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How to derivate Maxwell Boltzmann Distribution 
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#1
Jan513, 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) 


#2
Jan513, 10:02 AM

P: 1,055

There are many ways to derive it  some more insightful than others.
Have you taken/taking stat mech? 


#3
Jan513, 10:08 AM

P: 3

Thanks for the answer.
I haven't taken Statistical Mechanics but Statistics. Could it be useful for this? 


#4
Jan513, 10:35 AM

Mentor
P: 11,748

How to derivate Maxwell Boltzmann Distribution



#5
Jan613, 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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