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!

Finding average velocity in a velocity distribution

  1. Mar 14, 2016 #1
    1. The problem statement, all variables and given/known data
    A gas has a hypothetical speed distribution for N gas molecules with N(v) = Cv^2 for 0 < v < V0. Find (i) an expression for C in terms of N and v0 (ii) the average speed of the particles

    2. Relevant equations

    N/A
    3. The attempt at a solution
    (i)
    integrating N(v) with respect to v from 0 to V0 gives
    N = (C*V0^3)/3 (where is N is total number of molecules)
    rearranging gives C =3*N/(v^3)
    (ii)
    integrating N(v)*v with respect to v gives
    sum(v) = (C*V0^4)/4
    subbing in for C gives
    sum(v) = (3N/4)*V0

    sum(v)/N = Vav = (3/4)*V0

    I've been having difficulty with this question for a while and can't seem to find any similar question online so I have no idea if what I did is correct. Any help would be appreciated.
     
    Last edited: Mar 14, 2016
  2. jcsd
  3. Mar 14, 2016 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    What does that mean?
    In the preceding sentence we were told that ##N## is the number of molecules in the system. Now all of a sudden ##N## is being used to denote something completely different.
    From the fact that later on it is integrated to obtain an expected value, I presume that ##N(v)## is supposed to be a probability density function (pdf) for the random variable ##V## that is the speed of a randomly selected molecule. But if that's the case it needs to use a different letter. For instance it would be common practice to write ##F## for the cumulative distribution function so that

    $$Prob(V\leq v)\equiv F(v)$$
    and then
    $$f(v)=\frac{dF(v)}{dv}$$
    and then specify the distribution by the equation ##f(v)=Cv^2##.

    But I don't know whether that is what was intended.
     
  4. Mar 14, 2016 #3
    according to my lecture notes the dimensionless product N(v) dv gives the number of molecules having speeds in the range v to v +dv.
     
  5. Mar 14, 2016 #4

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In that case, they mean by ##N(v)## the same thing as I have written above as ##f(v)##. It's bad practice to use the same symbol ##N## for two different things, but there's not much you can do about the notation your lecturer uses.
    Using that interpretation, your calcs look correct. The only flaw is that in your final conclusion you have written 'sum(v)' where one would expect you have to written the average v0, since they have asked for an expression for C in terms of N and v0.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding average velocity in a velocity distribution
  1. Find average velocity (Replies: 3)

Loading...