Editing Gustav Kirchhoff (section)

== Life and work ==
Gustav Kirchhoff was born on 12 March 1824 in [[Königsberg]], [[Prussia]], the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke.<ref>{{Cite book |url=https://books.google.com/books?id=SPU8BQAAQBAJ&pg=PA288 |title=Modern Thermodynamics: From Heat Engines to Dissipative Structures |last1=Kondepudi |first1=Dilip |last2=Prigogine |first2=Ilya |date=5 November 2014 |publisher=John Wiley & Sons |isbn=9781118698709 |pages=288 |language=en }}</ref> His family were [[Lutheranism|Lutherans]] in the [[Evangelical Church of Prussia]]. He graduated from the Albertus [[University of Königsberg]] in 1847 where he attended the mathematico-physical seminar directed by [[Carl Gustav Jacob Jacobi]],<ref>{{cite book |title=The Biographical Encyclopedia of Astronomers |last=Hockey |first=Thomas |date=2009 |publisher=[[Springer Nature]] |isbn=978-0-387-31022-0 |access-date=22 August 2012 |chapter=Kirchhoff, Gustav Robert |chapter-url=http://www.springerreference.com/docs/html/chapterdbid/58778.html |title-link=The Biographical Encyclopedia of Astronomers }}</ref> [[Franz Ernst Neumann]] and [[Friedrich Julius Richelot]]. In the same year, he moved to [[Berlin]], where he stayed until he received a professorship at [[Breslau]]. Later, in 1857, he married Clara Richelot, the daughter of his mathematics professor Richelot. The couple had five children. Clara died in 1869. He married Luise Brömmel in 1872.<ref>{{cite web
 | url =http://www.kip.uni-heidelberg.de/oeffwiss/kirchhoff
 | title =Gustav Robert Kirchhoff – Dauerausstellung
 | publisher =Kirchhoff-Institute for Physics
 | access-date =18 March 2016
| quote =Am 16. August 1857 heiratete er Clara Richelot, die Tochter des Königsberger Mathematikers ... Frau Clara starb schon 1869. Im Dezember 1872 heiratete Kirchhoff Luise Brömmel. }}</ref>

[[File:Bunsen-Kirchhoff.jpg|thumb|left|upright|Kirchhoff (left) and [[Robert Bunsen]], {{Circa|1850}}|alt= Black-and-white image of two middle-aged men, either one leaning with one elbow on a wooden column in the middle. Both wear long jackets, and the shorter man on the left has a beard.]] 
Kirchhoff formulated [[Kirchhoff's circuit laws|his circuit laws]], which are now ubiquitous in [[electrical engineering]], in 1845, while he was still a student. He completed this study as a seminar exercise; it later became his doctoral dissertation. He was called to the [[University of Heidelberg]] in 1854, where he collaborated in spectroscopic work with [[Robert Bunsen]]. In 1857, he calculated that an electric signal in a [[electrical resistance|resistanceless]] wire travels along the wire at the [[speed of light]].<ref>
{{cite journal
 |last=Kirchhoff |first=Gustav
 |year=1857
 |title=On the motion of electricity in wires
 |journal=[[Philosophical Magazine]]
 |volume=13 |pages=393–412
 }}</ref><ref>{{cite journal
 |last1=Graneau |first1=Peter 
 |last2=Assis |first2=André Koch Torres 
 |title=Kirchhoff on the motion of electricity in conductors
 |url=http://www.ifi.unicamp.br/~assis/Apeiron-V19-p19-25%281994%29.pdf |archive-url=https://web.archive.org/web/20060108091219/http://www.ifi.unicamp.br/~assis/Apeiron-V19-p19-25(1994).pdf |archive-date=2006-01-08 |url-status=live
 |journal=Apeiron
 |volume=1
 |issue=19
 |date=1994
 |pages=19–25
}}</ref> He proposed his [[Kirchhoff's law of thermal radiation|law of thermal radiation]] in 1859, and gave a proof in 1861. Together Kirchhoff and Bunsen invented the [[spectroscopy|spectroscope]], which Kirchhoff used to pioneer the identification of the [[Sun#Composition|elements in the Sun]], showing in 1859 that the Sun contains [[sodium]]. He and Bunsen discovered [[caesium]] and [[rubidium]] in 1861.<ref name="Weeks">{{cite book |last1=Weeks |first1=Mary Elvira |title=The discovery of the elements |date=1956 |publisher=Journal of Chemical Education |location=Easton, PA |url=https://archive.org/details/discoveryoftheel002045mbp |edition=6th }}</ref> At [[Heidelberg]] he ran a mathematico-physical seminar, modelled on Franz Ernst Neumann's, with the mathematician [[Leo Koenigsberger]]. Among those who attended this seminar were [[Arthur Schuster]] and [[Sofia Kovalevskaya]].

He contributed greatly to the field of [[spectroscopy]] by formalizing three laws that describe the [[optical spectrum|spectral]] composition of [[light]] emitted by incandescent objects, building substantially on the discoveries of [[David Alter]] and [[Anders Jonas Ångström]]. In 1862, he was awarded the [[Rumford Medal]] for his researches on the fixed lines of the solar spectrum, and on the inversion of the bright lines in the spectra of artificial light.{{efn|Kirchhoff's banker, on hearing that Kirchhoff had identified the elements present in the Sun, remarked "of what use is gold in the Sun if it cannot be brought to Earth?" Kirchhoff deposited his prize money (gold sovereigns) with the banker, saying "here is gold from the Sun."<ref>[[Isaac Asimov|Asimov, Isaac]], ''The Secret of the Universe'', Oxford University Press, 1992, p. 109</ref>}} In 1875 Kirchhoff accepted the first chair dedicated specifically to [[theoretical physics]] at Berlin.

He also contributed to [[optics]], carefully solving the [[wave equation]] to provide a solid foundation for [[Huygens' principle]] (and correct it in the process).<ref>Baker, Bevan B.; and Copson, Edward T.; ''The Mathematical Theory of Huygens' Principle'', Oxford University Press, 1939, pp.{{nnbsp}}36–38.</ref><ref name=miller1991>Miller, David A. B.; "Huygens's wave propagation principle corrected", Optics Letters '''16''', 1370–1372, 1991</ref>

In 1864, he was elected as a member of the [[American Philosophical Society]].<ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=&title=&subject=&subdiv=&mem=&year=1864&year-max=1864&dead=&keyword=&smode=advanced |access-date=2021-04-16 |website=search.amphilsoc.org }}</ref>

In 1884, he became foreign member of the [[Royal Netherlands Academy of Arts and Sciences]].<ref>{{cite web |url=http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00001261 |title=G. R. Kirchhoff (1824–1887) |publisher=[[Royal Netherlands Academy of Arts and Sciences]] |access-date=22 July 2015 }}</ref>

Kirchhoff died in 1887, and was buried in the [[Alter St.-Matthäus-Kirchhof|St Matthäus Kirchhof Cemetery]] in [[Schöneberg]], Berlin (just a few meters from the graves of the [[Brothers Grimm]]). [[Leopold Kronecker]] is buried in the same cemetery.

===Kirchhoff's circuit laws===
{{main|Kirchhoff's circuit laws}}
Kirchhoff's first law is that the algebraic sum of currents in a network of conductors meeting at a point (or node) is zero. The second law is that in a closed circuit, the directed sums of the voltages in the system is zero.

=== Kirchhoff's three laws of spectroscopy ===
{{See also|History of spectroscopy}}
[[File:Kirchhof laws.svg|thumb|Visual depiction of Kirchhoff's laws of spectroscopy|alt=|left]]
#A solid, liquid, or dense gas excited to emit light will radiate at all wavelengths and thus produce a continuous spectrum.
#A low-density gas excited to emit light will do so at specific wavelengths, and this produces an [[emission spectrum]]. 
# If light composing a continuous spectrum passes through a cool, low-density gas, the result will be an absorption spectrum.

Kirchhoff did not know about the existence of [[energy level]]s in atoms. The existence of discrete spectral lines had been known since [[Fraunhofer lines|Fraunhofer]] discovered them in 1814. That the lines formed a discrete mathematical pattern was described by [[Johann Balmer]] in 1885. [[Joseph Larmor]] explained the splitting of the [[spectral line]]s in a [[magnetic field]] known as the [[Zeeman Effect]] by the [[oscillation]] of electrons.<ref>Buchwald, Jed Z.; and Warwick, Andrew; editors; ''Histories of the Electron: The Birth of Microphysics''</ref><ref>{{Citation |last=Larmor |first=Joseph |year=1897 |title=On a Dynamical Theory of the Electric and Luminiferous Medium, Part 3, Relations with material media |journal=Philosophical Transactions of the Royal Society |volume=190 |pages=205–300 |doi=10.1098/rsta.1897.0020|bibcode = 1897RSPTA.190..205L |title-link=s:Dynamical Theory of the Electric and Luminiferous Medium III |doi-access=free }}</ref> These discrete spectral lines were not explained as electron transitions until the [[Bohr model]] of the atom in 1913, which helped lead to [[quantum mechanics]].{{clear}}

=== Kirchhoff's law of thermal radiation ===
It was [[Kirchhoff's law of thermal radiation]] in which he proposed an unknown universal law for radiation that led [[Max Planck]] to the discovery of the quantum of action leading to [[quantum mechanics]].

=== Kirchhoff's law of thermochemistry ===
{{see also|Standard enthalpy of reaction#Variation with temperature or pressure}}
Kirchhoff showed in 1858 that, in [[thermochemistry]], the variation of the [[Standard enthalpy of reaction|heat of a chemical reaction]] is given by the difference in [[heat capacity]] between products and reactants:

:<math>\left(\frac{\partial \Delta H}{\partial T}\right)_p = \Delta C_p</math>.

Integration of this equation permits the evaluation of the heat of reaction at one temperature from measurements at another temperature.<ref>[[Keith J. Laidler|Laidler, Keith J.]]; and Meiser, J. H.; "Physical Chemistry", Benjamin/Cummings 1982, p. 62</ref><ref>[[Peter Atkins|Atkins, Peter]]; and de Paula, J.; "Atkins' Physical Chemistry", W. H. Freeman, 2006 (8th edition), p. 56</ref>

===Kirchhoff's theorem in graph theory===
Kirchhoff also worked in the mathematical field of [[graph theory]], in which he proved [[Kirchhoff's theorem|Kirchhoff's matrix tree theorem]].