On the Validity of Kirchhoff's Law for a Freely Radiating Body

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Abstract
In applying Kirchhoff's law to calculate the emission of a heated body radiating freely to the outside, one assumes that the emission of a body when radiating freely is the same as its emission when enclosed in a blackbody cavity. But the radiation field inside the body is everywhere smaller in the first case than in the second; consequently the emission arising from induced radiative transitions must be smaller for a freely radiating body than the emission arising from these transitions when the body is enclosed in a cavity. Since the emissions differ, one is apparently led to the conclusion that Kirchhoff's law cannot be valid for a freely radiating body. It is shown that this conclusion is false: Kirchhoff's law is valid as long as the distribution over material states is the equilibrium distribution, and is therefore, in this sense, independent of the state of the radiation field. One must, however, take proper account of the effect of induced emission in calculating the absorption coefficient.

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