1. Limited time only! Sign up for a free 30min personal 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!

Average Speed for Maxwell's Distribution of Molecular Speed

  1. Oct 8, 2015 #1

    RaulTheUCSCSlug

    User Avatar
    Gold Member

    e43e83c27b3d1737313dcfcb758091ab.png

    Using the Maxwell-Boltzmann equation above, there is an example in my book (Giancoli 4th edition p. 481) where they use this to find the average velocity. I understand that it would just be the sum of all the speeds of the molecules divided by the number of molecules. But then I'm having trouble on how they did the integration by parts? Could someone walk me through the process?

    upload_2015-10-8_13-17-27.png
     
  2. jcsd
  3. Oct 8, 2015 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    Let [itex]a=\frac{m}{2kT}[/itex]
    [itex]\int_0^{\infty}v^3e^{-av^2}dv=\frac{1}{a}\int_0^{\infty}ve^{-av^2}dv=\frac{1}{2a^2}=\frac{2k^2T^2}{m^2}[/itex]

    The first equality is integration by parts.
     
  4. Oct 8, 2015 #3

    phyzguy

    User Avatar
    Science Advisor

    Do you know how to do integration by parts? [itex] \int u dv = uv - \int v du[/itex] . Try [itex]u = x^2; dv = x e^{-x^2}dx [/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Average Speed for Maxwell's Distribution of Molecular Speed
Loading...