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Homework Help: Density of an ionised gas

  1. Dec 28, 2009 #1
    I have been wondering about this problem for quite some time now and any input is much appreciated. If a gas consisting of n atoms with individual mass m and charge q is put under an external pressure P what will the resulting density be? Assume spherical symmetry.

    An illustration of the problem (The external pressure is supplied by an electrically charged sphere)
    es_sphere.JPG

    The density of the gas must be
    [tex]\rho = \frac{mn}{V_{gas}}[/tex]

    If there is an average space of a between the atoms (and lets assume that the atoms does not occupy any space) then the total space occupied by the gas is Vgas = [tex]n \cdot 4/3 \pi a^3[/tex].

    The internal pressure of the gas must be equal to the external pressure.
    Fext = Fint
    PA = [tex]n \cdot \frac{1}{4 \pi \epsilon_0} \frac{q^2}{a^2} [/tex]
    From here its just substituting and expressing rho in terms of the stated variables.

    Can someone please comment on my derivation, does it seem sound? I am most concerned with the application of Columbs law.

    All the best
    Mikkel
     
  2. jcsd
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