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!

Thermal/Statistical Physics Problem

  1. Jan 26, 2006 #1

    NIQ

    User Avatar

    The problem set can be found here: http://www.physics.utoronto.ca/~poppitz/hw1.pdf I am mainly having a problem with question II Part 2.

    Here's what I have so far:

    II) 1. Since the probability that a given molecule is in a subvolume [tex]V[/tex] is [tex]\frac{V}{V_0}[/tex]. It follows that the mean number of molecules is proportional to this ratio as well.

    [tex]\frac{<N>}{N_0} = \frac{V}{V_0}[/tex]
    [tex]<N> = \frac{V N_0}{V_0}[/tex]

    2.
    [tex]<(N-<N>)^2> = <N^2 - 2 N <N> + <N>^2[/tex]
    [tex]<(N-<N>)^2> = <N^2> - 2 <N>^2 + <N>^2[/tex]
    [tex]<(N-<N>)^2> = <N^2> - <N>^2[/tex]

    [tex]\frac{\sqrt{<(N-<N>)^2>}}{<N>} = \frac{\sqrt{<N^2> - <N>^2}}{<N>}[/tex]

    Now from here I can substitute into the regular [tex]<N>[/tex] terms but I don't know how I'm supposed to find [tex]<N^2>[/tex]?? Any help would be greatly appreciated.. thanks!
     
  2. jcsd
  3. Jan 26, 2006 #2

    StatusX

    User Avatar
    Homework Helper

    This problem involves the binomial distribution. You know the probability of one molecule being in V, so you need to caculate the probability that exactly N will be (that is, that N are in V, and N0-N are not, and don't forget to multiply by the number of ways of choosing these N molecules). Once you have the distribution you can calculate any expectation value you want, or you could just look up the standard deviation of a binomial distribution.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Thermal/Statistical Physics Problem
Loading...