Kirchhoff's law (thermodynamics)

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Kirchhoff's law in thermodynamics, also called e.g. Kirchhoff's law of thermal radiation, is a general statement equating emission and absorption in heated objects, proposed by Gustav Kirchhoff in 1859 (and proved in 1861), following from general considerations of thermodynamic equilibrium. (See Kirchhoff's laws for other laws named after Kirchhoff.)

An object at some non-zero temperature radiates electromagnetic energy. If it is a perfect black body, absorbing all light that strikes it, it radiates energy according to the blackbody radiation formula. More generally, it radiates with some emissivity multiplied by the blackbody formula. Kirchhoff's law states that:

At thermal equilibrium, the emissivity of a body (or surface) equals its absorptivity.

Here, the absorptivity is the fraction of incident light (power) that is absorbed by the body/surface. In the most general form of the theorem, this power must be integrated over all wavelengths and angles. In some cases, however, emissivity and absorption may be defined to depend on wavelength and angle, as described below.

Kirchhoff's Law has a corollary: the emissivity cannot exceed one (because the absorptivity cannot, by conservation of energy), so it is not possible to thermally radiate more energy than a blackbody, at equilibrium. This has two caveats, however. First, if the surface is diffractive, so that incident energy at one angle is partially reflected to another angle, then the emissivity at one angle can exceed unity, but not the emissivity of power integrated over all angles. Second, if the object is nonlinear (e.g. fluorescent), so that incident power at one wavelength is reflected at another wavelength, then the emissivity at some wavelengths can exceed unity, but not the emissivity of power integrated over all wavelengths.

This theorem is sometimes informally stated as a poor reflector is a good emitter, and a good reflector is a poor emitter. It is why, for example, lightweight emergency thermal blankets are typically made of reflective material: they lose little heat by radiation.

References

E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics: Part 2, 3rd edition (Elsevier, 1980).