SED deviation from Black Body - real objects

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Nereid

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You heat an ideal material (solid, liquid, gas) and it emits electromagnetic radiation, with a spectral energy distribution (SED) following that of a "black body", per Planck.

You heat a homogeneous real material (a lump of iron, a body of water, some hydrogen; things like dust with a wide range of sizes suspended in a gas of mixed composition have their own complications) and the SED deviates from Planck.

To what extent can these deviations be estimated, from a modest set of input parameters (derivable 'from first principles'?)? How broad is the range of applicability of these estimates (e.g. SED BB deviations to the 10%/1%/ppm level? state of matter? composition? temperature?)? I'm assuming thermodynamic equilibrium, etc. In what circumstances is it necessary to resort to 'brute observation' (measure the SED), as a priori estimation is known to be 'wrong' (or, more likely, able to reliably estimate only wide ranges)?

And what happens when you have a plasma?
 

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