root mean square speed

Question

rms speed v_rms of molecules is given by:

RankGuru · Accepted Answer

The Root Mean Square (rms) speed is the square root of the average of the squares of the speeds of the molecules. From the relation $\frac{1}{2} m v_{rms}^2 = \frac{3}{2} k_B T$, we can solve for $v_{rms}$:
$v_{rms} = \sqrt{\frac{3 k_B T}{m}}$
Alternatively, in terms of the molar mass $M$ and gas constant $R$:
$v_{rms} = \sqrt{\frac{3 R T}{M}}$
This is a standard measure of the average speed of particles in a gas at a certain temperature.

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root mean square speed

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