(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is the problem: I need to prove from the Maxwell-Boltzmann distributions the expression for the rms speed.

2. Relevant equations

[tex] v_{rms} = \sqrt{\frac{3kT}{m}} [/tex]

[tex] < v^2 > = 4\pi(\frac{m}{2\pi kT})^{3/2} \int v^4 e^{\frac{-mv^2}{2kT}} dv [/tex]

The limits on the integral are infinity and 0.

From what I know;

[tex] v_{rms} = sqrt{ <v^2> } [/tex]

3. The attempt at a solution

I did a similar one like this to prove the corresponding expression for <v>. I used a substitution and then used parts on the resulting expression, but if use that method on this one, you get a factor of [itex] u^{3/2} [/itex] times by the exponential (assuming the substitution is [itex] u = v^2 [/itex]). This obviously causes problems, so I was wondering is there another way to do this proof without resorting to an integral or is there an easy way of doing this integral?

P.S. Sorry if this thread should be in the advanced physics part. I only thought of that after I posted.

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# Tricky integral problem

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