In heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium. It is a special case of Onsager reciprocal relations as a consequence of the time reversibility of microscopic dynamics, also known as microscopic reversibility. It was stated by Gustav Kirchhoff in 1860. 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 (Stefan–Boltzmann law), universal for all perfect black bodies. For a material that is not a perfect black body, 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. In slightly different terms, the emissive power of an arbitrary opaque body of fixed size and shape at a definite temperature can be described by a dimensionless ratio, sometimes called the emissivity: the ratio of the emissive power of the body to the emissive power of a black body of the same size and shape at the same fixed temperature. With this definition, Kirchhoff's law states, in simpler language:
Kirchhoff'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's emission; however, such systems are powered by an external source and are therefore not in thermodynamic equilibrium.
Spectral emission and absorption Kirchhoff's law of thermal radiation, as originally stated, says that the absorption coefficient for thermal radiation, α {\displaystyle \alpha } , is equal to the emissivity for thermal radiation, ϵ {\displaystyle \epsilon } . This applies in thermal equilibrium (that is, for the absorption and emission of same spectrum of light.) However, the law can be extended to the absorptivity and emissivity as a function of wavelength: not only is thermal emissivity equal to absorptivity overall, it is equal at each wavelength. Thus, at every wavelength λ {\displaystyle \lambda } , it will be true that α ( λ ) = ϵ ( λ ) {\displaystyle \alpha (\lambda )=\epsilon (\lambda )} . Expressed as a function of wavelength, the principle is independent of the requirement for thermal equilibrium. As an example, consider a leaf. It is a poor absorber of green light (around 470 nm), which is why it looks green. By the principle of detailed balance, it is an equally a poor emitter of green light. In other words, if a material is dark (well absorbing) at a certain frequency ν {\displaystyle \nu } , then its own thermal radiation will be strong (well emitting) at the same frequency ν {\displaystyle \nu } . More generally, all intensive properties are balanced in detail. So for example, the absorptivity at a certain incidence direction, for a certain frequency, of a certain polarization, is the same as the emissivity at the same direction, for the same frequency, of the same polarization. This is the principle of detailed balance.
In modern terminology, this is known as the principle of detailed balance, which is a direct consequence of the second law of thermodynamics.
History Before Kirchhoff'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. Kirchhoff's great insight was to recognize the universality and uniqueness of the function that describes the black body emissive power. But he did not know the precise form or character of that universal function. Attempts were made by Lord Rayleigh and Sir James Jeans 1900–1905 to describe it in classical terms, resulting in Rayleigh–Jeans law. This law turned out to be inconsistent yielding the ultraviolet catastrophe. The correct form of the law was found by Max Planck in 1900, assuming quantized emission of radiation, and is termed Planck's law. This marks the advent of quantum mechanics.
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