(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)

One mole of an ideal gas at $STP$ is heated in an insulated closed container until the average speed of its molecules is doubled. Its pressure would therefore increase by what factor?

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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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The $RMS$ velocity of oxygen molecules at $NTP$ is $0.5 \,km/s$. The $RMS$ velocity for the hydrogen molecule at $NTP$ is (in $\,km/s$)

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If the r.m.s. speed of a chlorine molecule is $490\,m/s$ at $27^{\circ}C$,the r.m.s. speed of argon molecules at the same temperature will be $......\,m/s$ (Atomic mass of argon $= 39.9\,u$,molecular mass of chlorine $= 70.9\,u$). (in $.7$)

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If the temperature of a gas is increased from $27^{\circ} C$ to $159^{\circ} C$, the increase in the rms speed of the gas molecules is (in $\%$)

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

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One mole of an ideal gas at $STP$ is heated in an insulated closed container until the average speed of its molecules is doubled. Its pressure would therefore increase by what factor?

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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