1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Maths (calculus) problem

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data
    The distribution of the speed v of molecules, mass m, in a gas in thermal equilibrium at temperature T is given by:

    P(v)dv=Av2e-(0.5mv^2)/(kT)dv

    where k is the boltzmann constant and A is the normalising constant. Determine A such that

    [tex]\int[/tex] between 0 and [tex]\infty[/tex] P(v)dv=1


    2. Relevant equations



    3. The attempt at a solution
    Obviously the main problem is I don't think it's very easy to directly integrate this equation and so I assume there is some trick for why between those values you can see a value for A where that last relationship will hold. Just a point in the right direction would be helpful, thanks.
     
  2. jcsd
  3. Nov 2, 2009 #2

    Mark44

    Staff: Mentor

    Here's your integral, nicely formatted in LaTeX:
    [tex]\int_0^{\infty} Av^2e^{-\frac{0.5mv^2}{kT}}dv[/tex]

    I don't think there is any trick -- integration by parts will probably do the job. I would split it up as u = v, dw = ve-(0.5mv2/kT)dw.
     
  4. Nov 2, 2009 #3
    To make it simpler I'll say that m/kT is B.

    But when you integrate ve^-Bv^2 the first time you get (-e^-Bv^2)/2B

    But then for integration by parts you need to integrate this again which as far as I can see you can't do using the basic integration techniques I know.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Maths (calculus) problem
  1. Calculus Problem (Replies: 9)

  2. Calculus Problem (Replies: 2)

  3. Calculus problem (Replies: 1)

  4. Calculus problem (Replies: 11)

  5. Calculus Problem (Replies: 2)

Loading...