### Topic Page: Boltzmann, Ludwig, 1844-1906

**Boltzmann, Ludwig Eduard (1844-1906)**

*The Hutchinson Dictionary of Scientific Biography*

Place: Austria

Subject: biography, physics

Austrian theoretical physicist who contributed to the development of the kinetic theory of gases, electromagnetism, and thermodynamics. His work in these fields led him to consider phenomena in terms of probability theory and atomic events, which led to the establishment of the branch of physics now known as statistical mechanics.

Boltzmann was born in Vienna on 20 February 1844 and educated at Linz and Vienna. He studied at the University of Vienna under Josef Stefan and Josef Loschmidt (1821-1895), and received his PhD in 1866 from that institution. In 1867 Boltzmann became an assistant at the Physikalisches Institut in Vienna, after which he held a series of professorial posts. He was professor of theoretical physics at the University of Graz 1869-73, of mathematics at the University of Vienna 1873-76, and of experimental physics at Graz 1876-79. He then became director of the Physikalisches Institut, moving in 1899 to Munich to become professor of theoretical physics at the university there. In 1894 he went back to Vienna to succeed Stefan as professor of theoretical physics. During these years there was a heated and sometimes unpleasant scientific debate between the ‘atomists’, championed by Boltzmann, and the ‘energeticists’, one of whose spokespersons was Wilhelm Ostwald. Ernst Mach, one of the ‘energeticists’, tried to reconcile the two schools of thought in an attempt to tone down the debate.

Boltzmann moved to the University of Leipzig in 1900, where he served as professor of theoretical physics. He suffered from depression and made an unsuccessful suicide attempt. He returned to his previous post at Vienna in 1902, with the added honour of the chair of natural philosophy from which Mach had just retired because of ill health. In 1904 Boltzmann travelled to the USA, lecturing at the World's Fair in St Louis and visiting Stanford University and the University of California at Berkeley. He still felt depressed at the hostility he sensed from some of his scientific colleagues, despite the fact that the revolutionary discoveries being made at the time about the structure of atoms and the properties of matter would ultimately support his theories. He committed suicide at Duino, near Trieste, on 5 September 1906.

Mechanics, dynamics, and electromagnetism were all being developed when Boltzmann was a student. He made contributions to all of these areas during the course of his career. One of his most important sources of stimulation was the work of James Clerk Maxwell, whose investigations in the field of electromagnetism were not well known by European scientists. Boltzmann contributed greatly to the dissemination of Maxwell's work, particularly through a book on the subject published in 1891.

Boltzmann wrote his first paper on the kinetic theory of gases in 1859 while he was only a student. In 1868 he published a paper on thermal equilibrium in gases, citing and extending Maxwell's work on this subject. He was concerned with the distribution of energy among colliding gas molecules. He derived an exponential formula to describe the distribution of molecules which relates the mean total energy of a molecule to its temperature. It includes the constant k, now known as the Boltzmann constant, which is equal to 1.38066 × 10^{−23} joules per Kelvin. This constant has become a fundamental part of virtually every mathematical formulation of a statistical nature in both classical and quantum physics.

Another important area of Boltzmann's investigation was thermodynamics. The second law of thermodynamics had been formulated in 1850 by Rudolph Clausius and William Thomson (Lord Kelvin). Boltzmann sought to find a mathematical description for the demonstration of the tendency of a gas to reach a state of equilibrium as the most probable state. In 1877 he published his famous equation

S = klog W

(which was later engraved on his tombstone) describing the relation between entropy and probability.

Boltzmann also determined a theoretical derivation for Josef Stefan's experimentally derived law of black-body radiation. Stefan had shown that the energy radiated by a black body is proportional to the fourth power of its absolute temperature, and this is now often known as the Stefan-Boltzmann law. Boltzmann's investigation of the phenomenon was based on the second law of thermodynamics and Maxwell's electromagnetic theory.

Boltzmann's most enduring contribution arose from his pioneering work in the field of statistical mechanics. He had begun his study of the equipartition of energy, which resulted in the Maxwell-Boltzmann distribution law, early in his career. He demonstrated that the average amount of energy required for atomic motion in all directions is equal, and so formulated an equation for the distribution of atoms due to collision. This led to the foundation of statistical mechanics. This discipline holds that macroscopic properties of matter such as conductivity and viscosity can be understood, and are determined by, the cumulative properties of the constituent atoms. Boltzmann held that the second law of thermodynamics should be considered from this viewpoint. Boltzmann's work on the relationship between probability and entropy and on the inevitable and irreversible processes that must therefore occur, influenced Willard Gibbs, Max Planck, and others.

Boltzmann was a theoretician with great intuitive powers and vision. It is a tragedy that he did not live to see his work vindicated and the remarkable advances achieved by the ‘atomists’ of the 20th century.

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