $47\,^oC$. Find the value of $T$.

Medium

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The rms speed of an oxygen molecule in a vessel at a particular temperature is $\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v$,where $v$ is the average speed of the molecule. The value of $x$ will be: (Take $\pi=\frac{22}{7}$)

MediumJEE MAIN 2023

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If ${V_H}$,${V_N}$,and ${V_O}$ denote the root-mean-square velocities of molecules of hydrogen,nitrogen,and oxygen respectively at a given temperature,then:

Medium

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For a mixture of three different gases with molecular masses $m_1 > m_2 > m_3$ at the same temperature,what is the relationship between their root mean square speeds $(v_{rms})$ and average kinetic energies $(\bar{K})$?

Similar Questions

An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by $2$ times the initial rms speed. If the initial gas temperature is $27^{\circ} C$, then the final temperature of the ideal gas is : (in $^{\circ} C$)

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic),the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement among the following is:

At $T$ $K$ temperature,the average speed of $O_2$ will be $\left( \frac{7}{4} \right)$ of the $rms$ speed of $N_2$ at $47\,^oC$. Find the value of $T$.

The rms speed of an oxygen molecule in a vessel at a particular temperature is $\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v$,where $v$ is the average speed of the molecule. The value of $x$ will be: (Take $\pi=\frac{22}{7}$)

If ${V_H}$,${V_N}$,and ${V_O}$ denote the root-mean-square velocities of molecules of hydrogen,nitrogen,and oxygen respectively at a given temperature,then:

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