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How to derivate Maxwell Boltzmann Distribution

by Troller
Tags: boltzmann, derivate, distribution, maxwell
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Troller
#1
Jan5-13, 09:50 AM
P: 3
Hi PFers. I am interested in Maxwell Boltzmann Distribution. I have searched in Internet for the derivation but I am not satified with them. Can somebody show me the way to derivate it? Thanks.
ψ(v)=(m/2*pi*kT)^(3/2) e^(-mv^2/2kT)
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Jorriss
#2
Jan5-13, 10:02 AM
P: 1,066
There are many ways to derive it - some more insightful than others.

Have you taken/taking stat mech?
Troller
#3
Jan5-13, 10:08 AM
P: 3
Thanks for the answer.
I haven't taken Statistical Mechanics but Statistics. Could it be useful for this?

jtbell
#4
Jan5-13, 10:35 AM
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How to derivate Maxwell Boltzmann Distribution

Quote Quote by Troller View Post
I have searched in Internet for the derivation but I am not satified with them.
It would help if you tell us why you are not satisfied. Then people won't waste time pointing you to the same things again.
Troller
#5
Jan6-13, 08:40 AM
P: 3
Thanks. Yeap, here.

1st http://www.eecis.udel.edu/~breech/ph...es/node32.html

Sorry I haven't used LaTeX well enough to type it here again. At derivation of ψ(v)=f(vx)f(vy)f(vz) by taking derivatives with respect to vx, it is very unclear to me. I think dψ/dvx = dψ/dv * dv/dvx. And after that I dont know how to solve it.

2nd http://www.maxwellsociety.net/Physic...Boltzmann.html

This seems better and easier. At the part argumenting for spherical shell, there are a lot of values of vx/y/z so that give the same value of v!? And the application of function g(v)=[itex]\alpha[/itex]v^n * e^(-[itex]\beta[/itex]v^2) is a bit evidencelessly.


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