German physicist and mathematician (1824–1887)
Gustav Robert Kirchhoff (German: [ˈgʊstaːf physicist andmathematician who contributed to the fundamental understanding ofelectrical circuits ,spectroscopy , and the emission ofblack-body radiation by heated objects.[ 3] [ 4] black body [ 5]
Several different sets of concepts are named "Kirchhoff's laws" after him, which includeKirchhoff's circuit laws ,Kirchhoff's law of thermal radiation ,Kirchhoff's diffraction formula , and Kirchhoff's law of thermochemistry.
TheBunsen–Kirchhoff Award for spectroscopy is named after Kirchhoff and his colleague,Robert Bunsen .
Gustav Robert Kirchhoff was born on 12 March 1824 inKönigsberg ,Prussia , the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke.[ 6] Lutherans in theEvangelical Church of Prussia .
Kirchhoff studied at theUniversity of Königsberg , where he attended the mathematico-physical seminar directed byC. G. J. Jacobi ,[ 7] Franz Ernst Neumann , andFriedrich Julius Richelot . In 1845, while a student, Kirchhoff formulatedtwo circuit laws —which are now ubiquitous inelectrical engineering . He completed this study as a seminar exercise; it later became his doctoral thesis, supervised by Neumann.
In 1847, Kirchhoff graduated from the University of Königsberg and became aPrivatdozent University of Berlin , where he stayed until 1850 when he was offered a professorship at theUniversity of Breslau . In 1854, he was called to theUniversity of Heidelberg , where he collaborated withRobert Bunsen in spectroscopic work. In 1875, Kirchhoff returned to Berlin, where he remained until his death in 1887.
In 1857, Kirchhoff married Clara Richelot, the daughter of his mathematics professor Richelot; the couple had five children. In 1872, after Clara's death in 1869, he married Luise Brömmel.[ 8]
In 1864, Kirchhoff was elected a Member of theAmerican Philosophical Society .[ 9] Royal Netherlands Academy of Arts and Sciences .[ 10]
Kirchhoff died on 17 October 1887 inBerlin at the age of 63. He is buried atAlter St.-Matthäus-Kirchhof Schöneberg , Berlin (just a few meters from the graves of theBrothers Grimm ).
Kirchhoff (left) andRobert Bunsen ,c. 1850 In 1857, Kirchhoff calculated that an electric signal in aresistanceless wire travels along the wire at thespeed of light .[ 11] [ 12]
In 1859, Kirchhoff proposeda law of thermal radiation , and gave a proof in 1861.
Together, Kirchhoff and Bunsen improved onJoseph von Fraunhofer 's 1814spectroscope , which Kirchhoff used to pioneer the identification of theelements in the Sun , showing in 1859 that the Sun containssodium . Kirchhoff and Bunsen discoveredcaesium andrubidium in 1861.[ 13]
Kirchhoff contributed greatly to the field ofspectroscopy by formalizing three laws that describe thespectral composition oflight emitted by incandescent objects, building substantially on the discoveries ofDavid Alter andAnders Jonas Ångström . In 1862, he was awarded theRumford 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".[ a]
Kirchhoff also contributed tooptics , carefully solving thewave equation to provide a solid foundation forHuygens' principle (and correct it in the process).[ 15] [ 16]
[ edit ] Kirchhoff's first law At any node in an electrical circuit where current can branch, the sum of the currents leaving the node is equal to the sum of the currents entering the node. The second law is that the algebraic sum of the potential drops along a closed circuit, taken in any direction of flow, is equal to zero.[ 17]
[ edit ] Visual depiction of Kirchhoff's laws of spectroscopy 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 anemission 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 ofenergy levels in atoms. The existence of discrete spectral lines had been known sinceFraunhofer discovered them in 1814. That the lines formed a discrete mathematical pattern was described byJohann Balmer in 1885.Joseph Larmor explained the splitting of thespectral lines in amagnetic field known as theZeeman Effect by the oscillation ofelectrons .[ 18] [ 19] electron transitions until theBohr model of the atom in 1913, which helped lead toquantum mechanics .
[ edit ] It wasKirchhoff's law of thermal radiation in which he proposed an unknown universal law for radiation that ledMax Planck to the discovery of the quantum of action leading toquantum mechanics .
[ edit ] Kirchhoff showed in 1858 that, inthermochemistry , the variation of theheat of a chemical reaction is given by the difference inheat capacity between products and reactants:
( ∂ Δ H ∂ T ) p = Δ C p {\displaystyle \left({\frac {\partial \Delta H}{\partial T}}\right)_{p}=\Delta C_{p}} Integration of this equation permits the evaluation of the heat of reaction at one temperature from measurements at another temperature.[ 20] [ 21]
[ edit ] Kirchhoff also worked in the mathematical field ofgraph theory , in which he provedKirchhoff's matrix tree theorem .
Gesammelte Abhandlungen Vorlesungen über Electricität und Magnetismus Vorlesungen über mathematische Physik . 4 vols., B. G. Teubner, Leipzig 1876–1894.Vol. 1:Mechanik . 1. Auflage, B. G. Teubner, Leipzig 1876 (online ). Vol. 2:Mathematische Optik . B. G. Teubner, Leipzig 1891 (Herausgegeben von Kurt Hensel,online ). Vol. 3:Electricität und Magnetismus . B. G. Teubner, Leipzig 1891 (Herausgegeben von Max Planck,online ). Vol. 4:Theorie der Wärme [ 22] ^ 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."[ 14] ^a b c d e f g h i j "Gustav Kirchhoff - The Mathematics Genealogy Project" .genealogy.math.ndsu.nodak.edu . Retrieved15 October 2025 .^a b c d e f g h i j "Gustav Robert Kirchhoff - Physics Tree" .academictree.org . Retrieved15 October 2025 .^ Marshall, James L.; Marshall, Virginia R. (2008)."Rediscovery of the Elements: Mineral Waters and Spectroscopy" (PDF) .The Hexagon :42– 48. Retrieved31 December 2019 . ^ Waygood, Adrian (19 June 2013).An Introduction to Electrical Science ISBN 9781135071134 ^ Schmitz, Kenneth S. (2018).Physical Chemistry . Elsevier. p. 278.ISBN 9780128005996 ^ Kondepudi, Dilip; Prigogine, Ilya (5 November 2014).Modern Thermodynamics: From Heat Engines to Dissipative Structures ISBN 9781118698709 ^ Hockey, Thomas (2009)."Kirchhoff, Gustav Robert" .The Biographical Encyclopedia of Astronomers Springer Nature .ISBN 978-0-387-31022-0 . Retrieved22 August 2012 . ^ "Gustav Robert Kirchhoff – Dauerausstellung" . Kirchhoff-Institute for Physics. Retrieved18 March 2016 .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. ^ "APS Member History" .search.amphilsoc.org . Retrieved16 April 2021 .^ "G. R. Kirchhoff (1824–1887)" .Royal Netherlands Academy of Arts and Sciences . Retrieved22 July 2015 .^ Kirchhoff, Gustav (1857). "On the motion of electricity in wires".Philosophical Magazine 13 :393– 412. ^ Graneau, Peter; Assis, André Koch Torres (1994)."Kirchhoff on the motion of electricity in conductors" (PDF) .Apeiron .1 (19):19– 25.Archived (PDF) from the original on 8 January 2006. ^ Weeks, Mary Elvira (1956).The discovery of the elements ^ Asimov, Isaac ,The Secret of the Universe , Oxford University Press, 1992, p. 109^ Baker, Bevan B.; and Copson, Edward T.;The Mathematical Theory of Huygens' Principle , Oxford University Press, 1939, pp. 36–38. ^ Miller, David A. B.; "Huygens's wave propagation principle corrected", Optics Letters16 , 1370–1372, 1991 ^ Corso di Fisicia 2 author Paul A .Tipler ^ Buchwald, Jed Z.; and Warwick, Andrew; editors;Histories of the Electron: The Birth of Microphysics ^ Larmor, Joseph (1897),"On a Dynamical Theory of the Electric and Luminiferous Medium, Part 3, Relations with material media" Philosophical Transactions of the Royal Society ,190 :205– 300,Bibcode :1897RSPTA.190..205L ,doi :10.1098/rsta.1897.0020 ^ Laidler, Keith J. ; and Meiser, J. H.; "Physical Chemistry", Benjamin/Cummings 1982, p. 62^ Atkins, Peter ; and de Paula, J.; "Atkins' Physical Chemistry", W. H. Freeman, 2006 (8th edition), p. 56^ Merritt, Ernest (1895)."Review ofVorlesungen über mathematische Physik. Vol. IV. Theorie der Wärme by Gustav Kirchhoff, edited by Max Planck" .Physical Review . American Physical Society:73– 75. Gustav Kirchhoff at theMathematics Genealogy Project O'Connor, John J.;Robertson, Edmund F. ,"Gustav Kirchhoff" ,MacTutor History of Mathematics Archive University of St Andrews Weisstein, Eric Wolfgang (ed.)."Kirchhoff, Gustav (1824–1887)" .ScienceWorld Klaus Hentschel : Gustav Robert Kirchhoff und seine Zusammenarbeit mit Robert Wilhelm Bunsen, in: Karl von Meyenn (Hrsg.)Die Grossen Physiker , Munich: Beck, vol. 1 (1997), pp. 416–430, 475–477, 532–534.Klaus Hentschel :Mapping the Spectrum. Techniques of Visual Representation in Research and Teaching Kirchhoff's 1857 paper on the speed of electrical signals in a wire
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