(D) The root mean square speed $(v_{rms})$ is given by $\sqrt{3RT/M}$,and the most probable speed $(v_{mp})$ is given by $\sqrt{2RT/M}$. Since $\sqrt{

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If both the Assertion and Reason are incorrect.

(D) The root mean square speed $(v_{rms})$ is given by $\sqrt{3RT/M}$,and the most probable speed $(v_{mp})$ is given by $\sqrt{2RT/M}$. Since $\sqrt{3} \neq \sqrt{2}$,these speeds are not the same. Thus,the Assertion is incorrect.The Maxwell-Boltzmann distribution curve for molecular speeds is skewed to the right (asymmetric),meaning it has a long tail towards higher speeds. Therefore,the distribution is not symmetrical. Thus,the Reason is also incorrect.

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

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$Assertion :$ The root mean square and most probable speeds of the molecules in a gas are the same.
$Reason :$ The Maxwell distribution for the speed of molecules in a gas is symmetrical.

AIIMS 2006 All AIIMS

A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

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Class 11

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Kinetic Theory of Gases

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

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AIIMS 2006 Paper All AIIMS years →

If a container is filled with a mixture of $H_2$ and $O_2$ gases at the same temperature,then:

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The rms speed of an oxygen molecule at a certain temperature is $600 \,ms^{-1}$. If the temperature is doubled and the oxygen molecule dissociates into atomic oxygen atoms,the new rms speed is (in $\,ms^{-1}$)

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At temperature $T$,$N$ molecules of gas $A$ each having mass $m$ and at the same temperature $2N$ molecules of gas $B$ each having mass $2m$ are filled in a container. The mean square velocity of molecules of gas $B$ is $v^2$ and the mean square of the $x$-component of velocity of molecules of gas $A$ is $w^2$. The ratio of $w^2/v^2$ is:

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Let $\bar{v}$,$v_{rms}$ and $v_p$ respectively denote the mean speed,root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature $T$. The mass of the molecule is $m$. Then:

Medium

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$A$ vessel is partitioned into two equal halves by a fixed diathermic separator. Two different ideal gases are filled in the left $(L)$ and right $(R)$ halves. The rms speed of the molecules in the $L$ part is equal to the mean speed of the molecules in the $R$ part. Then the ratio of the mass of a molecule in the $L$ part to that of a molecule in the $R$ part is

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$Assertion :$ The root mean square and most probable speeds of the molecules in a gas are the same.$Reason :$ The Maxwell distribution for the speed of molecules in a gas is symmetrical.

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If a container is filled with a mixture of $H_2$ and $O_2$ gases at the same temperature,then:

The rms speed of an oxygen molecule at a certain temperature is $600 \,ms^{-1}$. If the temperature is doubled and the oxygen molecule dissociates into atomic oxygen atoms,the new rms speed is (in $\,ms^{-1}$)

Let $\bar{v}$,$v_{rms}$ and $v_p$ respectively denote the mean speed,root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature $T$. The mass of the molecule is $m$. Then:

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$Assertion :$ The root mean square and most probable speeds of the molecules in a gas are the same.
$Reason :$ The Maxwell distribution for the speed of molecules in a gas is symmetrical.