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.
Kirchhoff's circuit laws
Gustav Kirchhoff
Gustav Kirchhoff | Kirchhoff's circuit laws
His  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. 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. The algebraic sum of currents in a network of conductors meeting at a point is zero and in a closed circuit, the directed sums of the voltages in a closed system is zero The algebraic sum of currents in a network of conductors meeting at a point is zero. In a closed circuit, the directed sums of the voltages in a closed system is zero.
where is rubidium found on the periodic table
user
It is the 37th element.
assistant
what letters are used to represent it?
user
Rb
assistant
who discovered it?
user
Robert Bunsen and Gustav Kirchhoff
assistant
who is the former?
user
German chemist
assistant
which university did he attend?
user
Sorry. I cannot find the answer based on the context.
assistant
what scientific law did the latter introduce?
user
Kirchhoff's circuit laws, laws of spectroscopy and law of thermochemistry.
assistant
can you briefly describe the first one?
user
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.
Gustav Kirchhoff | Kirchhoff's circuit laws
He married Luise Brömmel in 1872. 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. 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.
Gustav Kirchhoff | Life and work
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.
Gustav Kirchhoff | Kirchhoff's law of thermochemistry
Gustav Robert Kirchhoff (; 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. Several different sets of concepts are named "Kirchhoff's laws" after him, concerning such diverse subjects as black-body radiation and spectroscopy, electrical circuits, and thermochemistry. The Bunsen–Kirchhoff Award for spectroscopy is named after him and his colleague, Robert Bunsen.
Gustav Kirchhoff | Introduction
Assume an electric network consisting of two voltage sources and three resistors. According to the first law: Applying the second law to the closed circuit "s", and substituting for voltage using Ohm's law gives: The second law, again combined with Ohm's law, applied to the closed circuit "s" gives: This yields a system of linear equations in formula_6: which is equivalent to Assuming the solution is
Kirchhoff's circuit laws | Example
There are several Kirchhoff's laws, all named after Gustav Kirchhoff:
Kirchhoff's laws | Introduction
Kirchhoff's circuit 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.
Kirchhoff's circuit laws | Introduction
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.
Gustav Kirchhoff | Kirchhoff's three laws of spectroscopy
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).
Gustav Kirchhoff | Life and work
This law is also called Kirchhoff's second law, Kirchhoff's loop (or mesh) rule, and Kirchhoff's second rule. This law states thatThe directed sum of the potential differences (voltages) around any closed loop is zero. Similarly to Kirchhoff's current law, the voltage law can be stated as:
Kirchhoff's circuit laws | Kirchhoff's voltage law
In 1859, not knowing of Stewart's work, Gustav Robert Kirchhoff reported the coincidence of the wavelengths of spectrally resolved lines of absorption and of emission of visible light. Importantly for thermal physics, he also observed that bright lines or dark lines were apparent depending on the temperature difference between emitter and absorber. Kirchhoff then went on to consider bodies that emit and absorb heat radiation, in an opaque enclosure or cavity, in equilibrium at temperature . Here is used a notation different from Kirchhoff's. Here, the emitting power denotes a dimensioned quantity, the total radiation emitted by a body labeled by index at temperature .
Planck's law | Gustav Kirchhoff
In a blackbody enclosure that contains electromagnetic radiation with a certain amount of energy at thermodynamic equilibrium, this "photon gas" will have a Planck distribution of energies. One may suppose a second system, a cavity with walls that are opaque, rigid, and not perfectly reflective to any wavelength, to be brought into connection, through an optical filter, with the blackbody enclosure, both at the same temperature. Radiation can pass from one system to the other. For example, suppose in the second system, the density of photons at narrow frequency band around wavelength formula_1 were higher than that of the first system.
Kirchhoff's law of thermal radiation | Theory
Gustav Kirchhoff stated his law in several papers in 1859 and 1860, and then in 1862 in an appendix to his collected reprints of those and some related papers. Prior to Kirchhoff's studies, it was known that for total heat radiation, the ratio of emissive power to absorptive ratio was the same for all bodies emitting and absorbing thermal radiation in thermodynamic equilibrium. This means that a good absorber is a good emitter. Naturally, a good reflector is a poor absorber. For wavelength specificity, prior to Kirchhoff, the ratio was shown experimentally by Balfour Stewart to be the same for all bodies, but the universal value of the ratio had not been explicitly considered in its own right as a function of wavelength and temperature.
Kirchhoff's law of thermal radiation | Original statements
The first law of thermodynamics was developed empirically over about half a century. A main aspect of the struggle was to deal with the previously proposed caloric theory of heat. In 1840, Germain Hess stated a conservation law for the so-called 'heat of reaction' for chemical reactions. His law was later recognized as a consequence of the first law of thermodynamics, but Hess's statement was not explicitly concerned with the relation between energy exchanges by heat and work. In 1842, Julius Robert von Mayer made a statement that has been rendered by Truesdell (1980) in the words "in a process at constant pressure, the heat used to produce expansion is universally interconvertible with work", but this is not a general statement of the first law.
First law of thermodynamics | History
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.
Gustav Kirchhoff | Life and work
Kirchhoff's original contribution to the physics of thermal radiation was his postulate of a perfect black body radiating and absorbing thermal radiation in an enclosure opaque to thermal radiation and with walls that absorb at all wavelengths. Kirchhoff's perfect black body absorbs all the radiation that falls upon it.
Kirchhoff's law of thermal radiation | Original statements
First, Kirchhoff's first law is used to find the currents in junctions B and D: Then, Kirchhoff's second law is used for finding the voltage in the loops ABDA and BCDB: When the bridge is balanced, then , so the second set of equations can be rewritten as:
Wheatstone bridge | Full derivation using Kirchhoff's circuit laws
This yields Kirchhoff's law:
Kirchhoff's law of thermal radiation | Theory
If the optical filter passed only that frequency band, then there would be a net transfer of photons, and their energy, from the second system to the first. This is in violation of the second law of thermodynamics, which requires that there can be no net transfer of heat between two bodies at the same temperature. In the second system, therefore, at each frequency, the walls must absorb and emit energy in such a way as to maintain the black body distribution. Hence absorptivity and emissivity must be equal. The absorptivity formula_2 of the wall is the ratio of the energy absorbed by the wall to the energy incident on the wall, for a particular wavelength.
Kirchhoff's law of thermal radiation | Theory
Kirchhoff's law of thermal radiation is a succinct and brief account of a complicated physical situation. The following is an introductory sketch of that situation, and is very far from being a rigorous physical argument. The purpose here is only to summarize the main physical factors in the situation, and the main conclusions.
Planck's law | Kirchhoff's law of thermal radiation
Gottlieb Sigismund Constantin Kirchhoff (19 February 1764 – 14 February 1833) was a Russian chemist of German origin. In 1792–1802, Assistant Director and then Director of the Head Pharmacy at Saint Petersburg. Corresponding member (1807–1812) and since 1812 Full member of the Petersburg Academy of Sciences (Russia). In 1811, he became the first person to convert starch into a sugar (corn syrup), by heating it with sulfuric acid in acid-catalyzed reaction. This sugar was eventually named glucose. He also developed a method of refining vegetable oil, and established a factory that prepared two tons of refined oil a day. Since the sulfuric acid was not consumed, it was the first documented example of catalysis in organic chemistry.
Gottlieb Kirchhoff | Introduction
This law turned out to be inconsistent yielding the ultraviolet catastrophe. The correct form of the law was found by Max Planck in 1900, assuming quantized emission of radiation, and is termed Planck's law. This marks the advent of quantum mechanics.
Kirchhoff's law of thermal radiation | History
About 1850, Kirchhoff published his laws relating to branched or divided circuits. He also showed mathematically that according to the then prevailing electrodynamic theory, electricity would be propagated along a perfectly conducting wire with the velocity of light. Helmholtz investigated mathematically the effects of induction upon the strength of a current and deduced therefrom equations, which experiment confirmed, showing amongst other important points the retarding effect of self-induction under certain conditions of the circuit. In 1853, Sir William Thomson (later Lord Kelvin) predicted as a result of mathematical calculations the oscillatory nature of the electric discharge of a condenser circuit.
History of electromagnetic theory | Middle 19th century
His writings were numerous. With his first paper in 1825, Ohm looks into the decrease in the electromagnetic force produced by a wire as the length of the wire increased. In 1826, he gave a description of conduction in circuits modeled on Fourier's study of heat conduction. This paper continue Ohm's deduction of results from experimental evidence and, particularly in the second, he was able to propose laws which went a long way to explaining results of others working on galvanic electricity. The most important was his pamphlet published in Berlin in 1827, with the title "Die galvanische Kette mathematisch bearbeitet".
Georg Ohm | Study and publications
The first Hofstadter sequences were described by Douglas Richard Hofstadter in his book "Gödel, Escher, Bach". In order of their presentation in chapter III on figures and background (Figure-Figure sequence) and chapter V on recursive structures and processes (remaining sequences), these sequences are:
Hofstadter sequence | Sequences presented in "Gödel, Escher, Bach: an Eternal Golden Braid"
However, Plemelj neglected certain degenerate cases, and it was shown in 1989 by Andrei Bolibrukh that there are cases when the answer is 'no'. Here, we focus entirely on the generic case.
Isomonodromic deformation | Hilbert's twenty-first problem
Planck stated the second law as follows. Rather like Planck's statement is that of Uhlenbeck and Ford for "irreversible phenomena".
Second law of thermodynamics | Planck's statement
For experimental purposes, a hole in a cavity can be devised to provide a good approximation to a black surface, but will not be perfectly Lambertian, and must be viewed from nearly right angles to get the best properties. The construction of such devices was an important step in the empirical measurements that led to the precise mathematical identification of Kirchhoff's universal function, now known as Planck's law.
Kirchhoff's law of thermal radiation | A hole in the wall of a cavity
Thermochemistry rests on two generalizations. Stated in modern terms, they are as follows: These statements preceded the first law of thermodynamics (1845) and helped in its formulation. Lavoisier, Laplace and Hess also investigated specific heat and latent heat, although it was Joseph Black who made the most important contributions to the development of latent energy changes.
Thermochemistry | History
However, he made two mistakes: As shown by Max Abraham, Kaufmann overlooked that Searle's formula only applies in the longitudinal direction, but for deflection measurements the formula for the transverse direction was important. Therefore, Abraham introduced the "transverse electromagnetic mass" with the following velocity dependence:
Kaufmann–Bucherer–Neumann experiments | First experiments
Ohm's law first appeared in the famous book "Die galvanische Kette, mathematisch bearbeitet" (tr., "The Galvanic Circuit Investigated Mathematically") (1827) in which he gave his complete theory of electricity. In this work, he stated his law for electromotive force acting between the extremities of any part of a circuit is the product of the strength of the current, and the resistance of that part of the circuit. The book begins with the mathematical background necessary for an understanding of the rest of the work. While his work greatly influenced the theory and applications of current electricity, it was coldly received at that time.
Georg Ohm | Discovery of Ohm's law
Freiherr Christian Johann Dietrich Theodor von Grotthuss (January 20, 1785 – March 26, 1822) was a German chemist known for establishing the first theory of electrolysis in 1806 and formulating the first law of photochemistry in 1817. His theory of electrolysis is considered the first description of the so-called Grotthuss mechanism.
Theodor Grotthuss | Introduction
Ångström postulated that an incandescent gas emits luminous rays of the same wavelength as those it can absorb. Ångström was unaware of Foucalt's experimental results. At the same time [[Sir George Stokes, 1st Baronet|George Stokes]] and [[William Thomson, 1st Baron Kelvin|William Thomson (Kelvin)]] were discussing similar postulates. Ångström also measured the emission spectrum from hydrogen later labeled the [[Balmer lines]]. In 1854 and 1855, [[David Alter]] published observations on the spectra of metals and gases, including an independent observation of the [[Balmer lines]] of hydrogen. [[Image:Kirchhoffs first spectroscope.jpg|thumb|Spectroscope of Kirchhoff and Bunsen]] The systematic attribution of spectra to chemical elements began in the 1860s with the work of German physicist [[Robert Bunsen|Bunsen]] and [[Gustav Kirchhoff|Kirchhoff]] found that [[Fraunhofer lines]] correspond to emission spectral lines observed in laboratory light sources, and so they laid way for [[Spectrochemical Analysis|spectrochemical analysis]] in laboratory and astrophysics.
History of spectroscopy | Mid 19th Century (1830 - 1869)
He increased the power of his early automobiles by carrying a cylinder of nitrous oxide that he could inject into the carburetor. After eighteen productive years at Göttingen, investigating osmotic pressure and electrochemistry and presenting a theory of how nerves conduct, he moved to Berlin, and was awarded the title "Geheimrat" In 1905, he proposed his "New Heat Theorem", later known as the Third law of thermodynamics. He showed that as the temperature approached absolute zero, the entropy approaches zero while the free energy remains above zero. This is the work for which he is best remembered, as it enabled chemists to determine free energies (and therefore equilibrium points) of chemical reactions from heat measurements.
Walther Nernst | Career
Ernst Gustav Kirsch (September 13, 1841 – January 8, 1901) was a German engineer. He was educated at Sorbonne, in Zürich and in Berlin. He was a professor from 1874 at the Chemnitz University of Technology in Chemnitz, Germany. Kirsch is primarily known for the Kirsch equations describing the elastic stress state around a hole.
Ernst Gustav Kirsch | Introduction
This law is also called Kirchhoff's first law, Kirchhoff's point rule, or Kirchhoff's junction rule (or nodal rule). This law states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node; or equivalently:The algebraic sum of currents in a network of conductors meeting at a point is zero.Recalling that current is a signed (positive or negative) quantity reflecting direction towards or away from a node, this principle can be succinctly stated as: where "n" is the total number of branches with currents flowing towards or away from the node.
Kirchhoff's circuit laws | Kirchhoff's current law
In 1859, not knowing of Stewart's work, Gustav Robert Kirchhoff reported the coincidence of the wavelengths of spectrally resolved lines of absorption and of emission of visible light. Importantly for thermal physics, he also observed that bright lines or dark lines were apparent depending on the temperature difference between emitter and absorber. Kirchhoff then went on to consider some bodies that emit and absorb heat radiation, in an opaque enclosure or cavity, in equilibrium at temperature . Here is used a notation different from Kirchhoff's. Here, the emitting power denotes a dimensioned quantity, the total radiation emitted by a body labeled by index at temperature .
Black-body radiation | Gustav Kirchhoff
This framework did not presume a concept of energy in general, but regarded it as derived or synthesized from the prior notions of heat and work. By one author, this framework has been called the "thermodynamic" approach. The first explicit statement of the first law of thermodynamics, by Rudolf Clausius in 1850, referred to cyclic thermodynamic processes. Clausius also stated the law in another form, referring to the existence of a function of state of the system, the internal energy, and expressed it in terms of a differential equation for the increments of a thermodynamic process. This equation may be described as follows:
First law of thermodynamics | Original statements: the "thermodynamic approach"
The original nineteenth century statements of the first law of thermodynamics appeared in a conceptual framework in which transfer of energy as heat was taken as a primitive notion, not defined or constructed by the theoretical development of the framework, but rather presupposed as prior to it and already accepted. The primitive notion of heat was taken as empirically established, especially through calorimetry regarded as a subject in its own right, prior to thermodynamics. Jointly primitive with this notion of heat were the notions of empirical temperature and thermal equilibrium. This framework also took as primitive the notion of transfer of energy as work.
First law of thermodynamics | Original statements: the "thermodynamic approach"
In 1830, Hess took up chemistry full-time, researching and teaching, and later became an adjunct professor of Chemistry at the St. Petersburg Academy of Sciences. His most famous paper, outlining his law on thermochemistry, was published there in 1840. His principle, a progenitor for the first law of thermodynamics, came to be called Hess's law. It states that in a series of chemical reactions, the total energy gained or lost depends only on the initial and final states, regardless of the number or path of the steps. This is also known as the law of constant heat summation. Like most of his colleagues, Hess was primarily an experimental chemist interested in the discovery and analysis of new substances.
Germain Henri Hess | Contributions to chemistry
One of the first scientists to introduce experiments with apparatus in their lectures, Lichtenberg was a popular and respected figure in contemporary European intellectual circles. He maintained relations with most of the great figures of that era, including Goethe and Kant. In 1784, Alessandro Volta visited Göttingen especially to see him and his experiments. Mathematician Karl Friedrich Gauss sat in on his lectures. In 1793, he was elected a member of the Royal Society.
Georg Christoph Lichtenberg | Life
The Second Conference on the Epistemology of the Exact Sciences () was held on 5–7 September 1930 in Königsberg, then located in East Prussia. It was at this conference that Kurt Gödel first presented his incompleteness theorems, though just "in an off-hand remark during a general discussion on the last day". The real first presentation took place in Vienna. The conference was organised by Kurt Reidemeister of the University of Königsberg. The presentations were grouped around two themes: firstly, the foundation of mathematics and secondly philosophical questions arising from Quantum mechanics. The conference was closely related to the journal "Erkenntnis" who published the associated papers and accounts of the discussion in "Erkenntnis" (1931), 2 pp 87-190.
Second Conference on the Epistemology of the Exact Sciences | Introduction
The communication was given to Abraham Esau, head of the physics section of the "Reichsforschungsrat" (RFR, Reich Research Council) at the REM. On 29 April, a group, organized by Esau, met at the REM to discuss the potential of a sustained nuclear chain reaction. The group included the physicists Walther Bothe, Robert Döpel, Hans Geiger, Wolfgang Gentner (probably sent by Walther Bothe), Wilhelm Hanle, Gerhard Hoffmann, and Georg Joos; Peter Debye was invited, but he did not attend. After this, informal work began at Göttingen by Joos, Hanle, and their colleague Reinhold Mannfopff; the group of physicists was known informally as the first "Uranverein" (Uranium Club) and formally as "Arbeitsgemeinschaft für Kernphysik".
Gerhard Hoffmann | Career
Their impacts on a photographic plate produced a deflection curve, whose individual points corresponded to a certain velocity and a certain mass of the electrons. By reversing the charge on the condenser, thus inverting the electric field, two symmetric curves could be obtained, whose center line determined the direction of the magnetic deflection. Kaufmann published a first analysis of his data in 1901 – he actually was able to measure a decrease of the charge-to-mass ratio, thus demonstrating that mass or momentum increases with velocity. Using Searle's formula (1897) for the electromagnetic energy increase of charged bodies with velocity, he calculated the increase of the electron's electromagnetic mass as a function of velocity: Kaufmann noticed that the observed increase cannot be explained by this formula, so he separated the measured "total mass" into a "mechanical (true) mass" and an "electromagnetic (apparent) mass", the mechanical mass being considerably greater than the electromagnetic one.
Kaufmann–Bucherer–Neumann experiments | First experiments
He then became his assistant at his experimental lectures until 1791 when he was substituted by Johann Hermann Seyde. He received many orders from abroad, including, among other things, the title of court mechanic from the Duke Ernest II, Duke of Saxe-Gotha-Altenburg.
Johann Andreas Klindworth | Biography
This procedure was the first to produce fullerenes in large amounts for chemical experiments. Since 1993 he is an honorary professor ("Honorarprofessor") at the University of Heidelberg.
Wolfgang Krätschmer | Introduction
For the first time the experimental observation of Bloch oscillations in such super lattices at very low temperatures was shown by Jochen Feldmann and Karl Leo in 1992. Other realizations were
Bloch oscillation | Discovery and experimental realizations
Planck offered the following proposition as derived directly from experience. This is sometimes regarded as his statement of the second law, but he regarded it as a starting point for the derivation of the second law.
Second law of thermodynamics | Planck's proposition
Before Kirchhoff's law was recognized, it had been experimentally established that a good absorber is a good emitter, and a poor absorber is a poor emitter. Naturally, a good reflector must be a poor absorber. This is why, for example, lightweight emergency thermal blankets are based on reflective metallic coatings: they lose little heat by radiation. Kirchhoff's great insight was to recognize the universality and uniqueness of the function that describes the black body emissive power. But he did not know the precise form or character of that universal function. Attempts were made by Lord Rayleigh and Sir James Jeans 1900–1905 to describe it in classical terms, resulting in Rayleigh–Jeans law.
Kirchhoff's law of thermal radiation | History
Later, Nernst's theorem (or Nernst's postulate), which is now known as the third law, was formulated by Walther Nernst over the period 1906-12. While the numbering of the laws is universal today, various textbooks throughout the 20th century have numbered the laws differently. In some fields, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Gradually, this resolved itself and a zeroth law was later added to allow for a self-consistent definition of temperature. Additional laws have been suggested, but have not achieved the generality of the four accepted laws, and are generally not discussed in standard textbooks.
Laws of thermodynamics | History
Première Partie. Âge de la pierre (1868), Herzog, Zürich, 41 p.; but at closer look these are all reprints of papers that originally appeared in various science journals.
Adolph von Morlot | Publications
In 1831, Gauss developed a fruitful collaboration with the physics professor Wilhelm Weber, leading to new knowledge in magnetism (including finding a representation for the unit of magnetism in terms of mass, charge, and time) and the discovery of Kirchhoff's circuit laws in electricity. It was during this time that he formulated his namesake law. They constructed the first electromechanical telegraph in 1833, which connected the observatory with the institute for physics in Göttingen. Gauss ordered a magnetic observatory to be built in the garden of the observatory, and with Weber founded the "Magnetischer Verein" ("magnetic association"), which supported measurements of Earth's magnetic field in many regions of the world.
Carl Friedrich Gauss | Magnetism
Houtermans began his studies at the University of Göttingen in 1921, and he received his doctorate under James Franck in 1927, the same year Robert Oppenheimer received his doctorate under Max Born. He completed his Habilitation under Gustav Hertz at the Technical University of Berlin, in 1932. Hertz and Franck were Nobel Prize laureates; they shared the 1925 Nobel Prize in Physics. While at Göttingen, Houtermans met Enrico Fermi, George Gamow, Werner Heisenberg, Wolfgang Pauli, and Victor Frederick Weisskopf. Houtermans and Gamow did pioneering work on quantum tunneling in 1928. Houtermans, in 1929, with Robert d'Escourt Atkinson, made the first calculation of stellar thermonuclear reactions.
Fritz Houtermans | Education
Gottfried Kirch (; also Kirche , Kirkius; 18 December 1639 – 25 July 1710) was a German astronomer and the first 'Astronomer Royal' in Berlin and, as such, director of the nascent Berlin Observatory.
Gottfried Kirch | Introduction
The series started in 1932 with publication of "Knotentheorie" by Kurt Reidemeister as "Band 1" (English: volume 1). There seems to have been double numeration in this sequence.
Ergebnisse der Mathematik und ihrer Grenzgebiete | Original series
Kirchhoff's loop rule states that the sum of the voltage drops in a closed loop around a circuit equals zero. This comes from the conservation of energy, as voltage is defined as the energy per unit charge.
Introduction to electromagnetism | Kirchhoff's loop rule
The fundamental reason for this is that if the first atom is measured to be in formula_57, then there is a single mode of the electromagnetic field within the cavity that will subsequently affect the measurement outcome of the second atom.
Ramsey interferometry | Experiments of Serge Haroche
The communication was given to Abraham Esau, head of the physics section of the "Reichsforschungsrat" (RFR, Reich Research Council) at the REM. On 29 April, a group, organized by Esau, met at the REM to discuss the potential of a sustained nuclear chain reaction. The group included the physicists Walther Bothe, Robert Döpel, Hans Geiger, Wolfgang Gentner (probably sent by Walther Bothe), Wilhelm Hanle, Gerhard Hoffmann, and Georg Joos; Peter Debye was invited, but he did not attend. After this, informal work began at the Georg-August University of Göttingen by Joos, Hanle, and their colleague Reinhold Mannkopff; the group of physicists was known informally as the first "Uranverein" (Uranium Club) and formally as "Arbeitsgemeinschaft für Kernphysik".
Reinhold Mannkopff | Career
Friedrich Carl Alwin Pockels (18 June 1865 – 29 August 1913) was a German physicist. He was born in Italy to Captain Theodore Pockels and Alwine Becker. He obtained a doctorate from the University of Göttingen in 1888, and from 1900 to 1913 he was professor of theoretical physics at the University of Heidelberg. In 1893 he discovered that a steady electric field applied to certain birefringent materials causes the refractive index to vary, approximately in proportion to the strength of the field. The coefficient of proportionality is of the order of to . This phenomenon is now called the Pockels effect.
Friedrich Carl Alwin Pockels | Introduction
The first person to carry out any reported experimental programme to investigate the heat produced as a result of plastic deformation was Henri Tresca in June 1878 Tresca forged a bar of platinum (as well as many other metals); at the moment of forging the metal had just cooled down below red heat. The subsequent blow of the steam hammer, which left a depression in the bar and lengthened it, also reheated it in the direction of two lines in the form of a letter X. So great was this reheating, the metal along these lines was fully restored for some seconds to red heat.
Adiabatic shear band | History
The first mathematical description of electrons on a 2D lattice, acted on by a homogeneous magnetic field, was studied by Rudolf Peierls and his student R. G. Harper in the 1950s. Hofstadter described the structure in 1976 in an article on the energy levels of Bloch electrons in magnetic fields. It gives a graphical representation of the spectrum of Harper's equation at different frequencies. The intricate mathematical structure of this spectrum was independently discovered by Soviet physicist Mark Azbel in 1964 (the Azbel-Hofstadter model), but Azbel did not plot the structure as a geometrical object. Written while Hofstadter was at the University of Oregon, his paper was influential in directing further research.
Hofstadter's butterfly | History
After a few weeks assessment period he decided to study as part of his Ph.D. the three kinds of thermal evaporation processes in detail and, subsequently, he developed new process parameters for each. Accordingly, in 1989 Fostiropoulos was the first to synthesize C the first molecular carbon modification applying initially a contact arc process (2) with specific experimental conditions for fast electrode degradation, hence, accelerated carbon evaporation. Moreover, he developed a method to sinter graphite rods from commercially available "amorphous" C carbon dust. Applying a resistive heating process (3) and using such "isotopic" graphite rods, a few days before New Year's Eve 1989, he synthesized for the first time an unusual material which contained an exotic species: "isotopic" C, From that he, casually, proved the existence of an all-carbon molecule with icosahedral "platonic" symmetry and truncated icosahedron "archimedean" shape predicted by Kroto et al.
Konstantinos Fostiropoulos | The Heidelberg experiments
Bertram Huppert went to school in Bonn from 1934 until 1945. In 1950, he wrote his diploma thesis in mathematics at the University of Mainz. The thesis discussed ""nicht fortsetzbare Potenzreihen"" (discontinuous power series), and was written under the direction of Helmut Wielandt. When Wielandt moved to the University of Tübingen in April 1951, Huppert followed him later in the year, and gained his doctorate (as Wielandt's first doctoral student) with the work ""Produkte von paarweise vertauschbaren zyklischen Gruppen"" (products of pairwise permutable cyclic groups), in which he showed, among other things, that such groups were supersoluble. This was the first of more than forty further scientific works, not including his books and monographs.
Bertram Huppert | Education
This account first considers processes for which the first law is easily verified because of their simplicity, namely adiabatic processes (in which there is no transfer as heat) and adynamic processes (in which there is no transfer as work).
First law of thermodynamics | Evidence for the first law of thermodynamics for closed systems
Bernhard Minnigerode (1837–1896), another student of Neumann, first expressed this relation in written form in 1887 in the journal "Neues Jahrb. Mineral Geol. Paleontol". (Vol. 5, p. 145). Later, Neumann attacked the problem of giving mathematical expression to the conditions holding for a surface separating two crystalline media, and worked out from theory the laws of double refraction in strained crystalline bodies. He also made important contributions to the mathematical theory of electrodynamics, and in papers published in 1845 and 1847 established mathematically the laws of the induction of electric currents. His last publication, which appeared in 1878, was on spherical harmonics ("Beiträge zur Theorie der Kugelfunctionen").
Franz Ernst Neumann | Biography
The communication was given to Abraham Esau, head of the physics section of the "Reichsforschungsrat" (RFR, Reich Research Council) at the REM. On 29 April, a group, organized by Esau, met at the REM to discuss the potential of a sustained nuclear chain reaction. The group included the physicists Walther Bothe, Robert Döpel, Hans Geiger, Wolfgang Gentner (probably sent by Walther Bothe), Wilhelm Hanle, Gerhard Hoffmann, and Georg Joos; Peter Debye was invited, but he did not attend. After this, informal work began at Göttingen by Joos, Hanle, and their colleague Reinhold Mannfopff; the group of physicists was known informally as the first "Uranverein" (Uranium Club) and formally as "Arbeitsgemeinschaft für Kernphysik".
Klaus Clusius | Career
The joke later circulated in New Haven that "only one man lived who could understand Gibbs's papers. That was Maxwell, and now he is dead." Gibbs then extended his thermodynamic analysis to multi-phase chemical systems (i.e., to systems composed of more than one form of matter) and considered a variety of concrete applications. He described that research in a monograph titled "On the Equilibrium of Heterogeneous Substances", published by the Connecticut Academy in two parts that appeared respectively in 1875 and 1878. That work, which covers about three hundred pages and contains exactly seven hundred numbered mathematical equations, begins with a quotation from Rudolf Clausius that expresses what would later be called the first and second laws of thermodynamics: "The energy of the world is constant.
Josiah Willard Gibbs | Career, 1873–80
From there he was able to infer the principle of Sadi Carnot and the definition of entropy (1865). Established during the 19th century, the Kelvin-Planck statement of the Second Law says, "It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work." This was shown to be equivalent to the statement of Clausius.
Second law of thermodynamics | History
On 16 February 1951, Richter claimed he had successfully demonstrated fusion. He re-ran the experiment for members of the CNEA, later claiming that they had witnessed the world's first thermonuclear reaction. On 23 February, a technician working for the project expressed his concerns about the claims, suggesting that the measurement was likely due to the accidental tilting of the spectrograph's photographic plate while the experimental run was being set up. Richter refused to re-run the experiment. Instead, a week later he ordered the reactor to be disassembled so a new one could be built that included a magnetic confinement system.
Huemul Project | Announcement
Ernst Heinrich Weber (1795–1878) was one of the first people to approach the study of the human response to a physical stimulus in a quantitative fashion. Fechner was a student of Weber and named his first law in honor of his mentor, since it was Weber who had conducted the experiments needed to formulate the law. Fechner formulated several versions of the law, all stating the same thing. One formulation states: ""Simple differential sensitivity is inversely proportional to the size of the components of the difference; relative differential sensitivity remains the same regardless of size.""
Weber–Fechner law | Weber's law
Radó von Kövesligethy (in Hungarian usage, Kövesligethy Radó) (Verona, Austria, Austro-Hungarian Empire, 1 September 1862 – Budapest, Hungary 11 October 1934), was a Hungarian physicist, astronomer and geophysicist. The first successful spectral equation of black body radiation was the theory of the continuous spectra of celestial bodies by Rado von Kövesligethy, published 15 years before Planck, in 1885 in Hungarian and in 1890 in German. He derived a spectral equation with the following properties: the spectral distribution of radiation depends only on the temperature, the total irradiated energy is finite (15 years before Planck!), the wavelength of the intensity maximum is inversely proportional to the temperature (eight years before Wien!).
Radó von Kövesligethy | Introduction
His results were published in "Der Stochiometrie oder Messkunst chemischer Elemente" (1792–1794), and "Über die neueren Gegenstände in der Chemie" (1792–1802), but it was long before they were properly appreciated, or he himself accorded due credit for them. This was partly because some of his work was wrongly ascribed to Carl Wenzel by Jons Berzelius through a mistake which was only corrected in 1841 by Henri Hess, professor of chemistry at St. Petersburg, and author of the laws of constant heat-sums and of thermoneutrality.
Jeremias Benjamin Richter | Publications
In the low-frequency limit, the voltage drop around any loop is zero. This includes imaginary loops arranged arbitrarily in space – not limited to the loops delineated by the circuit elements and conductors. In the low-frequency limit, this is a corollary of Faraday's law of induction (which is one of Maxwell's equations). This has practical application in situations involving "static electricity".
Kirchhoff's circuit laws | Generalization
The "Trigonoides" were the nonmetals made from regular triangles, while the metallic "Tetragonoides" were made from squares. Algebraic formulas of how to mix squares and triangles yielded the periodic laws. His "controversial ideas and colorful personality" proved to be an obstacle to the acceptance of his theories.
Gustavus Detlef Hinrichs | Periodic law
The second law of thermodynamics may be expressed in many specific ways, the most prominent classical statements being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin (1851), and the statement in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms citing the impossibility of certain processes. The Clausius and the Kelvin statements have been shown to be equivalent.
Second law of thermodynamics | Various statements of the law
In 1858 Kirchenpauer was appointed, at his own request, the senatorial magistrate at Ritzebüttel, the coastal fort a couple of hours downstream from Hamburg. The fort marks the strategically vital point at which the Elbe meets the North Sea, He retained the office till 29 August 1864. On the administrative front he undertook the separation between justice and administration there. The appointment also allowed him the opportunity to pursue his passion for natural science: he devoted much time to studying under a microscope the life forms clinging to the buoys at the mouth of the estuary. Kirchenpauer continued with these studies after returning to Hamburg in 1864: between 1862 and 1884 he would publish six papers on hydroids, describing eight new nominal genera and seventy-seven new nominal hydroid species.
Gustav Heinrich Kirchenpauer | Ritzebüttel and science
His earlier scientific papers (from 1819) were published in the Annals of the Imperial and Royal Polytechnic Institute, and from 1830, his articles were included in Johann Joseph von Prechtl's "Technologische Encyklopädie". Among his principal works is the foillowing:
Georg Altmütter | Writings
In 1896 Arthur Schuster stated his law: "If we subtract the frequency of the fundamental vibration from the convergence frequency of the principal series , we obtain the convergence frequency of the supplementary series". But in the next issue of the journal he realised that Rydberg had published the idea a few months earlier.
Diffuse series | Laws for alkali metals
He was the first to use the vacuum tube with the capillary part now called a Geissler tube, by means of which the luminous intensity of feeble electric discharges was raised sufficiently to allow of spectroscopic investigation. He anticipated Robert Wilhelm Bunsen and Gustav Kirchhoff in announcing that the lines of the spectrum were characteristic of the chemical substance which emitted them, and in indicating the value of this discovery in chemical analysis. According to Hittorf, he was the first who saw the three lines of the hydrogen spectrum, which a few months after his death, were recognized in the spectrum of the solar protuberances.
Julius Plücker | Career
During 1816-1819 he was appointed professor of philosophy in Erlangen teaching physics and chemistry. 1816 he was elected member of the Leopoldina. 1819 he moved on to the university of Halle. In 1820 he built the first sensitive galvanometer, naming it after Luigi Galvani. He created this instrument, acceptable for actual measurement as well as detection of small amounts of electric current, by wrapping a coil of wire around a graduated compass. The instrument was initially called a multiplier.
Johann Schweigger | Introduction
In Ramanujan's first letter to G. H. Hardy, one of the theorems that impressed Hardy was: However, Bauer proved the theorem in 1859. Using a result of Bauer on generalized continued fractions, Oskar Perron published in 1952 the first proof of another formula of Ramanujan.
Gustav Conrad Bauer | Footnotes in the history of mathematics
After attending "Gymnasium" (grammar school) in Triest, he commenced studies in mathematics and physics at the University of Graz (Austria), continuing at the Technical University of Munich. He presented his first publications as an outside lecturer for Theoretical Mechanics. After a short stint in Göttingen, he succeeded Gustav Zeuner in 1897 as Professor of Mechanical Engineering at the Technischen Hochschule Dresden. His 1904 publication "New Graphs for Technical Thermodynamics" greatly simplified calculations involving thermodynamic processes. His "New Tables and Diagrams for Water Vapor", first published in 1906, appeared in six further editions through 1932, as he updated it to reflect new developments.
Richard Mollier | Education and career
The First Law of Thermodynamics is a statement of the conservation of energy; though it can be changed from one form to another, energy can be neither created nor destroyed. From the first law, a principle called Hess's Law arises. Hess’s Law states that the heat absorbed or evolved in a given reaction must always be constant and independent of the manner in which the reaction takes place. Although some intermediate reactions may be endothermic and others may be exothermic, the total heat exchange is equal to the heat exchange had the process occurred directly. This principle is the basis for the calorimeter, a device used to determine the amount of heat in a chemical reaction.
Biological thermodynamics | First Law of Thermodynamics
Kirchhoff'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.
Kirchhoff integral theorem | Introduction
Karl Hermann Wichelhaus (8 January 1842, Elberfeld – 28 February 1927, Heidelberg) was a German chemist. He studied chemistry at the universities of Bonn, Göttingen, where he became member of Burschenschaft Hannovera (fraternity) and Ghent, and also trained in London. In 1863 he received his doctorate from the University of Heidelberg, and four years later, obtained his habilitation at Berlin. From 1871 to 1916 he was a professor of chemical technology at the University of Berlin. In 1867 he was one of the founders of the "Deutsche Chemische Gesellschaft" (German Chemical Society). He is credited for establishing the first technological institute at the University of Berlin.
Hermann Wichelhaus | Introduction
First devised in 1884 by Heinrich Hertz, the emagram is used primarily in European countries. Other countries use similar thermodynamic diagrams for the same purpose. However, the details of their construction vary. Emagram is the first atmospheric thermodynamic diagram.
Emagram | Introduction
However, Hendrik Antoon Lorentz (1895) modified Fresnel's theory and showed that those experiments can be explained by a stationary aether as well:
Luminiferous aether | First order experiments
Stoletov's law (or the first law of photoeffect) for photoelectric effect establishes the direct proportionality between the intensity of electromagnetic radiation acting on a metallic surface and the photocurrent induced by this radiation. The law was discovered by Aleksandr Stoletov in 1888.
Stoletov's law | Introduction
First mathematical descriptions of Sommerfeld effect were suggested by I. Blekhman and V. Konenko.
Sommerfeld effect | Introduction
In his perennial 1898 paper, Lagergren formulated a so-called pseudo-first-order model for adsorption kinetics based on an extensive body of experimental measurements. Both the empirical data and the model were highly acclaimed by the contemporaries. In 1900, Wilhelm Ostwald (Nobel Prize winner in Chemistry in 1909) wrote an unusually extensive review of the paper in his Zeitschrift für physikalische Chemie. Beyond words of recognition, Ostwald also drafted some ideas to further develop the model. Actually, having abandoned research, Lagergren could not give thought to these advises. The path was followed, instead, by Herbert Freundlich. His paper based on his habilitation lecture heavily relies upon Lagergren's results.
Sten Lagergren | His classic work and its aftermath
The course commerced in September. During the winter months, the time is occupied in mathematics, and the first six books of Euclid were studied: and in the summer, the geometrical knowledge was practically applied to the measurement of land, timber, buildings, and other objects. The first principles of chemistry were unfolded. By a good but economical apparatus, various experiments were made, both on a large and small scale. For the larger experiments, the brew-house and stilLhouse with their respective fixtures were found highly useful. Much attention was paid to the analysation of various soils, and the different kinds, with the relative quantity of their component parts, were arranged with great order and regularity.
Albrecht Thaer | Thaer's Agricultural School
The third of Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question: given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces which can be reassembled to yield the second? Based on earlier writings by Gauss, Hilbert conjectured that this is not always possible. This was confirmed within the year by his student Max Dehn, who proved that the answer in general is "no" by producing a counterexample. The answer for the analogous question about polygons in 2 dimensions is "yes" and had been known for a long time; this is the Wallace–Bolyai–Gerwien theorem.
Hilbert's third problem | Introduction
This theorem would be rediscovered decades later by (and sometimes attributed to) Vincenzo Mollame and Otto Hölder.
Pierre Wantzel | Introduction
Now, with given monodromy data, can we find a Fuchsian system which exhibits this monodromy? This is one form of Hilbert's twenty-first problem. We do not distinguish between coordinates "x" and formula_5 which are related by Möbius transformations, and we do not distinguish between gauge equivalent Fuchsian systems - this means that we regard "A" and as being equivalent for any holomorphic gauge transformation "g"("x"). (It is thus most natural to regard a Fuchsian system geometrically, as a connection with simple poles on a trivial rank "n" vector bundle over the Riemann sphere). For generic monodromy data, the answer to Hilbert's twenty-first problem is 'yes' - as was first proved by Josip Plemelj.
Isomonodromic deformation | Hilbert's twenty-first problem
The first law of thermodynamics for closed systems was originally induced from empirically observed evidence, including calorimetric evidence. It is nowadays, however, taken to provide the definition of heat via the law of conservation of energy and the definition of work in terms of changes in the external parameters of a system. The original discovery of the law was gradual over a period of perhaps half a century or more, and some early studies were in terms of cyclic processes. The following is an account in terms of changes of state of a closed system through compound processes that are not necessarily cyclic.
First law of thermodynamics | Evidence for the first law of thermodynamics for closed systems
The same year, Kipp make a new design, created again by Geißler. This design would be the model for all future versions of the Kipp's apparatus. In 1844, Kipp published two descriptions in the Tijdschrift voor Handel and Nijverheid (Journal for trade and industry). The oldest known copy of the apparatus is owned by the Boerhaave Museum in Leiden. It is 62 cm high and was made between 1845 and 1875.
Petrus Jacobus Kipp | Biography
Three years later, he relocated to the University of Helmstedt as professor of medicine responsible for theoretical medicine and "materia medica." Starting in 1783 till 1810 he was professor for philosophy and medicine at the University of Helmstedt and from 1810 till his death in 1816 he was professor for chemistry at the University of Göttingen. In 1778 Crell published the first issue of the "Chemische Journal für die Freunde der Naturlehre, Arzneygelahrtheit, Haushaltungskunst und Manufacturen". He changed his journal's name two times, ending up in 1784 with Crell's Annalen. This periodic journal was the first journal focusing primary on chemistry.
Lorenz Florenz Friedrich von Crell | Life and work
Kuhn's conclusions, finding a period till 1908, when Planck consistently held his 'first theory', have been accepted by other historians. In the second edition of his monograph, in 1912, Planck sustained his dissent from Einstein's proposal of light quanta. He proposed in some detail that absorption of light by his virtual material resonators might be continuous, occurring at a constant rate in equilibrium, as distinct from quantal absorption. Only emission was quantal. This has at times been called Planck's "second theory".
Planck's law | Subsequent events
In 1855, he was the first to notice the phenomenon of Liesegang rings, observing them in the course of experiments on the precipitation of reagents in blotting paper.
Friedlieb Ferdinand Runge | Discoveries
The first mechanical argument of the Kinetic theory of gases that molecular collisions entail an equalization of temperatures and hence a tendency towards equilibrium was due to James Clerk Maxwell in 1860; Ludwig Boltzmann with his H-theorem of 1872 also argued that due to collisions gases should over time tend toward the Maxwell–Boltzmann distribution. Due to Loschmidt's paradox, derivations of the Second Law have to make an assumption regarding the past, namely that the system is uncorrelated at some time in the past; this allows for simple probabilistic treatment. This assumption is usually thought as a boundary condition, and thus the second Law is ultimately a consequence of the initial conditions somewhere in the past, probably at the beginning of the universe (the Big Bang), though other scenarios have also been suggested.
Second law of thermodynamics | Derivation from statistical mechanics