Rudolf Julius Emanuel Clausius (2.01.1822-24.08.1888) was a German theoretical physicist, one of the creators of thermodynamics and of the kinetic theory of gases, and a corresponding member of the Berlin Academy of Sciences (1876). He was born in Köslin (now Koszalin, the Polish People's Republic). He graduated from the University of Berlin (1848). From 1855 he was professor at the University of Zurich, from 1867 at Würzburg and from 1869 at Bonn.
His work was in the field of molecular physics, thermodynamics, the theory of steam engines, theoretical mechanics and mathematical physics. Developing the ideas of N. Carnot, he gave an exact formulation of the principle of the equivalence of heat and work. In 1850, independently of W. Rankine, he obtained general relations between heat and mechanical work (the first law of thermodynamics) and worked out the ideal thermodynamic cycle of the steam engine (the Rankine–Clausius cycle). He was the first to study the properties of water vapour (1851), and he indicated (1856) the way to raise the efficiency of a heat engine, namely raising the temperature of the working substance. He formulated (1850) the second law of thermodynamics: “heat cannot of itself pass from a colder body to a warmer one”. He gave a mathematical expression of the second law both for reversible cyclic processes (1854) and for irreversible ones (1862). Developing his thermodynamic ideas, he introduced a new and important concept, that of entropy (1865), and established its most important feature: in a closed system the entropy either remains unchanged (in the case of reversible processes) or increases (in the case of irreversible processes). Clausius thus showed that the change of entropy determines the direction in which a process runs. Extending the principle of increasing entropy to the whole Universe and regarding it as a closed system, he arrived at the erroneous conclusion of the heat death of the Universe, that is, at the very conclusion which followed from the idealist hypothesis of the heat death of the Universe put forward in 1852 by W. Thomson. The untenability of this hypothesis was proved by L. Boltzmann, who showed the statistical character of the second law of thermodynamics.
He made a significant contribution to the kinetic theory of gases, giving in 1857 a systematic exposition of the foundations of that theory. He introduced statistical ideas into it (the method of mean values) and the concept of the mean free path of molecules, and he calculated (1859) the mean length of their path between two collisions; he was the first to calculate theoretically the magnitude of the pressure of a gas on the walls of a vessel. He introduced the concept of the sphere of action of molecules (1859). In 1870 he proved the virial theorem, which relates the mean kinetic energy of a system of particles to the forces acting within it. He gave the equation of the gaseous state a more general form than the van der Waals equation (1880). He gave (1851) a theoretical justification of the Clapeyron equation, which relates the melting temperature of a substance to pressure (the Clapeyron–Clausius equation).
He gave a theoretical justification of the Joule–Lenz law, developed in 1853 the thermodynamic theory of thermoelectricity and introduced in 1857 the idea of electrolytic dissociation. He developed (1879) a theory of the polarisation of dielectrics, from which, independently of O. Mossotti, he derived the relation between the permittivity and the polarisability of a dielectric (the Clausius–Mossotti formula).
A member of a number of academies of sciences and scientific societies, in particular a foreign member of the St Petersburg Academy of Sciences (1878).