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Is the root-mean-square velocity of gas particles always faster than the average velocity? I've done a couple of calculations with both and that seems to be the case; however can you make a formal mathematical proof of it? (i.e. maybe using Cauchy-Schwarz)

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  • $\begingroup$ Do you mean speed or velocity? $\endgroup$ – Farcher Sep 25 '18 at 8:08
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The classical analysis is known as the Maxwell-Boltzmann distribution.

The RMS velocity is about 108% of the average velocity.

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Root-mean-square velocity is a scalar, average velocity is a vector. I am not sure how one can compare them. Maybe you meant the absolute value of average velocity?

EDIT (09/25/2018): So the OP confirmed that in his comment. So you can consider the difference between the squares of the rms velocity and average velocity $(\sum_i V_i^2)/n-(\sum_i V_i)^2/n^2$, which is a quadratic form, and find its minimum requiring that all derivatives with respect to $V_i$ vanish.

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  • $\begingroup$ Yep, pretty much. (It's a bit misleading how they're both named velocity.) $\endgroup$ – James Ko Sep 25 '18 at 16:08

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