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Semi-idealized atomic gas and it's free expansion in vacuum

  1. Jul 3, 2011 #1

    I was thinking about what would happen if an atomic gas was allowed to expand in vacuum and concluded I don't have much of a handle on the subject, so if anyone would help me out - I'd really appreciate it.

    So, let's say we have an ideal gas in a container located in vacuum maintained at temperature T. Let say that every atom has only two internal states - ground and excited. Now, I'm assuming this because I want to keep things as simple as possible, but if things are going to complicate due to limited spectrum of excitation, we may as well assume harmonic oscillator spectrum for this internal degree. We chose temperature and excitation energy so that that a significant number of atoms may be found excited (as in, comparable to number of atoms in ground state). Before releasing, I want to go through how is equilibrium maintained. To change internal state, atom, short of any "selection rules", may emitting/absorb photon, or interchange excitation energy with kinetic energy through inelastic collision, right?

    * Is there a previous work through which I can determine dominant mechanism of this idealized gas, by including appropriate cross-sections and other detail? Any reading recommendation?

    * Einstein's elaboration on black body radiation seems to assert quite strong argument that induced relaxation has same probability as excitation on the same level, making a strong constrain on any atomic theory. Is this mechanism relevant for the case at hand? It seems to me it would be unphysical to ignore induced relaxation. If it is included, does that imply that rate of inelastic collisions that produce excited atoms is different (higher, that is) than rate of inelastic collision which relax colliding atoms?

    * For a real gas, is loading of excited states collision dominated or absorption dominated? Or any other mechanism?

    * Does Doppler effect due to Maxwell-Boltzmann velocity distribution affect reabsorption effect? It doesn't seem so, but just to be complete ...

    Now, we release gas to freely expand in vacuum where it does no work and only way to lose energy is to radiate it away. It will dilute and I’m interested how will it “fall out of equilibrium”, how will coupling between atomic gas and photon gas break up. Specifically, I’d like to know velocity distribution after infinite time. As I see it, two things can happen.

    First, that dilution will shut down atomic collision mechanism first - in a sense that, collision will become rare on relevant time scales and atoms can still interact via photon exchange. Than, all energy stored in internal will get radiated away slowly, as in time required for random walking photon to get to the “surface”, but asymptotic velocity distribution will be relatively unaffected by this - it will kinda be “frozen” at M-B shape at temp T or somewhat smaller temperature.

    Other thing that could is that dilution would affect photon interaction, so that mean path of photon would become comparable to gas extent, that is - render gas transparent to light at relevant frequency. Furthermore, if average time between collisions becomes larger than decay time of excited states, then inelastic relaxation collision will effectively stop. What happens then is that gas will “bleed” it’s kinetic energy through electromagnetic radiation, by means of collision mechanism feeding internal degrees only to be radiated away, leaving much larger impact of excitation spectrum on asymptotic distribution of velocity. Or will something third happen? Or something in-between?

    As you can see, I’m no expert on atomic physics (nor thermodynamics, lol :) and, lacking knowledge or intuition how to sort out orders of magnitude and not wanting to reinvent all this, I’d would be grateful on any discussion on the subject or reading suggestions to start off my with my problem.
  2. jcsd
  3. Jul 4, 2011 #2
    As long as you don't have long range interactions (which is never really true, but usually good enough that the physical effect is tiny) you've describe Joule expansion: http://en.wikipedia.org/wiki/Joule_expansion

    Answer: no temperature changes at all. Remember that thermal equilibrium implies that the "correct" amount of kinetic vs. internal/potential energy is already set up, and further collisions, etc. will simply preserve it.
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