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Heat transfer by radiation between two plates

  1. Nov 22, 2014 #1
    1. The problem statement, all variables and given/known data
    Two large plates are parallel and close to each other, vacuum is between them. they are held at 2000K and 3000K.
    What is the energy transfer rate between them.

    2. Relevant equations
    The energy emission rate per unit area-the Stefan-Boltzmann Law: $$R=\varepsilon\sigma T^4$$
    ##\varepsilon## is the emissivity of the surface
    ##\sigma=5.672E-8[w/sec]##

    3. The attempt at a solution
    The solution is 368[w/m2], it's the answer if the emission is of a black body:
    ##1\cdot 5.672E-8\cdot\left(300^4-200^4\right)=368##
    But why don't the emissivities of the surfaces count? what if one surface emits more or less than the other?
    In the Stefan-Boltzman formula the outer temperature exists, not the nature of the surrounding surfaces.
    I guess it has something to do with the fact that the rest of the radiation, which isn't absorbed, is reflected and comes into account
     
  2. jcsd
  3. Nov 22, 2014 #2

    mfb

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    They do count, and the problem statement should specify that ideal black bodies are meant. The sign of the energy transfer cannot change, but the overall magnitude of exchanged energy can go down.
     
  4. Nov 22, 2014 #3
    What do you mean by "sign"?
     
  5. Nov 22, 2014 #4

    haruspex

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    Meaning which way the net flow goes.
    If one body has lower emissivity than that of a black body then it both emits less and absorbs less. Different emissivities cannot result in the net flow being from the cooler to the hotter.
     
  6. Nov 22, 2014 #5
    Of course not from the cooler to the hotter, but different emissivities must mean smaller energy flow. it doesn't matter which plate's emissivity is smaller, right?
     
  7. Nov 22, 2014 #6

    haruspex

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    You say 'of course', but if the emissivity affected only the emission rate and not the absorption rate then you could have the paradoxical situation that a hot body with low emissivity could gain energy from a cooler body.
    It's not that they're different, just that one, the other or both are lower than a black body's.
     
  8. Nov 22, 2014 #7
    Thanks
     
  9. Nov 23, 2014 #8
    Why in an insulated chamber the emission of a body and the emission of the walls is black body? why don't we take into account the emissivity of the walls?
     
  10. Nov 23, 2014 #9

    mfb

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    It is not.
    The energy density in the cavity does not depend on the emissivity, but the energy exchange rate with the objects does.
     
  11. Nov 23, 2014 #10
    Why? if the walls inside emit low radiation, because of small emissivity, then the energy density in the opening will also be low, no?
     
  12. Nov 23, 2014 #11

    haruspex

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    No. This is exactly the same point as for the two bodies at different temperatures. If the emissivity is low then the absorption from the cavity is correspondingly low. Equilibrium will still be achieved when the energy density corresponds to the temperature of the enclosure.
     
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