Rudolf Clausius

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Rudolf Julius Emanuel Clausius (born January 2, 1822 in Köslin , † August 24, 1888 in Bonn ) was a German physicist .

Clausius is considered to be the discoverer of the second law of thermodynamics , creator of the terms entropy and virial , and one of the first theoretical physicists in the middle of the 19th century. He was a contemporary among others. by Hermann von Helmholtz , James Prescott Joule , Gustav Robert Kirchhoff , John Tyndall , William Thomson, 1st Baron Kelvin , Johann Josef Loschmidt , Ludwig Boltzmann and James Clerk Maxwell .


As the son of a school councilor and pastor, Clausius studied mathematics and physics in Berlin from 1840 after graduating from high school in Stettin , among others with Heinrich Gustav Magnus , Peter Gustav Lejeune Dirichlet , Jakob Steiner and history with Leopold von Ranke . In 1848 he received his doctorate in Halle on the scattering of sunlight in the earth's atmosphere to obtain a doctorate in philosophy. From 1844 to 1850 he worked at the Friedrichswerder Gymnasium in Berlin as a candidate for teaching physics and mathematics. In 1850 he became professor of physics at the Royal Artillery and Engineering School in Berlin and private lecturer at Berlin University. In 1855 he was appointed to the newly founded Eidgenössische Polytechnikum in Zurich , in 1867 he moved to Würzburg , where he was able to obtain a second chair in mathematics, occupied by Friedrich Prym in 1869, and then to Bonn in 1869 until the end of his life . In 1884/85 he was the rector of the university.

As the leader of a student medical corps, he was wounded in the Franco-Prussian War in 1870 , which caused permanent pain in his knee.

He married in Zurich in 1859 Adelheid Rimpau (1833–1875), the daughter of the Brunswick merchant Justus Rimpau (1782–1840) and Mathilde Fritze, and cousin of the grain farmer Wilhelm Rimpau (1814–1892). His wife died of scarlet fever in 1875. The eldest daughter Mathilde (1861–1907), who had been running the household since 1875 and who had taken on the upbringing of the younger siblings, married the theologian Friedrich Zimmer in 1882 . Two years before his death, Clausius married again: in 1886 Sophie Sack, a daughter of the Essen judiciary Otto Sack and Johanne Budde, became his wife.

Rudolf Clausius, Zurich, after 1855


Rudolf Clausius, Bonn, after 1880

After the discovery of the law of conservation of energy ( 1st law of thermodynamics ) by Julius Robert von Mayer , James Prescott Joule and Hermann von Helmholtz , a new theory of heat had to be found, especially since William Thomson (later Lord Kelvin) had clearly shown that between Carnot's process and the Conservation of energy was a contradiction in terms. Clausius devoted himself to this task by subjecting himself to an in-depth study of the ability of heat to transform itself into work (1850). He recorded the 2nd law of thermodynamics for the first time , which states that heat does not pass from a cold to a warmer body without other changes and thus postulates the impossibility of a perpetual motion machine of the 2nd kind. In 1865 Clausius introduced the term entropy . The now outdated Clausius unit was also used for this purpose.

Clausius' first scientific work deals with topics of meteorological optics, e.g. B. the light scattering in the atmosphere and the phenomenon of the blue sky as well as the dawn and evening red. His famous treatise “On the Moving Power of Heat” in 1850 finally enabled him to do his habilitation and to teach at the Royal Artillery and Engineering School and at the same time as a private lecturer at Berlin University - his scientific career began.

Clausius' name is initially associated with the Clausius-Clapeyron equation , with the help of which the vapor pressure curve in the two-phase diagram of a substance can be determined from the enthalpy of vaporization , temperature and increase in volume. Thanks to the Clausius-Rankine process , the classic water-steam process for generating mechanical energy or electricity from chemically bound heat, it is also known in energy technology. What is far less common today is that he provided fundamental work on kinetic gas theory and electrolytic dissociation . In 1857 he refined August Krönig's very simple gas kinetic model, which he had set up a year earlier, and introduced the concept of the “mean free path” of a gas molecule. His work, which has also been translated into English, prompted James Clerk Maxwell and later Ludwig Boltzmann to make decisive discoveries that were decisive in establishing the kinetic theory of gases. In addition, Clausius also worked on the electrodynamics of moving bodies, which only found its solution through Einstein's work in 1905. Clausius used Maxwell's derivatives to determine the molar refraction of a substance ( Clausius-Mossotti equation ). This procedure was used to check the structure of an organic substance. The structures (functional groups, bonds) of organic molecules can be compared from the refractive index and the molar mass .

In 1850 Clausius began to occupy himself with the subject to which he owes his greatest fame: mechanical heat theory (thermodynamics). Clausius took up the principle of energy conservation as the first law of thermodynamics, already proposed by Sadi Carnot in 1824 and finally postulated by Julius Robert Mayer in 1842, and gave him the first quantitative formulation by establishing a relationship between the amount of heat Q , work W and internal energy U (d U = d Q + d W ). In contrast to the prevailing opinion until then, he realized that heat is not an immutable substance, but only represents a form of energy that can be converted into the known other forms (kinetic energy, etc.).

However, the principle of conservation of energy does not yet explain the common fact that energy conversion does not take place in any direction: why, for example, two differently warm bodies equalize their temperatures on contact, but heat never transfers from the colder to the warmer body by itself. Carnot had already clearly stated this fact, but only Clausius recognizes an energy flow behind it and not a phenomenon linked to a heat substance. In 1850 he called this experience the Second Law of Thermodynamics. The statement that energy conversions run irreversibly in one direction is no longer compatible with classical mechanical physics, the linear laws of which are traceable and reversible according to any process ( Poincaré's law of recurrence ).

Melting ice in a warm room is a simple example of increasing entropy (first described by Rudolf Clausius in 1862).

The starting point for both Carnot and Clausius' considerations was the mode of operation of steam engines. As early as 1824 Carnot had found that heat cannot be completely converted into mechanical work, since this not only requires a heat source (furnace with steam generator), but also a heat sink (cooler for steam condensation) in which part of the heat is required for conversion into Work is lost. Every thermal power process requires two heat reservoirs of different temperatures, from which heat is supplied and removed. Under idealized, i.e. H. reversible conditions are the ratios of the amount of heat supplied or removed to the respective temperatures at which the heat transfers take place, the same. In this case, the largest possible amount of mechanical energy, z. B. to generate electricity. However, this is not the case in real thermal power processes. The greater the difference between these ratios, the less useful work (exergy) that can be gained from the thermal energy.

The change in the amount of heat related to the heat transfer temperature in a thermodynamic process is therefore a measure of the convertibility of heat and technical work and thus of the quality of the process (d S = d Q / T ). Clausius later calls this “equivalent value of transformation” “entropy” (from ancient Greek: entrepein = to transform and tropé = potential for change). In 1882 Helmholtz defined Clausius' law of entropy more clearly in terms of the internal energy of a system: The maximum usable free energy in an isolated system is always smaller than the actually available internal energy. Although the internal energy of the system is retained when it is converted into useful work (1st main law), it is devalued (degradation), since part of it is always scattered (dissipated) in the system environment. Thus, the second law of thermodynamics can also be formulated as follows: An energy conversion never runs by itself from a state of low quality to a state of high quality; the entropy always increases. In the heat and power process, the process medium water has to be energetically "refined" by supplying heat from outside (firing) by creating water vapor under high pressure and temperature before it can work in the cylinder of the steam engine or in the turbine to generate electricity. The energy of the processed steam is worthless and has to be released into the environment via the cooler. Even under ideal conditions, the production of dissipated energy, such as waste heat, would be unavoidable.

Because of the central importance of Clausius's knowledge for the classic thermal power plant process (Rankine process), this is also called the Clausius-Rankine process.

In 1870, Clausius gave the virial theorem , which is a relationship between the time average of the kinetic energy and the time average of the potential energy of a closed stationary physical system. It is related to mechanics and to a closed thermodynamic system.

Clausius introduced the mean free path to physics in 1857 , a fundamental concept of statistical mechanics.

In 1875 Clausius also published a general law of electrodynamics based on the ether theory.

"Helmholtz occasionally characterized the importance of thermodynamic theorems for our knowledge of nature by calling them 'world laws', apparently to express [...] that they can be safely applied to the entire universe", so Walther Nernst 1922 on 100th birthday of Clausius at the University of Bonn.

Memorial stone at the Technical University of Koszalin

Honors and memberships (selection)

In Zurich , the Clausiusstrasse and the Clausiussteig, not far from the ETH Zurich , were named after him in 1895 . In 1935 the lunar crater Clausius and in 2002 the asteroid (29246) Clausius were named after him. Since 2009 a memorial stone has been commemorating him in his hometown of Köslin .

See also


  • About the moving force of heat and the laws which can be derived from it for the theory of heat itself , Poggendorffs Annalen , Volume 79, 1850, pp. 368-397, 500-524
    • Edited with commentary by Max Planck 1898, 1921, Leipzig, (Ostwald's Classics of Exact Sciences 99), Reprint, 1982, Akademische Verlagsgesellschaft Geest & Portig, Archive
  • About the application of mechanical heat theory to the steam engine. In: Annals of Physics and Chemistry , Series 4, 97 (1856), pp. 441-476, 513-558. ( Digitized and full text in the German text archive )
  • About various forms of the main equations of mechanical heat theory that are convenient to use , Annalen der Physik und Chemie, Volume 125, 1865, pp. 353-400 (introduction of entropy)
    • also lecture to the Zürcher Naturforschenden Gesellschaft, quarterly journal of Naturf. Ges. Zurich, 10th year 1865, issue 1, 1–59, pdf
  • About the second law of mechanical heat theory: a lecture given at a general meeting of the 41st meeting of German natural scientists and doctors in Frankfurt a. M. on September 23, 1867 , Vieweg 1867
  • About the type of movement, which call for heat , Annalen der Physik und Chemie, Volume 100, 1857, p. 353 (reprinted in Stephen Brush , Kinetic Theory, Volume 1, WTB 1970)
  • About the mean distance covered by the individual molecules during the molecular movement of gaseous bodies, along with some other remarks on mechanical heat theory , Annalen der Physik und Chemie, Volume 105, 1858, p. 239 (reprinted in Stephen Brush, Kinetic Theory , Volume 1, WTB, 1970, introduction of the mean free path)
  • The potential function and the potential: a contribution to mathematical physics , published by Johann Ambrosius Barth, Leipzig 1859, archive
  • Treatises on mechanical heat theory , 2 volumes, Vieweg 1864, 1867 (as treatises on mechanical heat theory ), 2nd edition 1876, 1879, Archives, volume 1, 3rd edition
  • The kinetic theory of gases , Die mechanical Wärmetheorie , Volume 3, 2nd edition, Vieweg 1889–1891, Ed. Max Planck, Carl Pulfrich
  • About a mechanical sentence applicable to heat , Annalen der Physik, Volume 217, 1870, pp. 124-130 (virial sentence )


  • Edward E. Daub: Clausius, Rudolf . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 3 : Pierre Cabanis - Heinrich von Dechen . Charles Scribner's Sons, New York 1971, p. 303-311 .
  • Max von Laue:  Clausius, Rudolf Julius Emanuel. In: New German Biography (NDB). Volume 3, Duncker & Humblot, Berlin 1957, ISBN 3-428-00184-2 , pp. 276-278 ( digitized version ).
  • Walther Nernst : Rudolf Clausius, born January 2, 1822, died August 24, 1888, 1869–1888 Professor of Physics at the University of Bonn: Speech given on June 24, 1922. Röhrscheid, Bonn 1922.
  • Günter Bierhalter: Clausius mechanical foundation of the second law of heat theory from 1871, Archive for history of exact sciences, Volume 24, 1981, pp. 207-219
  • Grete Ronge: Rudolf Clausius, a 19th century physicist, Urania, Volume 19, 1956, 231-238
  • Grete Ronge: The Zurich years of the physicist Rudolf Clausius, Gesnerus, Volume 12, 1955, 73-108
  • Eduard Riecke : Rudolf Clausius, treatises d. Ges. Wiss. Göttingen, Math-phys. Class 35, 1888 (with catalog raisonné)
  • Friedrich Krüger: Rudolf Clausius, in Pommersche Lebensbilder, Volume 1, 1934, 208-211
  • Ivo Schneider : Clausius first application of probability calculation in the context of atmospheric light scattering, Archive for history of exact sciences, Volume 14, 1974, pp. 143–158
  • Ivo Schneider: Rudolph Clausius´ contribution to the introduction of probabilistic methods in the physics of gases after 1856, Archive for history of exact sciences, Volume 14, 1974, pp. 237-261
  • Werner Ebeling and Johannes Orphal : The Berlin years of the physicist Rudolph Clausius (1840–1855). Scientific journal of the Humboldt University, Mathematisch-Naturwissenschaftliche Reihe 39, 1990, pp. 210–222
  • Stefan L. Wolff: Clausius' way to kinetic gas theory , Sudhoffs Archiv, Volume 79, Issue 1, 1995, pp. 54–72.
  • Stefan L. Wolff: Rudolph Clausius - a pioneer of the modern theory of heat , Vacuum, Volume 90, 2013, pp. 102-108
  • Johannes Orphal and Dieter Hoffmann, Rudolph Clausius, Gustav Magnus and the origin of the second law of thermodynamics, pp. 85–130, in: “Gustav Magnus and his house”, Ed. D. Hoffmann, ISBN 978-3-86225-119 -3 , GNT Verlag, Berlin and Diepholz, 2020.

Individual evidence

  1. Hans-Joachim Vollrath : About the appointment of Aurel Voss to the chair for mathematics in Würzburg. In: Würzburger medical history reports , Volume 11, 1993, pp. 133–151, here: p. 133.
  2. Manfred Berger:  ZIMMER, Karl Friedrich. In: Biographisch-Bibliographisches Kirchenlexikon (BBKL). Volume 25, Bautz, Nordhausen 2005, ISBN 3-88309-332-7 , Sp. 1583-1600. (accessed on May 17, 2010).
  3. ^ List of members since 1666: Letter C. Académie des sciences, accessed on October 30, 2019 (French).
  4. Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 60.
  5. Member entry by Rudolf Clausius (with a link to an obituary) at the Bavarian Academy of Sciences , accessed on January 16, 2017.
  6. Literary Central Gazette for Germany . 1882, no. 35 (August 26), col. 1216.
  7. ^ Fellows Directory. Biographical Index: Former RSE Fellows 1783–2002. Royal Society of Edinburgh, accessed October 17, 2019 .
  8. The Clausiusstrasse ,, accessed on April 23, 2014.
  9. ^ The Pomeranian Newspaper . No. 33/2013, p. 3.

Web links

Commons : Rudolf Clausius  - Collection of images, videos and audio files
Wikisource: Rudolf Clausius  - Sources and full texts