Density of an ionised gas

  • Thread starter MikkelR60
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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
 

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