KirchhofFs identity

Equation (8-8) is called Kirchhoffs identity. At this point we note that the emissivities and absorptivities which have been discussed are the total properties of the particular material i.e., they represent the integrated behavior of the material over all wavelengths. Real substances emit less radiation than ideal black surfaces as measured by the emissivity of the material. In reality, the emissivity of a material varies with temperature and the wavelength of the radiation. 

What is KirchhofFs identity When does it apply ... 

In the 1859 the chemist Robert Wilhelm Bunsen and his younger colleague, the physicist Gustav Kirchhoff, discovered a surprising phenomenon of spectroscopy. The emission and absorption spectra of an element are identical. They thus put into place an ideal tool for the discovery and identification of elements. Indeed, they themselves discovered cesium (1860) and rubidium (1861). In total, at least 20 elements were found by using spectroscopic technigues (including X-ray spectroscopy). 

After Bunsen had detected and isolated caesium, spectroscopy was taken up with great enthusiasm by William Crookes, and this led to his detection and isolation of thallium in 1861.191 Crookes letters to Charles Hanson Greville Williams, who was also working with the spectroscope, and who felt he deserved some of the credit for the discovery of thallium, have been published.192 The use of spectrochemistry in the search for hitherto unknown chemical elements in Britain over the period 1860-1869 has been described. It was perceived that, like Crookes, a scientist could make his reputation by discovering a new element. This resulted in several claims for the existence of new elements that later proved to be unfounded.193 Once Kirchhoff had established beyond doubt that the dark Fraunhofer lines were caused by the same element that caused emission lines of identical wavelengths, the way was open for the chemical analysis of the atmosphere of the sun and stars. This was a process which had been declared to be an impossibility by Auguste Comte less than 30 years previously.194... 

Atomic absorption spectrometry (AAS) is nowadays one of the most important instrumental techniques for quantitative analysis of metals (and some few metalloids) in various types of samples and matrices. The history of atomic absorption spectrometry dates back to the discovery of dark lines in the continuous emission spectrum of the sun by WoUaston in 1802. The lines are caused by the absorption of the elements in the atmosphere of the sun. His work was taken up and further pursued by Fraunhofer in 1814. In 1860, Kirchhoff and Bunsen demonstrated that the yellow hne emitted by sodium salts when introduced into a flame is identical with the so-caUed D-Hne in the emission spectrum of the sun. However, it took nearly one century before this important discovery was transferred into a viable analytical technique. In 1955, Alan Walsh published the first paper on atomic absorption spectroscopy [4]. At the same time, and independently of Walsh, AUce-made and Wilatz pubhshed the results of their fundamental AAS experiments [5, 6]. But it was the vision of Walsh and his indefatigable efforts that eventually led to the general acceptance and commercialisation of AAS instrumentation in the mid-1960s. Further instrumental achievements, such as the introduction of the graphite furnace and the hydride generation technique, in the second half of the 1960s further promoted the popularity and applicability of the technique. 

The Wiener-like distance index, named the Kirchhoff index (Bonchev et al., 1994 Gutman et al., 2003 Zhou and Trinajstic, 2008, 2009b), is based on the resistance-distance matrix. However, it has been elegantly demonstrated (Gutman and Mohar, 1996) that the quasi-Wiener index (Mohar et al., 1993 Gutman et al., 1994 Markovid et al., 1995) and the Kirchhoff index are identical topological indices. 

This results in the equality of emissivity and absorptivity of any body (known as Kirchhoff s identity) ... 

Heln holtz that the energy of a charge in any position is proportional to the electrostatic potential there. Joule s experiments showed that the energy liberated by a charge in passing from one place to another in a circuit is proportional to the difference of electric tensions in the two places, and by comparing the results of Helmholtz and Joule, Kirchhoff showed that the tension (Spannung) is identical with the potential difference. 

Following the work of Kirchhoff on the connection between emission and absorption coefficients, it had been proved that the radiation inside a totally enclosed cavity maintained at a uniform temperature was a function of the temperature alone and was identical with the radiation which would be emitted by a perfectly black body at the same temperature. The spectral distribution of the radiation had been investigated experimentally and it was found that the intensity increased slowly with decreasing frequency until it reached a peak, after which it decreased very rapidly (Fig.1.1). However, all attempts to derive an equation giving the intensity as a function of frequency had failed. The most convincing approach made by Rayleigh and Jeans on the basis of classical thermodynamics gave the result... 

There is a certain connection between the emitting and absorbing capacity of a body namely the Kirchhoff law the ratio of the body s emitting and absorbing capacity does not depend on the nature of the body but is identical, i.e., universal, for all bodies functions of frequency and temperatures (function/(co,T)... 

The Kirchhoff law defines one of the most important properties of thermal radiation, distinguishing it from other types of radiation (fluorescence, luminescent, etc.) thermal radiation is an equilibrium one. From eq. (6.6.9), it follows that the more a body absorbs, the more it radiates. Hence, in an isolated system of bodies their temperature will eventually be equalized, becoming identical. If a body absorbs more, it also radiates more. The values r(to,T) and a(to,T) can differ, but their ratio is identical. 

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