(D) The root mean square speed of molecules in part $L$ is given by: $v_{rms, L} = \sqrt{\frac{3KT}{m_L}}$The average speed of molecules in part $R$ i

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(D) The root mean square speed of molecules in part $L$ is given by: $v_{rms, L} = \sqrt{\frac{3KT}{m_L}}$The average speed of molecules in part $R$ is given by: $v_{av, R} = \sqrt{\frac{8KT}{\pi m_R}}$Given that $v_{rms, L} = v_{av, R}$,we equate the two expressions:$\sqrt{\frac{3KT}{m_L}} = \sqrt{\frac{8KT}{\pi m_R}}$Squaring both sides:$\frac{3KT}{m_L} = \frac{8KT}{\pi m_R}$Canceling $KT$ from both sides:$\frac{3}{m_L} = \frac{8}{\pi m_R}$Rearranging to find the ratio $\frac{m_L}{m_R}$:$\frac{m_L}{m_R} = \frac{3\pi}{8}$

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

Difficult

$A$ container is divided into two equal parts $L$ and $R$. If the root mean square (rms) speed of the molecules in part $L$ is equal to the average speed of the molecules in part $R$,find the ratio of the mass of a molecule in part $L$ to the mass of a molecule in part $R$.

A
$\sqrt{3/2}$
B
$\sqrt{\pi/4}$
C
$\sqrt{2/3}$
D
$3\pi/8$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Kinetic Theory of Gases

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

If $V_{rms}$ of $O_2$ molecule is equal to $V_{rms}$ of $H_2$ molecule at $20 K$,the temperature of $O_2$ is:

Medium

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The root mean square velocity of the molecules in a sample of helium is $(5/7)^{th}$ that of the molecules in a sample of hydrogen. If the temperature of the hydrogen sample is $0^{\circ}C$,then the temperature of the helium sample is about:

Medium

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To increase the rms speed of gas molecules by $25 \%$,the percentage increase in absolute temperature of the gas is to be

MediumAP EAMCET 2025

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The given diagram shows isotherms for a fixed mass of an ideal gas at temperatures $T_1$ and $T_2$. What is the value of the ratio $\frac{\text{r.m.s. speed of the molecules at temperature } T_2}{\text{r.m.s. speed of the molecules at temperature } T_1}$?

Difficult

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At room temperature,the $rms$ speed of a gas is $V_1$. If the pressure of the gas is doubled at the same room temperature,the $rms$ speed becomes $V_2$. Then:

Medium

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$A$ container is divided into two equal parts $L$ and $R$. If the root mean square (rms) speed of the molecules in part $L$ is equal to the average speed of the molecules in part $R$,find the ratio of the mass of a molecule in part $L$ to the mass of a molecule in part $R$.

Similar Questions

If $V_{rms}$ of $O_2$ molecule is equal to $V_{rms}$ of $H_2$ molecule at $20 K$,the temperature of $O_2$ is:

The root mean square velocity of the molecules in a sample of helium is $(5/7)^{th}$ that of the molecules in a sample of hydrogen. If the temperature of the hydrogen sample is $0^{\circ}C$,then the temperature of the helium sample is about:

To increase the rms speed of gas molecules by $25 \%$,the percentage increase in absolute temperature of the gas is to be

The given diagram shows isotherms for a fixed mass of an ideal gas at temperatures $T_1$ and $T_2$. What is the value of the ratio $\frac{\text{r.m.s. speed of the molecules at temperature } T_2}{\text{r.m.s. speed of the molecules at temperature } T_1}$?

At room temperature,the $rms$ speed of a gas is $V_1$. If the pressure of the gas is doubled at the same room temperature,the $rms$ speed becomes $V_2$. Then:

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