Rudolf Clausius

Rudolf Clausius
Born(1822-01-02)2 January 1822
Köslin, Province of Pomerania, Prussia (present-day Koszalin, Poland)
Died24 August 1888(1888-08-24) (aged 66)
Known forSecond law of thermodynamics
Originator of the concept of entropy
Clausius-Mossotti relation
Clausius-Clapeyron relation
Clausius theorem
Clausius–Duhem inequality
Virial theorem
AwardsCopley Medal (1879)
Scientific career
Rudolf Clausius signature.svg

Rudolf Julius Emanuel Clausius (German pronunciation: [ˈʁuːdɔlf ˈklaʊ̯zi̯ʊs];[1][2] 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics.[3] By his restatement of Sadi Carnot's principle known as the Carnot cycle, he gave the theory of heat a truer and sounder basis. His most important paper, "On the Moving Force of Heat",[4] published in 1850, first stated the basic ideas of the second law of thermodynamics. In 1865 he introduced the concept of entropy. In 1870 he introduced the virial theorem which applied to heat.[5]


Clausius was born in Köslin (now Koszalin in Poland) in the Province of Pomerania in Prussia. His father was a Protestant pastor and school inspector,[6] and Rudolf studied in the school of his father. After a few years, he went to the Gymnasium in Stettin (now Szczecin). Clausius graduated from the University of Berlin in 1844 where he studied mathematics and physics with, among others, Gustav Magnus, Peter Gustav Lejeune Dirichlet and Jakob Steiner. He also studied history with Leopold von Ranke. During 1847, he got his doctorate from the University of Halle on optical effects in Earth's atmosphere. He then became professor of physics at the Royal Artillery and Engineering School in Berlin and Privatdozent at the Berlin University. In 1855 he became professor at the ETH Zürich, the Swiss Federal Institute of Technology in Zürich, where he stayed until 1867. During that year, he moved to Würzburg and two years later, in 1869 to Bonn.



In 1886, he married Sophie Sack, and then had another child.

Two years later, on 24 August 1888, he died in Bonn, Germany.[7]


Clausius's PhD thesis concerning the refraction of light proposed that we see a blue sky during the day, and various shades of red at sunrise and sunset (among other phenomena) due to reflection and refraction of light. Later, Lord Rayleigh would show that it was in fact due to the scattering of light, but regardless, Clausius used a far more mathematical approach than some have used.

His most famous paper, Ueber die bewegende Kraft der Wärme ("On the Moving Force of Heat and the Laws of Heat which may be Deduced Therefrom")[8] was published in 1850, and dealt with the mechanical theory of heat. In this paper, he showed that there was a contradiction between Carnot's principle and the concept of conservation of energy. Clausius restated the two laws of thermodynamics to overcome this contradiction (the third law was developed by Walther Nernst, during the years 1906–1912). This paper made him famous among scientists.

Clausius' most famous statement of thermodynamics second law was published in German in 1854,[9] and in English in 1856.[10]


During 1857, Clausius contributed to the field of kinetic theory after refining August Krönig's very simple gas-kinetic model to include translational, rotational and vibrational molecular motions. In this same work he introduced the concept of 'Mean free path' of a particle.[11][12][13]

Clausius deduced the Clausius–Clapeyron relation from thermodynamics. This relation, which is a way of characterizing the phase transition between two states of matter such as solid and liquid, had originally been developed in 1834 by Émile Clapeyron.


In 1865, Clausius gave the first mathematical version of the concept of entropy, and also gave it its name.[7] Clausius chose the word because the meaning (from Greek ἐν en "in" and τροπή tropē "transformation") is "content transformative" or "transformation content" ("Verwandlungsinhalt").[4][14] He used the now abandoned unit 'Clausius' (symbol: Cl) for entropy[citation needed].

1 Clausius (Cl) = 1 calorie/degree Celsius (cal/°C) = 4.1868 joules per kelvin (J/K)

The landmark 1865 paper in which he introduced the concept of entropy ends with the following summary of the first and second laws of thermodynamics:[4]

The energy of the universe is constant.

The entropy of the universe tends to a maximum.


Memorial stone in front of Koszalin University of Technology, with the laws of thermodynamics as formulated by Clausius


See also[edit]


  1. ^ Dudenredaktion; Kleiner, Stefan; Knöbl, Ralf (2015) [First published 1962]. Das Aussprachewörterbuch [The Pronunciation Dictionary] (in German) (7th ed.). Berlin: Dudenverlag. pp. 280, 744. ISBN 978-3-411-04067-4.
  2. ^ Krech, Eva-Maria; Stock, Eberhard; Hirschfeld, Ursula; Anders, Lutz Christian (2009). Deutsches Aussprachewörterbuch [German Pronunciation Dictionary] (in German). Berlin: Walter de Gruyter. pp. 416, 884. ISBN 978-3-11-018202-6.
  3. ^ Cardwell, D.S.L. (1971), From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age, London: Heinemann, ISBN 978-0-435-54150-7
  4. ^ a b c Clausius, R. (1867). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst. Retrieved 19 June 2012. Contains English translations of many of his other works.
  5. ^ Clausius, RJE (1870). "On a Mechanical Theorem Applicable to Heat". Philosophical Magazine. 4th Series. 40: 122–127.
  6. ^ Emilio Segrè (2012). From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries. Courier Dover Publications. p. 228
  7. ^ a b Cropper, William H. (2004). "The Road to Entropy Rudolf Clausius". Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking. Oxford University Press. pp. 93–105. ISBN 978-0-19-517324-6. Retrieved 25 March 2014.
  8. ^ Clausius, R. (1850). "Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen". Annalen der Physik. 79 (4): 368–397, 500–524. Bibcode:1850AnP...155..500C. doi:10.1002/andp.18501550403.. See English Translation: On the Moving Force of Heat, and the Laws regarding the Nature of Heat itself which are deducible therefrom. Phil. Mag. (1851), series 4, 2, 1–21, 102–119. Also available on Google Books.
  9. ^ Clausius, R. (1854). "Ueber eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheoriein". Annalen der Physik und Chemie. 93 (12): 481–506. Bibcode:1854AnP...169..481C. doi:10.1002/andp.18541691202. Retrieved 25 June 2012.
  10. ^ Clausius, R. (August 1856). "On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat". Phil. Mag. 4. 12 (77): 81–98. doi:10.1080/14786445608642141. Retrieved 25 June 2012.
  11. ^ Clausius, R. (1857), "Über die Art der Bewegung, die wir Wärme nennen", Annalen der Physik, 100 (3): 353–379, Bibcode:1857AnP...176..353C, doi:10.1002/andp.18571760302
  12. ^ Clausius, R. (1862), "Ueber die Wärmeleitung gasförmiger Körper", Annalen der Physik, 115: 1–57, Bibcode:1862AnP...191....1C, doi:10.1002/andp.18621910102
  13. ^ Clausius, R. (1864), Abhandlungen über die Mechanische Wärmetheorie. Electronic manuscript from the Bibliothèque nationale de France.
  14. ^ Clausius, R. (1865), "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie", Annalen der Physik, 125 (7): 353–400, Bibcode:1865AnP...201..353C, doi:10.1002/andp.18652010702
  15. ^ "R.J.E. Clausius (1822 - 1888)". Royal Netherlands Academy of Arts and Sciences. Retrieved 21 July 2015.

External links[edit]