Kirchhoff's law of thermal radiation

See also: Kirchhoff's laws for other laws named after Kirchhoff.

In thermodynamics, Kirchhoff's law of thermal radiation, or Kirchhoff's law for short, 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.

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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 black-body radiation formula. More generally, it is a "grey body" that radiates with some emissivity multiplied by the black-body formula. Kirchhoff's law states that:

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

Here, the absorptivity (or absorbance) 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 black body, at equilibrium. In negative luminescence the angle and wavelength integrated absorption exceeds the material's emission, however, such systems are powered by an external source and are therefore not in thermal equilibrium.

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 based on reflective metallic coatings: they lose little heat by radiation.

References

• Evgeny Lifshitz and L. P. Pitaevskii, Statistical Physics: Part 2, 3rd edition (Elsevier, 1980).
• F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill: Boston, 1965).