User:The Lamb of God/sandbox-Kirchoff's Law

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 objects of non-zero, finite temperatures. Kirchoff's law was proposed by Gustav Kirchhoff in 1859, it was derived from general considerations of thermodynamic equilibrium and detailed balance.

In order to quantify Kirchoff's law it necessary to define some radiative terminology. The first of these is the irradiation, which is given here by the capital greek letter gamma,

($\Gamma \,\equiv irradiation$).

Irradiation is defined as the rate of all radiation incident to a surface averaged over all wavelengths and in all directions, that is, the incident radiation due to emission and reflection from all other surfaces in a system and is in units of W/m².

$\alpha \,+\rho \,+\tau \,=1$

Where...

$\alpha \,$ is the total hemisphirical absorptivity and is given by the fraction of the irradiation absorbed by the surface to the total irradiation incident to the surface.

$\alpha \,\equiv {\cfrac {\Gamma \,_{absorbed}}{\Gamma \,}}$

$\rho \,$ is the total hemispherical reflectivity and is given by the fraction of the irradiation reflected by the surface to the total irradiation incident to the surface.

$\rho \,\equiv {\cfrac {\Gamma \,_{reflected}}{\Gamma \,}}$

$\tau \,$ is the total hemispherical transmissivity and is given by the fraction of the irradiation transmitted through the surface to the total irradiation incident to the surface.

$\tau \,\equiv {\cfrac {\Gamma \,_{transmitted}}{\Gamma \,}}$

The transmissivity term is generally only considered for semitransparent materials. If the material is opaque, as is most often the case, there is no consideration for transmission phenomenon. Thus, the following equation gives the radiation balance.

$\alpha \,+\rho \,=1$

An object at some non-zero, finite temperature radiates electromagnetic energy. If the obeject is a black body, (absorbing all light that strikes it), it radiates energy according to the black-body radiation formula, other wise known as the Planck's distribution. More generally, it is a "gray 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.

${\cfrac {\epsilon \,}{\alpha \,}}=1\qquad or\qquad \epsilon \,=\alpha \,$

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).

See also

• ASTM_Subcommittee_E20.02_on_Radiation_Thermometry

External links

• Kirchhoff's Law