Draft:Kirchhoff-Clausius's Law
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In thermal radiation using geometrical optics, the Kirchhoff-Clausius law was named after Gustav Kirchhoff and Rudolf Clausius, who published their initial findings in 1862 [1] and 1863[2].
The Kirchhoff-Clausius law state that:
"The emissive power of perfectly black bodies is directly proportional to the square of the index of refraction of the surrounding medium (Kirchoff)', and therefore inversely proportional to the squares of the velocities of propagation in the surrounding medium (Clausius)."[3][4][5][6]
With the formula:
(where e = emissive power, n = index of refraction, and E = emissive power of a perfectly black body).
See also HELMHOLTZ; STEWART AND KIRCHHOFF
History
Before Kirchhoff's law was recognized,
In physics, the Kirchhoff-Clausius Law is defined by:
Temperature
(SI units: W⋅m-2)
Wavelength and temperature
(SI units: W⋅m-2⋅sr-1⋅nm-1)
Frequency and temperature
(SI units: W⋅m-2⋅sr-1⋅Hz-1)
Max Planck interpreted and used this law for the first time in his 1901 article[7][8][9]> justifying his black body distribution law.
The Law
Max Planck's statement in 1914
Origin
Gustav Kirchhoff's formula in 1862
So, with n=c/c'
The Clausius form is obtained by:
and the Planck form:
( as heat radiation intensity in vacuum and in media, c as speed of light, and n as refractive index)
Rudolf Clausius's statement in 1863
He gives these formulas:
(Here for heat radiation intensity and for the speed of light, for the medium planes a and c)
[11] [12] [13] [14] [15] [16] [17] [18] [19] [20][21]
References
- ^ Kirchhoff, Gustav; Boltzmann, Ludwig (1882). "KIRCHHOFF, GESAMMELT ABHANDLUNGEN". Kirchhoff, Collected Treatises. By Ludwig Boltzmann (in German). LEIPZIG: Johann Ambrosius BARTH.: 571.
- ^ Clausius, Rudolf (1867). "The Mechanical Theory of Heat, with its Applications to the Steam-Engine and to the Physical Properties of Bodies". Google Books from T. ARCHER HIRST, F.R.S., 1867. P: 290.
- ^ Clausius, Rudolf (1867). "The Mechanical Theory of Heat, with its Applications to the Steam-Engine and to the Physical Properties of Bodies". Google Books from T. ARCHER HIRST, F.R.S., 1867. P: 310, 326.
- ^ Clausius, Rudolf (1879). "Mechanical Theory Of Heat" (PDF). Internet Archive Tr. By Walter R. Browne 1879. P: 315, 330–331.
- ^ Planck, Max (1914). "The theory of heat radiation" (PDF). Project Gutenberg: 43.
- ^ Barrow, John D.; Magueijo, João (2014). "Redshifting of cosmological black bodies in Bekenstein-Sandvik-Barrow-Magueijo varying-alpha theories". Phys. Rev. D90 (2014) 123506. 90 (12): 6. arXiv:1406.1053. Bibcode:2014PhRvD..90l3506B. doi:10.1103/PhysRevD.90.123506. S2CID 53700017.
- ^ Planck, Max (1901-01-07). "Ueber das Gesetz der Energieverteilung im Normalspectrum". Annalen der Physik (in German). 309 (3): 425–648. Bibcode:1901AnP...309..553P. doi:10.1002/andp.19013090310.
- ^ Translated in Ando, K, (2011-10-06); Planck, Max (1901-01-07). "On the Law of the Energy Distribution in the Normal Spectrum" (PDF). Internet Archive. Archived from the original (PDF) on 2011-10-06.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link) - ^ Shamos, Morris H. Shamos (1959). "Great Experiments in Physics: Firsthand Accounts from Galileo to Einstein". Edited by Morris H. Shamos: 310. ISBN 978-0-486-25346-6.
- ^ Kirchhoff, Gustav (1862). "Gesammelte Abhandlungen". Google Books from Edition by Ludwig Boltzmann & Johann Ambrosius Barth. LEIPZIG, 1882. P.: 594.
- ^ Pauli, Wolfgang (1973). "Optics and the Theory of Electrons". Physics. 2: 12. ISBN 0-486-41458-2.
- ^ Teske, Andrzej. "SMOLUCHOWSKI, MARIAN". encyclopedia.com.
- ^ Smoluchowski de Smolan, Marian (1896). "Recherches sur une loi de Clausius au point de vue d'une théorie générale de la radiation". J. Phys. Theor. Appl. (in French): 488-499. Archived from the original on Jan 15, 2024.
- ^ Zagorodnii, A. G; Usenko, A. S.; Yakimenko, I . P. (1993). "Thermal radiation energy density in inhomogeneous transparent media" (PDF). Jetp 77. 3 (3): 361. Bibcode:1993JETP...77..361Z.
- ^ MOLCHANOV, A.P. (1966). "PHYSICS OF THE SOLAR SYSTEM Volume 3 of A Course in Astrophysics and Stellar Astronomy Chapter IX". NASA Technical Translation. 3: 187.
- ^ SIVOUKHINE, D. (1984). "COURS DE PHYSIQUE GENERALE Tome IV OPTIQUE Deuxième partie Chapitre X $ 114. Formule de Kirchhoff-Clausius". Editions MIR (in French): 296–299.
- ^ Straubel, R. (1902). "On a general theorem of geometric optics and some applications" (PDF). Phys. Zeit. 4 (1902-03), 114-117.
- ^ Ilinsky, Roman; Ulyanov, Andrey (2014). "Fluence Rate in UV Photoreactor for Disinfection of Water: Isotropically Radiating Cylinder". International Journal of Chemical Engineering: 1–13. doi:10.1155/2014/310720.
- ^ Straubel, Rudolf. "Rudolf Straubel". Wikipedia (in ger).
{{cite journal}}
: CS1 maint: unrecognized language (link) - ^ HALL, Carl W. (2000). "Laws and models : science, engineering, and technology". Boca Raton CRC Press: 261–262.
- ^ Navas, Rosario Domingo (2011). "Kirchhoff, Gustav Robert (1824-1887)". MCNbiografias (in Spanish).
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- CS1 maint: multiple names: authors list
- CS1 maint: numeric names: authors list
- CS1 French-language sources (fr)
- CS1 maint: unrecognized language
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