(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:

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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 density of hydrogen gas at standard atmospheric pressure $(P = 1.01 \times 10^{5} \ Pa)$ is $0.09 \ kg/m^{3}$. Find the root mean square velocity $(v_{rms})$ and the average kinetic energy of $1 \ mole$ of the gas.

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If at $STP$,the velocity of sound in a gas $(\gamma = 1.5)$ is $600 \, m/s$,the $r.m.s.$ velocity of the gas molecules at $STP$ will be ........... $m/s$.

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At what temperature is the $rms$ speed of air molecules doubled compared to its value at $NTP$?

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The temperature at which the rms speed of molecules in hydrogen gas will be double of its initial value at $27^{\circ} C$ is (in $^{\circ} C$)

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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:

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The density of hydrogen gas at standard atmospheric pressure $(P = 1.01 \times 10^{5} \ Pa)$ is $0.09 \ kg/m^{3}$. Find the root mean square velocity $(v_{rms})$ and the average kinetic energy of $1 \ mole$ of the gas.

At $27\,^oC$,the $rms$ velocity of $H_2$ gas is $100\, m/s$. Find the $rms$ velocity of $O_2$ gas at $327\,^oC$.

If at $STP$,the velocity of sound in a gas $(\gamma = 1.5)$ is $600 \, m/s$,the $r.m.s.$ velocity of the gas molecules at $STP$ will be ........... $m/s$.

At what temperature is the $rms$ speed of air molecules doubled compared to its value at $NTP$?

The temperature at which the rms speed of molecules in hydrogen gas will be double of its initial value at $27^{\circ} C$ is (in $^{\circ} C$)

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