# Gustav Kirchhoff

Gustav Robert Kirchhoff (German:; 12 March 1824 – 17 October 1887) was a German chemist, mathematician and physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy and the emission of black-body radiation by heated objects. He also 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, and Kirchhoff's law of thermochemistry.
The Bunsen–Kirchhoff Award for spectroscopy is named after Kirchhoff and his colleague, Robert Bunsen.

## 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. 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, 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.
Kirchhoff formulated 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 resistanceless wire travels along the wire at the speed of light. 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 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 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. 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).
In 1864, he was elected as a member of the American Philosophical Society.
In 1884, he became foreign member of the Royal Netherlands Academy of Arts and Sciences.
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 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

* 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 levels in atoms. The existence of discrete spectral lines had been known since 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 lines in a magnetic field known as the Zeeman Effect by the oscillation of electrons. 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.

### 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

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:
    $\left({\frac {\partial \Delta H}{\partial T}}\right)_{p}=\Delta C_{p}$.
Integration of this equation permits the evaluation of the heat of reaction at one temperature from measurements at another temperature.

### Kirchhoff's theorem in graph theory

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

## Works

* Gesammelte Abhandlungen (in German). Leipzig: Johann Ambrosius Barth. 1882.
* Vorlesungen über Electricität und Magnetismus (in German). Leipzig: Benedictus Gotthelf Teubner. 1891.
* 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. B. G. Teubner, Leipzig 1894, Herausgegeben von Max Planck