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Stefans Law vs UV catastrophe

  1. Dec 22, 2009 #1
    I was watching two small lectures on youtube about black body radiation, they are interesting but I am questioning some of the information they provide :



    My question is related to the graph of the Stefan-Boltzman law that the lecturer draws on the blackboard. Specifically he introduces the law as usual saying that the total power radiated by a body at temperature T, scales as the fourth power of T. This is fine. He then says that experimentally this law breaks down for real bodies and drops off to zero at high temperatures. Is this true?

    If it was true then if I heat a real body beyond a certain temperature then it will stop radiating, hence it cannot maintain thermodynamic equilibrium and will just heat up, increase its temperature and radiate even less, heat up even more etc.?

    My understanding is that this is not explained by the ultraviolet catastrophe (which seems to be an entirely different thing). In particular from wikipedia, it is possible to derive the T^4 law from plancks law as well classical thermodynamics, so solving the UV catastrophe does not change Stefans Law. So the T^4 law must be true at all temperatures in the real world right?

    A further thought occurs to me which is touched on in the lecturer with the 'rock star' example. In the real world, interatomic molecular bonds radiate in the infra red, electron orbital changes radiate in the UV. There is therefore a discontinuous distribution of absorption. Furthermore at certain temperatures interatomic bonds might break and essentially free the atoms from each other, or electrons might escape their orbitals. In other words the absorbtion/emission spectrums are very complicated!

    So, the theoretical model obviously doesnt take any of this into account, plancks little oscillators appear to have an infinite number of energy levels. So I guess they are really analogous to interatomic bonds which never break and there are no other forms of electromagnetic emission and the particles never escape the potential well. This ok?

    So, given that the real world is complicated and that no real object really emits plancks spectrum, isnt it remarkable? that all bodies can radiate enough energy to maintain thermodynamic equilibrium?
    Last edited: Dec 22, 2009
  2. jcsd
  3. Dec 23, 2009 #2
    Does anyone have a comment on this?
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