Kirchhoff’s law of thermal radiation

Kirchhoff’s law of thermal radiation

In thermodynamics, Kirchhoff ##Q##s law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium.

A body at temperature T radiates electromagnetic energy. A perfect black body in thermodynamic equilibrium absorbs all light that strikes it, and radiates energy according to a unique law of radiative emissive power for temperature T, universal for all perfect black bodies. Kirchhoff ##Q##s law states that:

For a body of any arbitrary material, emitting and absorbing thermal electromagnetic radiation in thermodynamic equilibrium, the ratio of its emissive power to its dimensionless coefficient of absorption is equal to a universal function only of radiative wavelength and temperature, the perfect black-body emissive power.[1][2][3][4][5][6]

Here, the dimensionless coefficient of absorption (or the absorptivity) is the fraction of incident light (power) that is absorbed by the body when it is radiating and absorbing in thermodynamic equilibrium. The black-body emissive power being known, the emissive power of an arbitrary body at a definite temperature can be described by a dimensionless emissivity multiplied by the black-body emissive power. In some cases, emissivity and absorptivity may be defined to depend on angle, as described below. With these definitions, a corollary of Kirchhoff ##Q##s law is that for an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity.

Kirchhoff ##Q##s Law has another 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##Q##s emission, however, such systems are powered by an external source and are therefore not in thermodynamic equilibrium.

Before Kirchhoff ##Q##s law was recognized, it had been experimentally established that a good absorber is a good emitter, and a poor absorber is a poor emitter. Naturally, a good reflector must be a poor absorber. This is why, for example, lightweight emergency thermal blankets are based on reflective metallic coatings: they lose little heat by radiation.