(D) The root mean square (r.m.s.) speed of an ideal gas is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation,we can see that $

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(D) The root mean square (r.m.s.) speed of an ideal gas is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$.From this relation,we can see that $V_{rms} \propto \sqrt{T}$.Let $T_1 = 200 \ K$ and $T_2 = 800 \ K$.Given $V_{rms,1} = v_0$.We have the ratio: $\frac{V_{rms,2}}{V_{rms,1}} = \sqrt{\frac{T_2}{T_1}}$.Substituting the values: $\frac{V_{rms,2}}{v_0} = \sqrt{\frac{800}{200}} = \sqrt{4} = 2$.Therefore,$V_{rms,2} = 2 v_0$.

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

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The temperature of an ideal gas is increased from $200 \ K$ to $800 \ K$. If the r.m.s. speed of the gas at $200 \ K$ is $v_0$,then the r.m.s. speed of the gas at $800 \ K$ will be:

JEE MAIN 2023 All JEE MAIN

A
$v_0$
B
$4 v_0$
C
$\frac{v_0}{4}$
D
$2 v_0$

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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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The temperature at which the $r.m.s.$ speed of hydrogen molecules is equal to the escape velocity on the Earth's surface will be ...... $K$.

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Two vessels having equal volume contain molecular hydrogen at $1 \text{ atm}$ and helium at $2 \text{ atm}$ respectively. If both samples are at the same temperature,the mean velocity of hydrogen molecules is

Medium

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For a given gas at temperature $T$,the root mean square velocity is $\nu_{rms}$,the average velocity is $\nu_{av}$,and the most probable velocity is $\nu_{mp}$. Which of the following relations is correct?

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At what temperature $(K)$ will the $r.m.s.$ velocity of hydrogen gas be equal to the escape velocity from the Earth?

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The value closest to the thermal velocity of a Helium atom at room temperature $(300\,K)$ in $m/s$ is $[k_B = 1.4 \times 10^{-23}\,J/K; m_{He} = 7 \times 10^{-27}\,kg]$.

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The temperature of an ideal gas is increased from $200 \ K$ to $800 \ K$. If the r.m.s. speed of the gas at $200 \ K$ is $v_0$,then the r.m.s. speed of the gas at $800 \ K$ will be:

Similar Questions

The temperature at which the $r.m.s.$ speed of hydrogen molecules is equal to the escape velocity on the Earth's surface will be ...... $K$.

Two vessels having equal volume contain molecular hydrogen at $1 \text{ atm}$ and helium at $2 \text{ atm}$ respectively. If both samples are at the same temperature,the mean velocity of hydrogen molecules is

For a given gas at temperature $T$,the root mean square velocity is $\nu_{rms}$,the average velocity is $\nu_{av}$,and the most probable velocity is $\nu_{mp}$. Which of the following relations is correct?

At what temperature $(K)$ will the $r.m.s.$ velocity of hydrogen gas be equal to the escape velocity from the Earth?

The value closest to the thermal velocity of a Helium atom at room temperature $(300\,K)$ in $m/s$ is $[k_B = 1.4 \times 10^{-23}\,J/K; m_{He} = 7 \times 10^{-27}\,kg]$.

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