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Maxwell Boltzmann Distribution

  1. Jun 10, 2014 #1
    I don't know how to integrate the Maxwell-Boltzmann distribution without approximation or help from Maple.

    Given the Maxwell-Boltzmann distribution:

    f(v) = 4*pi*[m/(2*pi*k*T)]^(3/2)*v^2*exp[(-m*v^2)/(2*k*T)]

    Observe the appearance of the Boltzmann factor exp[(-m*v^2)/(2*k*T)] with E = 1/2(mv^2)

    Assuming a fixed temperature and mass, one can simplify this equation:

    f(v) = a*v^2*exp[-bv^2]
    a = 4*pi*[m/(2*pi*k*T)]^(3/2)
    b = m/(2*k*T)

    In order to calculate the fraction of particles between two speeds v1 and v2, one should evaluate the definite integral:


    Here is an link to integral-tables, http://integral-table.com/
    How would I solve this problem for let's say a certain amount of moles with hydrogen between two different velocities? Best regards, Tor
  2. jcsd
  3. Jun 10, 2014 #2


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    What have you tried in terms of integrating the M-B distribution?
  4. Jun 10, 2014 #3
    I've just put in some values to calculate how many atoms gets affected from let's say 400-401 m/s for hydrogen. I'm not sure what solution to pick for this kind of integration, that's what I'm asking. To calculate between higher speeds like 400-500 m/s, an integration is needed.
    Last edited: Jun 10, 2014
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