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The Stefan-Boltzmann law describes blackbody radiation in terms of radiant flux per unit area i.e. how much energy passes through a 2D surface per unit time. I find this very simple and I understand how to do calculations with it.

Planck's law describes blackbody radiation (per frequency) either as volumetric energy density (which volume?) or as radiance which seems to have the units of flux per unit area per steradian. This supposedly makes the unit invariant over distance, but I haven't been able to wrap my head around what it's actually describing or how to do calculations with it.

How do I convert the values of Planck's law into the same units as Stefan-Boltzmann's law? Once I have that I know how to find the total radiative power of the object by multiplying by its surface area, and I find that a very concrete quantity to think about.

Qmechanic
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Volbla
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1 Answers1

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Planck's law describes a black body that is in equilibrium with its environment i.e. the energy emitted by the black body is the same as the energy absorbed by the body.

An example of this is the cavity with a small hole that we use as an approximation to a black body. Inside the cavity the radiation emitted from an area element on one side of the cavity is absorbed by the walls on the other side of the cavity so the emission and absorption rates are the same. Planck's law then gives us the energy density of the EM field inside the cavity. This energy density is the same everywhere in the cavity.

The Stephan-Boltzmann just tells how much energy the black body is emitting. It may or may not be in equilibrium i.e. the energy it is absorbing from its environment may or may not be the same as the energy it is emitting.

John Rennie
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