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Homework Help: Speed distribution function

  1. Feb 1, 2009 #1
    1. The problem statement, all variables and given/known data

    The speed distribution function of a group N particles is given by:
    dNv=k*dv if U>v>0
    dNv=0 if v>U

    1) find k in terms of N and U.
    2) draw a graph of distribution function
    3) compute the average and rms speed in terms of U.
    4) compute the most probable speed

    2. Relevant equations

    f(v)=[tex]\left[\frac{m}{2\pi\kappa*T}\right]^{\frac{3}{2}}*exp\left(-\frac{mv^{2}}{2\kappa*T}\right)[/tex] - Maxwell-Boltzmann distribution

    [tex]\frac{dn_{v}}{n}[/tex]=4[tex]\pi*v^{2}*f(v)*dv[/tex] - speed distribution function

    3. The attempt at a solution

    1) k=4[tex]\pi*n*v^{2}*f(v)[/tex] - so I can draw a graph of the distribution function.
    2) which function and how should I integrate in order to obtain k in terms of N and U?
    3) is average speed = [tex]\int^{V}_{0}v*4\pi*v^{2}*f(v)dv[/tex] ?

    Please help with the solution or link to a similar problem solution.
    Last edited: Feb 1, 2009
  2. jcsd
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