(A) The root mean square (r.m.s.) speed is given by $V_{rms} = \sqrt{\frac{(2u)^2 + (10u)^2 + (11u)^2}{3}} = \sqrt{\frac{4u^2 + 100u^2 + 121u^2}{3}} =

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The r.m.s. speed exceeds the mean speed by about $u$.

(A) The root mean square (r.m.s.) speed is given by $V_{rms} = \sqrt{\frac{(2u)^2 + (10u)^2 + (11u)^2}{3}} = \sqrt{\frac{4u^2 + 100u^2 + 121u^2}{3}} = \sqrt{\frac{225u^2}{3}} = \sqrt{75}u = 5\sqrt{3}u \approx 8.66u$.The mean (average) speed is given by $V_{avg} = \frac{2u + 10u + 11u}{3} = \frac{23u}{3} \approx 7.66u$.Comparing the two values,$V_{rms} - V_{avg} \approx 8.66u - 7.66u = 1u$.Therefore,the r.m.s. speed exceeds the mean speed by about $u$.

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

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Three particles have speeds of $2u$,$10u$,and $11u$. Which of the following statements is correct?

A
The r.m.s. speed exceeds the mean speed by about $u$.
B
The mean speed exceeds the r.m.s. speed by about $u$.
C
The r.m.s. speed equals the mean speed.
D
The r.m.s. speed exceeds the mean speed by more than $2u$.

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Kinetic Theory of Gases

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

An $HCl$ molecule has rotational,translational,and vibrational motions. If the $rms$ velocity of $HCl$ molecules in its gaseous phase is $\bar{v}$,$m$ is its mass,and $k_B$ is the Boltzmann constant,then its temperature will be:

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The $rms$ speed of air molecules in a vessel is $90 \times 10^2 \ m/s$. If half of the gas leaks out at constant temperature,the $rms$ speed of the remaining air molecules will be

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The number of molecules in a closed container is doubled. What will be the effect on $v_{rms}$?

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At what temperature in $K$ will the $r.m.s.$ speed of a hydrogen molecule be equal to the escape velocity from the Earth?

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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:

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Three particles have speeds of $2u$,$10u$,and $11u$. Which of the following statements is correct?

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