Gustav Robert Kirchhoff (German: [ˈgʊstaːf ˈʁoːbɛʁt ˈkɪʁçhɔf]; 12 March 1824 – 17 October 1887) was a German physicist and mathematician who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coined the term black body in 1860.
Several different sets of concepts are named "Kirchhoff's laws" after him, which include Kirchhoff's circuit laws, Kirchhoff's law of thermal radiation, Kirchhoff's diffraction formula, and Kirchhoff's law of thermochemistry.
The Bunsen–Kirchhoff Award for spectroscopy is named after Kirchhoff and his colleague, Robert Bunsen.
Gustav Robert Kirchhoff was born on 12 March 1824 in Königsberg, Prussia, the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke. His family were Lutherans in the Evangelical Church of Prussia.
Kirchhoff studied at the University of Königsberg, where he attended the mathematico-physical seminar directed by C. G. J. Jacobi, Franz Ernst Neumann, and Friedrich Julius Richelot. In 1845, Kirchhoff formulated two circuit laws, which are now ubiquitous in electrical 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 a Privatdozent (unsalaried lecturer) at the University of Berlin, where he stayed until 1850 when he was offered a professorship at the University of Breslau. In 1854, he was called to the University of Heidelberg, where he collaborated with Robert 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.
Kirchhoff died on 17 October 1887 in Berlin at the age of 63. He is buried at Alter St.-Matthäus-Kirchhof in Schöneberg, Berlin (just a few meters from the graves of the Brothers Grimm).
In 1850, Kirchhoff's paper "Über das Gleichgewicht und die Bewegung einer elastischen Scheibe" resolved a specific technical flaw that had dogged plate theory since Germain's original work: the boundary condition problem.
In 1857, Kirchhoff calculated that an electric signal in a resistanceless wire travels along the wire at the speed of light.
In 1859, Kirchhoff proposed a law of thermal radiation, and gave a proof in 1861.
Together, Kirchhoff and Bunsen improved on Joseph von Fraunhofer's 1814 spectroscope, which Kirchhoff used to pioneer the identification of the elements in the Sun, showing in 1859 that the Sun contains sodium. Kirchhoff and Bunsen discovered caesium and rubidium in 1861.
Kirchhoff contributed greatly to the field of spectroscopy by formalizing three laws that describe the 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".
Kirchhoff also contributed to optics, carefully solving the wave equation to provide a solid foundation for Huygens' principle (and correct it in the process).
The biharmonic plate equation is 4th-order, so mathematically we need two boundary conditions per edge to get a well-posed problem. But naive derivations gave three conditions per edge — an over-determined, inconsistent system. This made Germain's, Poisson's, and others' earlier plate theories internally inconsistent or wrong at the boundary, even though the interior equation was basically right. Kirchhoff provided the first rigorous mathematical grounding for exactly the free-edge boundary conditions that real Chladni plates have.
Kirchhoff showed, using the calculus of variations applied to the plate's strain energy, that the twisting moment along an edge is statically equivalent to a distribution of vertical shear forces (via Kelvin's earlier notion that a twisting couple can be replaced by an equivalent transverse force). It made the plate biharmonic eigenvalue problem well-posed — a solvable, unique 4th-order boundary value problem, matching the order of the governing PDE. It's essentially the origin of using energy/variational methods to derive both the governing equation and its boundary conditions together and consistently — a technique that became standard well beyond plate theory. This is why the standard theory of thin plates today is called Kirchhoff–Love plate theory (Love extended it to shells later, in 1888).
Kirchhoff's first law states that 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 states that the algebraic sum of the potential drops along a closed circuit, taken in any direction of flow, is equal to zero.
Kirchhoff's three laws of spectroscopy