(B) The root mean square velocity $(v_{rms})$ of a gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since the temperature $T$ is constant

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(B) The root mean square velocity $(v_{rms})$ of a gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since the temperature $T$ is constant,$v_{rms} \propto \frac{1}{\sqrt{M}}$.Therefore,the ratio of the root mean square velocities $v_1$ and $v_2$ for two gases with molecular weights $M_1$ and $M_2$ is:$\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}}$.

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

Easy

If the molecular weights of two gases are $M_1$ and $M_2$,then at a constant temperature,the ratio of their root mean square velocities $v_1$ and $v_2$ will be:

A
$\sqrt{\frac{M_1}{M_2}}$
B
$\sqrt{\frac{M_2}{M_1}}$
C
$\sqrt{\frac{M_1 + M_2}{M_1 - M_2}}$
D
$\sqrt{\frac{M_1 - M_2}{M_1 + M_2}}$

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Class 11

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Chapter

Kinetic Theory of Gases

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

Light gases like $H_2$ and $He$ are found in negligible amounts in the atmosphere. Why?

Medium

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The $r.m.s.$ speed of the molecules of a gas in a vessel is $400 \; m/s$. If half of the gas leaks out,at constant temperature,the $r.m.s.$ speed of the remaining molecules will be ..... $m/s$.

Easy

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At a temperature of $27^{\circ}C$ and a pressure of $1 \, atm$,the ratio of the root mean square velocities $(\nu_{rms})_{H_2} / (\nu_{rms})_{O_2}$ for hydrogen and oxygen molecules is:

Medium

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At temperature $T,$ the $r.m.s.$ speed of helium molecules is the same as the $r.m.s.$ speed of hydrogen molecules at normal temperature and pressure $(NTP)$. The value of $T$ is ....... $^\circ C$.

Medium

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If the $rms$ speed of hydrogen gas is equal to the $rms$ speed of oxygen gas at $47^{\circ}C$,find the temperature of the hydrogen gas in $K$.

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If the molecular weights of two gases are $M_1$ and $M_2$,then at a constant temperature,the ratio of their root mean square velocities $v_1$ and $v_2$ will be:

Similar Questions

Light gases like $H_2$ and $He$ are found in negligible amounts in the atmosphere. Why?

The $r.m.s.$ speed of the molecules of a gas in a vessel is $400 \; m/s$. If half of the gas leaks out,at constant temperature,the $r.m.s.$ speed of the remaining molecules will be ..... $m/s$.

At a temperature of $27^{\circ}C$ and a pressure of $1 \, atm$,the ratio of the root mean square velocities $(\nu_{rms})_{H_2} / (\nu_{rms})_{O_2}$ for hydrogen and oxygen molecules is:

At temperature $T,$ the $r.m.s.$ speed of helium molecules is the same as the $r.m.s.$ speed of hydrogen molecules at normal temperature and pressure $(NTP)$. The value of $T$ is ....... $^\circ C$.

If the $rms$ speed of hydrogen gas is equal to the $rms$ speed of oxygen gas at $47^{\circ}C$,find the temperature of the hydrogen gas in $K$.

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