Rudolf Clausius

Rudolf Clausius books and biography


Rudolf Clausius

Rudolf Clausius

Rudolf Julius Emanuel Clausius (January 2, 1822 – August 24, 1888), was a German physicist and mathematician.

Clausius was one of the founders of thermodynamics. 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 mechanical theory of heat, published in 1850, first stated the basic ideas of the second law of thermodynamics. In 1865 he introduced the concept of entropy.



Rudolf Clausius started his education at the school of his father. After a few years, he went to the Gymnasium in Stettin. Clausius graduated from the University of Berlin in 1844 where he studied Mathematics and Physics with, among others, Heinrich Magnus, Johann Dirichlet and Jakob Steiner. He also studied History with Leopold von Ranke. In 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. In 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.


Clausius' PhD thesis on 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 his predecessors.

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")[1] 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 caused his scientific career to take off.

In 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.

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.


Main article: history of entropy

In his "Abhandlungen über die mechanische Wärmetheorie, Zweite Abteilung", published in 1867, Clausius first gave a mathematical version of the concept of entropy, and gave it its name. He used the now abandoned unit 'Clausius' (symbol: Cl) for entropy.

1 Cl = 1 cal/°C = 4.1868 joules per kelvin (J/K)


  • He was elected a Fellow of the Royal Society of London in 1868 and received its Copley Medal in 1879.
  • He received the Huygens Medal in 1870.
  • He received the Poncelet Prize in 1883.
  • He received an honorary doctorate from the University of Würzburg in 1882.
  • The Clausius crater on the Moon was named in his honor.


The energy of the universe is constant.
The entropy of the universe tends to a maximum.
Rudolf Clausius


  1. ^ Ann. Phys. (1850), 79, 368–397, 500–524; translated into English in: Phil. Mag. (1851), 2, 1–21, 102–119
  • Cardwell, D.S.L. (1971). From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age. London: Heinemann. ISBN 0-435-54150-1. 

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