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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


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    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.
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