**Gustav Robert Kirchhoff** (German: [ˈkɪʁçhɔf]; 12 March 1824 – 17 October 1887) was a German physicist 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 radiation in 1862, and at least two different sets of concepts are named "Kirchhoff's laws" after him. The Bunsen–Kirchhoff Award for spectroscopy is named after him and his colleague, Robert Bunsen.

Gustav Kirchhoff | |
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Gustav Kirchhoff | |

Born | Gustav Robert Kirchhoff 12 March 1824 |

Died | 17 October 1887 (aged 63) |

Residence | Prussia / German Empire |

Nationality | Prussian (1824-1871) German (1871-1887) |

Alma mater | University of Königsberg |

Known for | Kirchhoff's circuit laws Kirchhoff's law of thermal radiation Kirchhoff's laws of spectroscopy Kirchhoff's law of thermochemistry |

Awards | Rumford medal (1862) Davy Medal (1877) Matteucci Medal (1877) Janssen Medal (1887) |

Scientific career | |

Fields | Physics Chemistry |

Institutions | University of Berlin University of Breslau University of Heidelberg |

Doctoral advisor | Franz Ernst Neumann |

Notable students | Loránd Eötvös Edward Nichols Gabriel Lippmann Dmitri Ivanovich Mendeleev Max Planck Jules Piccard Max Noether Heike Kamerlingh Onnes Ernst Schröder |

Gustav Kirchhoff was born in Königsberg, Prussia, the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke. His family were 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,^{[1]} 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.^{[2]}

Kirchhoff formulated his circuit laws, which are now ubiquitous in electrical engineering, in 1845, while 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 resistanceless wire travels along the wire at the speed of light.^{[3]}^{[4]} He proposed his law of thermal radiation in 1859, and gave a proof in 1861. Together Kirchhoff and Bunsen invented the spectroscope, which Kirchhoff used to pioneer the identification of the elements in the Sun, showing in 1859 that the Sun contains sodium. He and Bunsen discovered caesium and rubidium in 1861. At Heidelberg he ran a mathematico-physical seminar, modelled on 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 spectral composition of light emitted by incandescent objects, building substantially on the discoveries of David Alter and Anders Jonas Ångström (see also: spectrum analysis). 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.^{[a]} In 1875 Kirchhoff accepted the first chair specifically dedicated to theoretical physics at Berlin.

He also contributed to optics, carefully solving Maxwell's equations to provide a solid foundation for Huygens' principle (and correct it in the process).^{[6]}

In 1884 he became foreign member of the Royal Netherlands Academy of Arts and Sciences.^{[7]}

Kirchhoff died in 1887, and was buried in the 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 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 a closed system is zero.

- 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. (
*See also:*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 levels in atoms. The existence of discrete spectral lines was later explained by the Bohr model of the atom, which helped lead to quantum mechanics.

Kirchhoff showed in 1858 that, in thermochemistry, the variation of the heat of a chemical reaction is given by the difference in heat capacity between products and reactants:

.

Integration of this equation permits the evaluation of the heat of reaction at one temperature from measurements at another temperature.^{[8]}^{[9]}

- Kirchhoff equations
- Kirchhoff Institute of Physics
- Kirchhoff integral theorem
- Kirchhoff stress tensor
- Kirchhoff's diffraction formula
- Kirchhoff's theorem
- Kirchhoff–Love plate theory
- List of German inventors and discoverers
- Spectroscope

**^**Kirchoff'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."^{[5]}

**^**Hockey, Thomas (2009). "Kirchhoff, Gustav Robert".*The Biographical Encyclopedia of Astronomers*. Springer Nature. ISBN 978-0-387-31022-0. Retrieved August 22, 2012.**^**"Gustav Robert Kirchhoff - Dauerausstellung". Kirchhoff-Institute for Physics. Retrieved 18 Mar 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.

**^**Kirchhoff, G. (1857). "On the motion of electricity in wires".*Philosophical Magazine*.**13**: 393–412.**^**Graneau, P.; Assis, A.K.T. (1994). "Kirchhoff on the motion of electricity in conductors" (PDF).*Apeiron*.**1**(19): 19–25.**^**Asimov, Isaac*The Secret of the Universe*(Oxford University Press, 1992) p. 109**^**D. Miller, "Huygens’s wave propagation principle corrected", Opt. Lett.**16**, 1370–1372 (1991)**^**"G.R. Kirchhoff (1824 - 1887)". Royal Netherlands Academy of Arts and Sciences. Retrieved 22 July 2015.**^**Laidler K.J. and Meiser J.H., "Physical Chemistry" (Benjamin/Cummings 1982), p.62**^**Atkins P. and de Paula J., "Atkins' Physical Chemistry" (8th edn, W.H. Freeman 2006), p.56

- Warburg, E. (1925). "Zur Erinnerung an Gustav Kirchhoff".
*Die Naturwissenschaften*.**13**(11): 205. Bibcode:1925NW.....13..205W. doi:10.1007/BF01558883. - Stepanov, B. I. (1977). "Gustav Robert Kirchhoff (on the ninetieth anniversary of his death)".
*Journal of Applied Spectroscopy*.**27**(3): 1099. Bibcode:1977JApSp..27.1099S. doi:10.1007/BF00625887. - Everest, A S (1969). "Kirchhoff-Gustav Robert 1824–1887".
*Physics Education*.**4**(6): 341. Bibcode:1969PhyEd...4..341E. doi:10.1088/0031-9120/4/6/304. - Kirchhoff, Gustav (1860). "Ueber die Fraunhoferschen Linien".
*Monatsberichte der Königliche Preussische Akademie der Wissenschaften zu Berlin*: 662–665. ISBN 978-1-113-39933-5. HathiTrust full text. Partial English translation available in Magie, William Francis,*A Source Book in Physics*(1963). Cambridge: Harvard UP. p. 354-360.

- Gustav Kirchhoff at the Mathematics 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*, Oxford: OUP, 2002. - Kirchhoff's 1857 paper on the speed of electrical signals in a wire
- Texts on Wikisource:
*Encyclopedia Americana*. 1920.
. - . . 1914.
*Encyclopædia Britannica*(11th ed.). 1911.
. *New International Encyclopedia*. 1905.
. *Popular Science Monthly*.**33**. May 1888.
. *The American Cyclopædia*. 1879. .

- Quotations related to Gustav Kirchhoff at Wikiquote
- Media related to Gustav Robert Kirchhoff at Wikimedia Commons
- Open Library

The Bunsen–Kirchhoff Award is a prize for "outstanding achievements" in the field of analytical spectroscopy. It has been awarded since 1990 by the German Working Group for Applied Spectroscopy, and is endowed with €2500 by PerkinElmer, Germany. The prize is named in honor of chemist Robert Bunsen and physicist Gustav Kirchhoff.

Dmitry LachinovDmitry Aleksandrovich Lachinov (Russian: Дмитрий Александрович Лачи́нов) (10 May 1842 – 15 October 1902) was a Russian physicist, electrical engineer, inventor, meteorologist and climatologist.

Dmitry Lachinov studied in the St. Petersburg University, where he was a pupil of Heinrich Lenz, Pafnuty Chebyshev and Feodor Petrushevsky. In 1862, when the University was closed because of the students' unrest, Lachinov went to Germany and for two and a half years studied there under the guidance of Gustav Kirchhoff, Robert Bunsen and Hermann Helmholtz, attending practical lessons in their laboratories in Heidelberg and Tübingen.

In a paper released in 1880, Lachinov became the first one to point out the possibility of electricity transmission over long distances, and to propose the means of achieving it — 18 months before the first publication of the article with similar conclusions by Marcel Deprez.

In 1889 Lachinov wrote the first textbook on meteorology and climatology in Russia. In its 2nd edition (July 1895) he gave the first description of the lightning detector invented earlier by Alexander Popov (the device was also a prototype of the first practical radio receiver).

Lachinov's own inventions include a mercury pump, economizer for electricity consumption, electrical insulation tester (or defectoscope), optical dynamometer, a special types of photometer and electrolyser. One of his main achievements was a method of industrial synthesis of hydrogen and oxygen through electrolysis (1888).

Dmitry Lachinov is great-grandfather of physical chemist Mikhail Schultz.

Lachinov was The Officer of the Order Légion d'honneur.

Heidelberg University Faculty of Physics and AstronomyThe Faculty of Physics and Astronomy is one of twelve faculties at the University of Heidelberg. It comprises the Kirchhoff Institute of Physics, the Institute of Physics, Theoretical Physics, Environmental Physics and Theoretical Astrophysics.

Janssen Medal (French Academy of Sciences)The Janssen Medal is an astrophysics award presented by the French Academy of Sciences to those who have made advances in this area of science.The award was founded in 1886, though the first medal was not awarded until a year later. The commission formed to decide on the first recipient of the medal selected the German physicist Gustav Kirchhoff for his work on the science of spectroscopy. However, Kirchhoff died aged 63 on 17 October 1887, a few months before the award would have been announced. Rather than chose a new recipient for the award, the commission announced at the Academy's session of 26 December 1887 that the inaugural medal would be placed on his grave, in "supreme honour of the memory of this great scholar of Heidelberg".The award had been intended to be biennial, but was awarded in 1888 and again in 1889. A statement in the 1889 volume of Comptes rendus de l'Académie des sciences clarified that the award would be presented annually for the first seven years, and then biennially from 1894 onwards.This award is distinct from the Prix Jules Janssen (created in 1897), an annual award presented by the French Astronomical Society. Both awards are named for the French astronomer Pierre Janssen (1824–1907) (better known as Jules Janssen). Janssen founded the Academy award, and was a member of the inaugural commission.

KirchhoffKirchhoff, Kirchoff or Kirchhoffer is a German surname. Notable people with the surname include:

Adolf Kirchhoff (1826–1908), German classical scholar and epigrapher

Alfred Kirchhoff (1838–1907), German geographer and naturalist

Alphonse Kirchhoffer (1873–1913), French Olympic fencer

Charles William Henry Kirchhoff (1853-1916), American editor and metals expert

Detlef Kirchhoff (1967–), German rower

Fritz Kirchhoff (1901–1953), German screenwriter, film producer and director

Gustav Kirchhoff (1824–1887), German physicist, the discoverer of "Kirchhoff's laws"

Gottlieb Kirchhoff (1764–1833), German chemist (died in Saint Petersburg)

Jan Kirchhoff (1990–), German footballer, currently playing for Sunderland FC

Mary Kirchoff (born 1959), American fantasy novelist

Paul Kirchhoff (1900–1972), German anthropologist and ethnologist of pre-Columbian Mesoamerican cultures

Robert Kirchhoff (born 1962), Slovak film director

Ulrich Kirchhoff (1967–), German show jumping champion

Kirchhoff's circuit lawsKirchhoff's laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of James Clerk Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws. These laws can be applied in time and frequency domains and form the basis for network analysis.

Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits.

Kirchhoff's diffraction formulaKirchhoff's diffraction formula (also Fresnel–Kirchhoff diffraction formula)

can be used to model the propagation of light in a wide range of configurations, either analytically or using numerical modelling. It gives an expression for the wave disturbance when a monochromatic spherical wave passes through an opening in an opaque screen. The equation is derived by making several approximations to the Kirchhoff integral theorem which uses Green's theorem to derive the solution to the homogeneous wave equation.

Kirchhoff's law of thermal radiationIn heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium.

A body at temperature T radiates electromagnetic energy. A perfect black body in thermodynamic equilibrium absorbs all light that strikes it, and radiates energy according to a unique law of radiative emissive power for temperature T, universal for all perfect black bodies. Kirchhoff's law states that:

Here, the dimensionless coefficient of absorption (or the absorptivity) is the fraction of incident light (power) that is absorbed by the body when it is radiating and absorbing in thermodynamic equilibrium.

In slightly different terms, the emissive power of an arbitrary opaque body of fixed size and shape at a definite temperature can be described by a dimensionless ratio, sometimes called the emissivity: the ratio of the emissive power of the body to the emissive power of a black body of the same size and shape at the same fixed temperature. With this definition, Kirchhoff's law states, in simpler language:

In some cases, emissive power and absorptivity may be defined to depend on angle, as described below. The condition of thermodynamic equilibrium is necessary in the statement, because the equality of emissivity and absorptivity often does not hold when the material of the body is not in thermodynamic equilibrium.

Kirchhoff's law has another corollary: the emissivity cannot exceed one (because the absorptivity cannot, by conservation of energy), so it is not possible to thermally radiate more energy than a black body, at equilibrium. In negative luminescence the angle and wavelength integrated absorption exceeds the material's emission, however, such systems are powered by an external source and are therefore not in thermodynamic equilibrium.

Kirchhoff's lawsThere are several Kirchhoff's laws, all named after Gustav Kirchhoff:

Kirchhoff's circuit laws in electrical engineering

Kirchhoff's law of thermal radiation

Kirchhoff equations in fluid dynamics

Kirchhoff's three laws of spectroscopy

Kirchhoff's law of thermochemistry

Kirchhoff's theoremIn the mathematical field of graph theory, **Kirchhoff's theorem** or **Kirchhoff's matrix tree theorem** named after Gustav Kirchhoff is a theorem about the number of spanning trees in a graph, showing that this number can be computed in polynomial time as the determinant of a matrix derived from the graph. It is a generalization of Cayley's formula which provides the number of spanning trees in a complete graph.

Kirchhoff's theorem relies on the notion of the Laplacian matrix of a graph that is equal to the difference between the graph's degree matrix (a diagonal matrix with vertex degrees on the diagonals) and its adjacency matrix (a (0,1)-matrix with 1's at places corresponding to entries where the vertices are adjacent and 0's otherwise).

For a given connected graph *G* with *n* labeled vertices, let *λ*_{1}, *λ*_{2}, ..., *λ _{n}*

Equivalently the number of spanning trees is equal to *any* cofactor of the Laplacian matrix of *G*.

Kirchhoff is a small lunar impact crater that is located in the northern part of the Montes Taurus range. It was named after German physicist Gustav Kirchhoff. It lies to the west of the crater Newcomb, and southeast of the crater pair of Hall and G. Bond.

This is a circular, bowl-shaped feature that lies in the midst of rugged lunar terrain. The satellite crater Kirchhoff C adjoins the eastern rim. There is a low rise at the midpoint of the interior floor.

Kirchhoff equationsIn fluid dynamics, the **Kirchhoff equations**, named after Gustav Kirchhoff, describe the motion of a rigid body in an ideal fluid.

where and are the angular and linear velocity vectors at the point , respectively; is the moment of inertia tensor, is the body's mass; is a unit normal to the surface of the body at the point ; is a pressure at this point; and are the hydrodynamic torque and force acting on the body, respectively; and likewise denote all other torques and forces acting on the body. The integration is performed over the fluid-exposed portion of the body's surface.

If the body is completely submerged body in an infinitely large volume of irrotational, incompressible, inviscid fluid, that is at rest at infinity, then the vectors and can be found via explicit integration, and the dynamics of the body is described by the Kirchhoff – Clebsch equations:

Their first integrals read

- .

Further integration produces explicit expressions for position and velocities.

Kirchhoff integral theoremKirchhoff's integral theorem (sometimes referred to as the Fresnel–Kirchhoff integral theorem) uses Green's identities to derive the solution to the homogeneous wave equation at an arbitrary point P in terms of the values of the solution of the wave equation and its first-order derivative at all points on an arbitrary surface that encloses P.

LepidoliteLepidolite is a lilac-gray or rose-colored member of the mica group of minerals with formula K(Li,Al,Rb)2(Al,Si)4O10(F,OH)2. It is the most abundant lithium-bearing mineral and is a secondary source of this metal. It is a phyllosilicate mineral and a member of the polylithionite-trilithionite series.It is associated with other lithium-bearing minerals like spodumene in pegmatite bodies. It is one of the major sources of the rare alkali metals rubidium and caesium. In 1861, Robert Bunsen and Gustav Kirchhoff extracted 150 kg (330 lb) of lepidolite and yielded a few grams of rubidium salts for analysis, and therefore discovered the new element rubidium.It occurs in granite pegmatites, in some high-temperature quartz veins, greisens and granites. Associated minerals include quartz, feldspar, spodumene, amblygonite, tourmaline, columbite, cassiterite, topaz and beryl.Notable occurrences include Brazil; Ural Mountains, Russia; California, United States; Tanco Mine, Bernic Lake, Manitoba, Canada; and Madagascar.

Matteucci MedalThe Matteucci Medal is an Italian award for physicists, named after Carlo Matteucci. It was established to award physicists for their fundamental contributions. Under an Italian Royal Decree dated July 10, 1870, the Italian Society of Sciences was authorized to receive a donation from Carlo Matteucci for the establishment of the Prize.

Matteucci MedalistsSource: Italian Society of Sciences

Robert BunsenRobert Wilhelm Eberhard Bunsen (; German: [ˈbʊnzən]; 30 March 1811 – 16 August 1899) was a German chemist. He investigated emission spectra of heated elements, and discovered caesium (in 1860) and rubidium (in 1861) with the physicist Gustav Kirchhoff. Bunsen developed several gas-analytical methods, was a pioneer in photochemistry, and did early work in the field of organoarsenic chemistry. With his laboratory assistant, Peter Desaga, he developed the Bunsen burner, an improvement on the laboratory burners then in use. The Bunsen–Kirchhoff Award for spectroscopy is named after Bunsen and Kirchhoff.

RubidiumRubidium is a chemical element with symbol Rb and atomic number 37. Rubidium is a soft, silvery-white metallic element of the alkali metal group, with a standard atomic weight of 85.4678. Elemental rubidium is highly reactive, with properties similar to those of other alkali metals, including rapid oxidation in air. On Earth, natural rubidium comprises two isotopes: 72% is the stable isotope, 85Rb; 28% is the slightly radioactive 87Rb, with a half-life of 49 billion years—more than three times longer than the estimated age of the universe.

German chemists Robert Bunsen and Gustav Kirchhoff discovered rubidium in 1861 by the newly developed technique, flame spectroscopy. The name comes from the Latin word rubidus, meaning deep red, the color of its emission spectrum. Rubidium's compounds have various chemical and electronic applications. Rubidium metal is easily vaporized and has a convenient spectral absorption range, making it a frequent target for laser manipulation of atoms. Rubidium is not a known nutrient for any living organisms. However, rubidium ions have the same charge as potassium ions, and are actively taken up and treated by animal cells in similar ways.

SpectroscopySpectroscopy is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, by a prism. Later the concept was expanded greatly to include any interaction with radiative energy as a function of its wavelength or frequency, predominantly in the electromagnetic spectrum, though matter waves and acoustic waves can also be considered forms of radiative energy; recently, with tremendous difficulty, even gravitational waves have been associated with a spectral signature in the context of LIGO and laser interferometry. Spectroscopic data are often represented by an emission spectrum, a plot of the response of interest as a function of wavelength or frequency.

Spectroscopy, primarily in the electromagnetic spectrum, is a fundamental exploratory tool in the fields of physics, chemistry, and astronomy, allowing the composition, physical structure and electronic structure of matter to be investigated at atomic scale, molecular scale, macro scale, and over astronomical distances. Important applications arise from biomedical spectroscopy in the areas of tissue analysis and medical imaging.

Stress measuresThe most commonly used measure of stress is the Cauchy stress tensor, often called simply *the* stress tensor or "true stress". However, several other measures of stress can be defined. Some such stress measures that are widely used in continuum mechanics, particularly in the computational context, are:

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