(A) The $r.m.s.$ speed of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since the temperature $T$ is the same for all gases

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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 $r.m.s.$ speed of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since the temperature $T$ is the same for all gases in the mixture,$v_{rms} \propto \frac{1}{\sqrt{M}}$.Given $m_1 > m_2 > m_3$,it follows that $(v_{rms})_1 The average kinetic energy of a gas molecule is given by $\bar K = \frac{3}{2} k_B T$.Since the temperature $T$ is the same for all gases in the mixture,the average kinetic energy $\bar K$ is the same for all types of molecules,i.e.,$(\bar K)_1 = (\bar K)_2 = (\bar K)_3$.

Class 11 Physics Kinetic Theory of Gases Mixture of Gases

Medium

$A$ gas mixture consists of molecules of type $1, 2$ and $3$,with molar masses $m_1 > m_2 > m_3$. $v_{rms}$ and $\bar K$ are the $r.m.s.$ speed and average kinetic energy of the gases. Which of the following is true?

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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Mixture of Gases

$2$ moles of $O_2$ and $4$ moles of $Ar$ are filled in a container at temperature $T$. What is the total internal energy (in $, RT$)?

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The container shown in the figure has two chambers,separated by a partition,with volumes $V_1 = 2.0 \, L$ and $V_2 = 3.0 \, L$. The chambers contain $\mu_1 = 4.0 \, mol$ and $\mu_2 = 5.0 \, mol$ of a gas at pressures $P_1 = 1.00 \, atm$ and $P_2 = 2.00 \, atm$. Calculate the pressure after the partition is removed and the mixture attains equilibrium.

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Three identical containers contain three different gases. The masses of the molecules are $m_1, m_2$,and $m_3$,and the number of molecules in the containers are $N_1, N_2$,and $N_3$,respectively. The pressures of the gases in the containers are $P_1, P_2$,and $P_3$,respectively. If these three gases are mixed and filled into a single container of the same volume,what will be the pressure of the mixture?

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$A$ container holds $8 \, g$ of $O_2$ and $7 \, g$ of $N_2$ at a pressure of $10 \, atm$. If $O_2$ is removed,the pressure becomes ... $atm$.

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If $1 \text{ mole}$ of a monoatomic gas $\left[ \gamma = \frac{5}{3} \right]$ is mixed with $1 \text{ mole}$ of a diatomic gas $\left[ \gamma = \frac{7}{5} \right]$,then the $\gamma$ of the mixture is ..........?

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$A$ gas mixture consists of molecules of type $1, 2$ and $3$,with molar masses $m_1 > m_2 > m_3$. $v_{rms}$ and $\bar K$ are the $r.m.s.$ speed and average kinetic energy of the gases. Which of the following is true?

Similar Questions

$2$ moles of $O_2$ and $4$ moles of $Ar$ are filled in a container at temperature $T$. What is the total internal energy (in $, RT$)?

$A$ container holds $8 \, g$ of $O_2$ and $7 \, g$ of $N_2$ at a pressure of $10 \, atm$. If $O_2$ is removed,the pressure becomes ... $atm$.

If $1 \text{ mole}$ of a monoatomic gas $\left[ \gamma = \frac{5}{3} \right]$ is mixed with $1 \text{ mole}$ of a diatomic gas $\left[ \gamma = \frac{7}{5} \right]$,then the $\gamma$ of the mixture is ..........?

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