Radiation in an enclosure. Kirchhoffs law

Thermodynamic relationships exist between the emission and absorption capabilities of a body. These were first discovered in 1860 by G.R. Kirchhoff3 [5.5]. These relationships also show that an upper limit exists for the emitted radiation flow. 

In order to derive these we will consider an adiabatic evacuated enclosure, like that shown in Fig. 5.19, with walls of any material. In this enclosure a state of thermodynamic equilibrium will be reached The walls assume the same temperature T overall and the enclosure is filled with radiation, which is known as hollow enclosure radiation. In the sense of quantum mechanics this can also be interpreted as a photon gas in equilibrium. This equilibrium radiation is fully homogeneous, isotropic and non-polarised. It is of equal strength at every point in the hollow enclosure and is independent of direction it is determined purely by the temperature T of the walls. Due to its isotropic nature, the spectral intensity L x of the hollow enclosure radiation does not depend on / and p, but is, as Kirchhoff was the first to recognise, a universal function of wavelength and temperature L x = L x X,T), which is also called Kirchhoff s function. As the enclosure is filled with the same diffuse radiation, the incident spectral intensity Kx for every element of any area that is oriented in any position, will, according 

3 Gustav Robert Kirchhoff (1824-1887) first formulated and published the laws named after him for electrical networks when he was still a student at university in Konigsberg. In 1850 he was nominated professor in Breslau and in 1854 he became a professor in Heidelberg. It was here that he worked with R. Bunsen for over 10 years and carried out investigations into the emission and absorption of radiation. Their results became known as Kirchhoff s radiation laws and as Bunsen-Kirchhoff spectral analysis. In 1875 he became Professor of Theoretical Physics of the University of Berlin. Alongside his teacher F. Neumann, Kirchhoff was a founder of mathematical (theoretical) physics in Germany. 

A small body is located in the enclosure that, once thermodynamic equilibrium has been reached, assumes the same temperature T as the walls, Fig. 5.20. This body shall have the special property that it completely absorbs all incident radiation from every direction at every wavelength. Its directional spectral absorptivity is (independent of A, / , p and T) always one  

according to 5.1.4, its three other absorptivities aA, a and a are also equal to one. Kirchhoff named this ideal absorber a black body. 

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