Kirchhoff's law of thermal radiation
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 (Stefan–Boltzmann law), universal for all perfect black bodies.
Kirchhoff's law states that: Here, the dimensionless coefficient of absorption (or the absorptivity) is the fraction of incident light (power) at each spectral frequency that is absorbed by the body when it is radiating and absorbing in thermodynamic equilibrium.
With this definition, Kirchhoff's law states, in simpler language: In some cases, emissive power and absorptivity may be defined to depend on angle, as described below.
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 thermodynamic equilibrium.
This is why, for example, lightweight emergency thermal blankets are based on reflective metallic coatings: they lose little heat by radiation.
Kirchhoff's great insight was to recognize the universality and uniqueness of the function that describes the black body emissive power.
Attempts were made by Lord Rayleigh and Sir James Jeans 1900–1905 to describe it in classical terms, resulting in Rayleigh–Jeans law.
[10] One may suppose a second system, a cavity with walls that are opaque, rigid, and not perfectly reflective to any wavelength, to be brought into connection, through an optical filter, with the blackbody enclosure, both at the same temperature.
For example, suppose in the second system, the density of photons at narrow frequency band around wavelength
If the optical filter passed only that frequency band, then there would be a net transfer of photons, and their energy, from the second system to the first.
This is in violation of the second law of thermodynamics, which requires that there can be no net transfer of heat between two bodies at the same temperature.
In the second system, therefore, at each frequency, the walls must absorb and emit energy in such a way as to maintain the black body distribution.
For the maintenance of thermal equilibrium, these two quantities must be equal, or else the distribution of photon energies in the cavity will deviate from that of a black body.
Historically, Planck derived the black body radiation law and detailed balance according to a classical thermodynamic argument, with a single heuristic step, which was later interpreted as a quantization hypothesis.
, then Planck argued that the thermal equilibrium of the small resonator is the same when connected to either Hohlraum.
Using a heuristic of quantization, which he gleaned from Boltzmann, Planck argued that a resonator tuned to frequency
, then detach and attach to another Hohlraum at the same temperature, thus transporting energy from one to another, violating the second law.
We may apply the same argument for polarization and direction of radiation, obtaining the full principle of detailed balance.
Nano-porous materials can achieve refractive indices nearly that of vacuum, in one case obtaining average reflectance of 0.045%.
Planck analyzed such bodies with the approximation that they be considered topologically to have an interior and to share an interface.
The opaque body is considered to have a material interior that absorbs all and scatters or transmits none of the radiation that reaches it through refraction at the interface.
[2] The walls of a cavity can be made of opaque materials that absorb significant amounts of radiation at all wavelengths.
In thermodynamic equilibrium the cavity radiation will precisely obey Planck's law.
In this sense, thermodynamic equilibrium cavity radiation may be regarded as thermodynamic equilibrium black-body radiation to which Kirchhoff's law applies exactly, though no perfectly black body in Kirchhoff's sense is present.
A theoretical model considered by Planck consists of a cavity with perfectly reflecting walls, initially with no material contents, into which is then put a small piece of carbon.
Without the small piece of carbon, there is no way for non-equilibrium radiation initially in the cavity to drift towards thermodynamic equilibrium.
[2] For experimental purposes, a hole in a cavity can be devised to provide a good approximation to a black surface, but will not be perfectly Lambertian, and must be viewed from nearly right angles to get the best properties.
The construction of such devices was an important step in the empirical measurements that led to the precise mathematical identification of Kirchhoff's universal function, now known as Planck's law.
Planck also noted that the perfect black bodies of Kirchhoff do not occur in physical reality.
Kirchhoff's perfect black bodies absorb all the radiation that falls on them, right in an infinitely thin surface layer, with no reflection and no scattering.
