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The Maxwell Speed Distribution in 2D

  1. Jan 8, 2011 #1
    1. The problem statement, all variables and given/known data
    [​IMG]

    It seemed much easier to screencap than to write out.

    2. Relevant equations

    It helps to know that the number of states with speed between u and u+du is 2pi*u du

    3. The attempt at a solution

    I've tried quite a few things but every time I get to trying to normalise I either get stuck integrating by parts over and over, or using http://en.wikipedia.org/wiki/Gaussian_integral<that, which doesn't arrive at the answer wanted.

    If someone could give me a push in the right direction it would be much appreciated.
     
  2. jcsd
  3. Jan 8, 2011 #2
    You need some substitution to make the integral doable.
     
  4. Jan 9, 2011 #3
    Ok so I have the integral of v*exp(-[tex]\alpha[/tex]v2) dv between 0 and infinity to normalise. I don't know how a substitution would help because you would still have two functions multiplied by one another.

    Edit: I think I'm being stupid. I've substituted for alpha*v^2. Hopefully it will work.
     
    Last edited: Jan 9, 2011
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