Rms speed

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Question

Velocity of sound in a mono atomic ideal gas at $27^{o} C$ is 330 m/s. Then the rms speed of molecules of that gas at same temperature is $(Take \sqrt{5} = 2 .23)$

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Solution

$V_{S} = \sqrt{\frac{γRT}{M}} and V_{rms} = \sqrt{\frac{3 RT}{M}}$
For mono atomic gas, $γ = \frac{3 + 2}{3} = \frac{5}{3}$
$\begin{array}{l} Now, \frac{V_{rms}}{V_{s}} = \sqrt{\frac{3}{γ}} = \sqrt{\frac{3}{5 / 3}} = \frac{3}{\sqrt{5}} = \frac{3}{2 .23} = 1 .345 \\ ∴ V_{rms} = 1 .345 \times 330 m / s = 444 m / s \end{array}$

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Rms speed

Remember concepts with our Masterclasses.

Velocity of sound in a mono atomic ideal gas at 27oC is 330 m/s. Then the rms speed of molecules of that gas at same temperature is (Take 5=2.23)

VS=γRTM and Vrms=3RTMFor mono atomic gas, γ=3+23=53Now, VrmsVs=3γ=35/3=35=32.23=1.345∴Vrms=1.345×330 m/s =444 m/s

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Velocity of sound in a mono atomic ideal gas at $27^{o} C$ is 330 m/s. Then the rms speed of molecules of that gas at same temperature is $(Take \sqrt{5} = 2 .23)$