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Rudolf Clausius

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Title: Rudolf Clausius  
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Subject: Second law of thermodynamics, Entropy, Thermodynamics, First law of thermodynamics, History of thermodynamics
Collection: 1822 Births, 1888 Deaths, Eth Zurich Faculty, Fellows of the German Academy of Sciences Leopoldina, Foreign Members of the Royal Society, German Military Personnel of the Franco-Prussian War, German Physicists, Humboldt University of Berlin Alumni, Members of the Royal Netherlands Academy of Arts and Sciences, Members of the Royal Swedish Academy of Sciences, People from Koszalin, People from the Province of Pomerania, Prussian Army Personnel, Recipients of the Copley Medal, Recipients of the Iron Cross (1870), Recipients of the Pour Le Mérite for Arts and Sciences, Theoretical Physicists, Thermodynamicists, University of Bonn Faculty, University of Würzburg Faculty
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Rudolf Clausius

Rudolf Clausius
Born (1822-01-02)2 January 1822
Köslin, Province of Pomerania, Prussia (present-day Koszalin, Poland)
Died 24 August 1888(1888-08-24) (aged 66)
Bonn, Rhine Province, Prussia
Nationality German
Fields Physics
Known for Second law of thermodynamics
Originator of the concept of entropy
Notable awards Copley Medal (1879)

Rudolf Julius Emanuel Clausius (born Rudolf Gottlieb;[1] 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.[2] By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis. His most important paper, On the Moving Force of Heat,[3] 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.[4]


  • Life 1
  • Work 2
    • Entropy 2.1
  • Tributes 3
  • Publications 4
  • See also 5
  • References 6
  • External links 7


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,[5] 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 the 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 1870 Clausius organized an ambulance corps in the Franco-Prussian War. He was wounded in battle, leaving him with a lasting disability. He was awarded the Iron Cross for his services.

His wife, Adelheid Rimpham, died in childbirth in 1875, leaving him to raise their six children. He continued to teach, but had less time for research thereafter.

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

Two years later, on 24 August 1888, he died in Bonn, Germany.[6]


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, "Über die bewegende Kraft der Wärme" ("On the Moving Force of Heat and the Laws of Heat which may be Deduced Therefrom")[7] 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 the second law of thermodynamics was published in German in 1854,[8] and in English in 1856.[9]

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.[10][11][12]

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.[6] He used the now abandoned unit 'Clausius' (symbol: Cl) for entropy. Clausius chose the word "entropy" because the meaning, from Greek, en+tropein, is "content transformative" or "transformation content" ("Verwandlungsinhalt").[3][13]

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:[3]



  • 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.  English translations of nine papers.

See also


  1. ^ Atkins, P.W. (1984), The Second Law, New York: Scientific American Library,  
  2. ^ Cardwell, D.S.L. (1971), From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age, London: Heinemann,  
  3. ^ 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.
  4. ^ Clausius, RJE (1870). "On a Mechanical Theorem Applicable to Heat". Philosophical Magazine, Ser. 4 40: 122–127. 
  5. ^ Emilio Segrè (2012). From Falling Bodies to Radio Waves: Classical Physicists and Their Discoveries. Courier Dover Publications. p. 228
  6. ^ 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.  
  7. ^ Clausius, R. (1850). Annalen der Physik 79: 368–397, 500–524.   . 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.
  8. ^ Clausius, R. (1854). "Ueber eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheoriein".  
  9. ^ Clausius, R. (August 1856). "On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat".  
  10. ^ Clausius, R. (1857), "Über die Art der Bewegung, die wir Wärme nennen", Annalen der Physik 100: 353–379,  
  11. ^ Clausius, R. (1862), "Über die Wärmeleitung gasförmiger Körper", Annalen der Physik 115: 1–57,  
  12. ^ Clausius, R. (1864), Abhandlungen über die Mechanische Wärmetheorie. Electronic manuscript from the Bibliothèque nationale de France.
  13. ^ Clausius, R. (1865), "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie", Annalen der Physik 125: 353–400,  
  14. ^ "R.J.E. Clausius (1822 - 1888)". Royal Netherlands Academy of Arts and Sciences. Retrieved 21 July 2015. 

External links

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