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!

Maxwell-boltzmann distribution

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

    The area under the Maxwell-Boltzmann distribution of speeds of molecules of mass m in a gas at temperature T above a speed v can be estimated as

    1/2 (m/2πkT)^(1/2) v exp(-(mv^2)/kT)

    Show that the maximum likely speed of a gas molecule in the air in a typical room (i.e. the speed above which the Maxwell-Boltzmann distribution gives a probability of 1/N, where N is the number of molecules in the room) is of order 4<v^2>^1/2 (where <v^2>^1/2 = (3kT/m)^1/2).

    2. Relevant equations

    3. The attempt at a solution

    I think the question means that the Maxwell-Boltzmann distribution curve is approx a 1/N curve at and above a certain value of N. I was going to equate the max-bolt curve equation to 1/N, except the question gives the equation for the area. Then I thought I should integrate the 1/N curve to get the area then 1/N dN gives ln N. Then I can equate the areas. Then use PV=NkT so that

    ln(PV/kT) = 1/2 (m/2 pi kT) exp -(mv/kT)

    I was then going to plug in values for T (293Kelvin) and m (mass of nitrogen molecule) but this is really hard to solve for v so I think it must be wrong.

    Any help would be really great! Thanks
  2. jcsd
  3. Aug 7, 2009 #2
    If you recall from calc, when you want to find a max or min, you need to take a derivative...
  4. Aug 7, 2009 #3
    Oh yeah! So if iI have the formula for the area then I need to differentiate twice then set equal to zero to get the maxima? I did this and got V^2=(18 pi k T/m)^1/2. This doesn't match the answer so I don't know if my working is wrong or something else.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?