Rudolf Clausius

Major contributions

• Showed in 1850 that Carnot's results on heat engines remain valid if heat is a form of energy rather than a conserved fluid, stating that heat cannot by itself pass from a colder to a warmer body (the Clausius statement of the second law)
• Introduced entropy as a state function in 1865, coining the word from the Greek for “transformation”, and proved the Clausius inequality ∮ δQ/T ≤ 0 (see Entropy)
• Advanced the kinetic theory of gases, introducing the mean free path (1858) to explain why gas diffusion is slow despite high molecular speeds, and deriving the ideal gas law from molecular motion (see Ideal Gas Law)
• Formulated the virial theorem (1870), relating average kinetic and potential energy of a bound system, later central in astrophysics (see Galaxy Clusters)
• Derived the Clausius–Clapeyron relation for the slope of phase-coexistence curves

Named concepts

Concept	Statement	Codex page
Clausius statement	Heat does not spontaneously flow from cold to hot	View entry
Entropy (coined 1865)	dS = δQrev/T	View entry
Virial theorem	2⟨K⟩ + ⟨U⟩ = 0 for gravitating systems	View entry

Career

Clausius was born in Köslin, Pomerania (now Koszalin, Poland). He studied at the University of Berlin and received his doctorate from the University of Halle in 1847, with a thesis on the optics of the atmosphere. After teaching in Berlin, he became professor at the Swiss Federal Polytechnic (ETH) in Zurich in 1855, then moved to Würzburg in 1867 and Bonn in 1869, where he remained until his death.

During the Franco-Prussian War (1870–1871) he organised a volunteer ambulance corps and was wounded. His collected papers on the mechanical theory of heat were translated into English in 1867. He engaged in priority disputes, notably with British physicists over the history of thermodynamics, and was sceptical of some aspects of Boltzmann's statistical approach.

Key publications

• Clausius, R. (1850). Annalen der Physik, 79, 368–397, 500–524.
• Clausius, R. (1865). Annalen der Physik, 125, 353–400.
• Clausius, R. (1858). “Über die mittlere Länge der Wege, welche bei der Molecularbewegung gasförmiger Körper von den einzelnen Molecülen zurückgelegt werden.” Annalen der Physik, 105, 239–258.

Nobel Prize

Clausius died in 1888, before the Nobel Prizes were first awarded in 1901. He received the Copley Medal of the Royal Society in 1879.

Historical context

Clausius worked at the moment when the caloric theory gave way to the mechanical theory of heat (see Heat). William Thomson (Lord Kelvin) reached an equivalent statement of the second law in 1851, and the two are now credited jointly with founding classical thermodynamics, building on Sadi Carnot's 1824 analysis. Clausius's phrasing of the two laws for the universe as a whole, while influential, raised the question of the “heat death” of the universe that is still discussed in cosmology (see Fate of the Universe). His work set the stage for Boltzmann's statistical interpretation of entropy.