# Ludwig Boltzmann

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## Boltzmann, Ludwig

**Boltzmann, Ludwig**(lo͝otˈvĭkh bôltsˈmän), 1844–1906, Austrian physicist, b. Vienna, educated at Univ. of Vienna. He began teaching (1869) at Graz Univ. In 1873 he became mathematics professor at Vienna and then physics professor at Graz (1876), Munich (1890), Vienna (1895), and Leipzig (1900). Boltzmann made important contributions to the kinetic theory of gases and to statistical mechanics—the Boltzmann constant, which relates the mean total energy of a molecule to its absolute temperature, is used widely in statistics and is named for him. Working independently, he demonstrated a law on blackbody radiation that had been stated by the Austrian physicist Josef Stefan; hence the law is sometimes known as the Stefan-Boltzmann law.

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Boltzmann, Ludwig

Born Feb. 20, 1844, in Vienna; died Sept. 5,1906, in Duino near Trieste. Austrian physicist; one of the founders of statistical physics and physical kinetics. Member of the Vienna Academy of Sciences (1895) and of many academies of the world.

Boltzmann graduated from the University of Vienna in 1866, becoming a privatdocent there in 1867. He was a professor of theoretical physics at the university in Graz (1869–73), a professor of mathematics at the University of Vienna (1873–76), and a professor of experimental physics at the university in Graz (1876–89). He occupied the chair of theoretical physics in Munich from 1889 to 1894, in Vienna from 1894 to 1900, in Leipzig from 1900 to 1902, and then again in Vienna.

Boltzmann’s scientific interests encompassed virtually all branches of physics and a number of branches of mathematics as well. He is the author of works on mathematics, mechanics, hydrodynamics, the theory of elasticity, the theory of the electromagnetic field, optics, thermodynamics, and the kinetic theory of gases. However, his work on the kinetic theory of gases and his statistical substantiation of thermodynamics are of the most importance. Between 1868 and 1871, Boltzmann generalized J. C. Maxwell’s law of the distribution of the velocities of gas molecules to gases located in an external power field and established Boltzmann’s distribution formula, which penetrated all branches of statistical physics. Applying statistical methods in the kinetic theory of ideal gases, Boltzmann derived the basic kinetic equation of gases, which is the foundation of physical kinetics. Great credit goes to Boltzmann for investigating irreversible processes and for the statistical interpretation of the second law of thermodynamics. In 1872, Boltzman introduced the so-called H-function, which characterizes the state of a closed macroscopic system, and he proved that the H-function cannot increase with the passage of time (the H-theorem). Identifying the H-function with entropy 5 (with an inverse sign), Boltzmann related entropy to the thermodynamic probability *W: S = K* In *W.* This relationship, which is engraved on Boltzmann’s monument in Vienna, statistically substantiates the second law of thermodynamics and is the foundation of statistical physics. The universal constant *k* is called Boltzmann’s constant in his honor.

Boltzmann was an ardent follower of Maxwell’s electromagnetic theory. The first experimental work to check the accuracy of the conclusions of Maxwell’s theory of the electromagnetic field was done by Boltzmann. He measured the dielectric penetrability of gases and solids and established its relationship with the optical index of refraction. Boltzmann presented his views on Maxwell’s theory in the *Lectures on Maxwell’s Theory of Electricity and Light* (1891–93). In 1884, Boltzmann theoretically derived the law of black-body radiation—the Stefan-Boltzmann law of radiation—which had previously been established experimentally by J. Stefan. This work played a large role in the development of the current theory of radiation. Boltzmann’s other works include the study of the polarization of dielectrics, the theory of thermoelectricity, and diamagnetism. In particular, Boltzmann developed the theory of the Hall effect.

Boltzmann was a confirmed advocate of molecular theory. He sharply opposed the theories of Machism and energeticism, which were very popular in Austria and Germany at the turn of the 20th century. The proponents of these theories—E. Mach, W. Ostwald, and others—rejected the explanation of the internal mechanism of physical phenomena and recognized only a “pure description.” Boltzmann had to wage an intensive ideological struggle to defend the molecularatomic theory’s right to exist; his works were not recognized by a number of his countrymen. It is possible that this played a certain part in Boltzmann’s tragic end; sick and depressed, he ended his life by suicide.

### WORKS

*Wissenschaftliche Abhandlungen,*vols. 1–3. Leipzig, 1909.

*Populare Schriften,*2nd ed. Leipzig, 1919.

*In Russian translation:*

*Ocherki metodologiifiziki.*Moscow, 1929.

*Lektsii po teorii gazov.*Moscow, 1956.

### REFERENCES

Flamm, L. “Pamiati Liudviga Bol’tsmana.”*Uspekhi fizicheskikh nauk,*1957, vol. 61, issue 1.

O. V. KUZNETSOVA