(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 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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$A$ 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

$A$ jar has a mixture of hydrogen and oxygen gas in the ratio of $1 : 5$. The ratio of mean kinetic energies of hydrogen and oxygen molecules is

Two ideal gases at absolute temperatures $T_1$ and $T_2$ are mixed. There is no loss of energy. The masses of the molecules are $m_1$ and $m_2$ and the number of molecules in the gases are $n_1$ and $n_2$ respectively. The temperature of the mixture will be:

Three ideal gases at absolute temperatures $T_1, T_2,$ and $T_3$ are mixed. The number of molecules are $n_1, n_2,$ and $n_3$ respectively. Assuming no loss of energy,what is the final temperature of the mixture?

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