1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Boltzmann statistics - finding the number of particles

  1. Oct 14, 2008 #1
    Boltzmann statistics -- finding the number of particles

    1. The problem statement, all variables and given/known data
    A column of water contains fine spherical metal particles of radius 2 x10-8m, which are in thermal equilibrium at 25C. If there are 1000 particles per unit volume at a given height, how many particles would be found in the same volum 1 mm higher? The density of the metal is 2 x104 kg m-3. Hint: use gravitational force and buoyancy in water and compute change in potential energy

    2. Relevant equations
    Fnet= [tex]\rho[/tex]Vg - mg ([tex]\rho[/tex] is density, V is volume, g is gravity, m is mass)

    F*d = -mg [tex]\Delta[/tex]h (h is height, d = height, F = Fnet

    n(E) = g(E)fb(E) = A g(E)e-E/kT
    n(E) = number of particles with energy E
    g(E) = statistical weight of the state with energy E
    A = normalization constant whose value depends of the system
    k = boltzmann constant
    T = temperature
    E = energy

    3. The attempt at a solution

    What I did was just substitute Fnet= [tex]\rho[/tex]Vg - mg
    into F*d = -mg [tex]\Delta[/tex]h which gives me the change in potential energy. I'm not sure what to do with the boltmann distribution formula after that or do I even need it? I'm just stuck and don't know where to go. Any help will be appreciated

    Thank you
  2. jcsd
  3. Oct 14, 2008 #2


    User Avatar
    Homework Helper

    Re: Boltzmann statistics -- finding the number of particles

    you need the density as a function of height. that's why you need the boltmann distribution function for the density.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook