## The black-body radiation

January 17, 2010 by micropore

Sometimes I face this simple question from students: how can it be that the total radiation of a black body does not depend on any of its detailed atomic properties?! The key is to understand the concept of** thermodynamic equilibrium**.

Assume *I(**ν**)*, the intensity at frequency *ν*, differed for two enclosures at the same temperature, *T*, over some frequency interval, *dν*. Connect the enclosures with a filter that passes only radiation of that frequency interval. Radiant energy would now flow from one enclosure to another, making it possible to extract useful work from two reservoirs at the same temperature, *T*, in violation of the second law of thermodynamics. Thus our assumptions must be in error, and the monochromatic specific intensity of a radiation field in thermodynamic equilibrium with matter must be a universal function of *T*; in modern notation;

**Kirchhoff law : I(***ν*) = B(*ν, T*)

Kirchhoff set a goal for future generations of finding the correct functional form of **B(***ν, T*). Max Planck found the approximate formula.

Reference: *The Physics of Astrophysics: (I) Rdiation*, by Frank Shu

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