Further Studies on the Thermal Equilibrium of Gas Molecules

Further Studies on the Thermal Equilibrium of Gas Molecules (1872)
Boltzmann's 1872 "Further Studies on the Thermal Equilibrium of Gas Molecules" introduced the H-theorem, the precursor to the S = k ln W Planck entropy formula.
In famous publications, “Further Studies on the Thermal Equilibrium of Gas Molecules” is a ninety-five page article by Austrian physicist Ludwig Boltzmann, published in October of 1872, which contains what Boltzmann called his 'minimum theorem', later christened the “H-theorem”, otherwise known as the Boltzmann equation, the first explicit probabilistic expression for the entropy of an ideal gas. [1] In this paper, called “great paper of 1872”, by Boltzmann’s biographer Italian physicist Carlo Cercignani, Boltzmann is said to have presented one of the first proofs of the second law. [2]

Boltzmann wrote to his mother in Vienna in September 1872 saying that he had given a lecture on his theorem to the Physical Society in Berlin, but that hardly anyone was able to follow him—apart from German physicist Hermann Helmholtz, with whom an interesting discussion developed. [3]

A noted quote from Boltzmann’s Further Studies, in which he compares people to molecules (human molecules), is: [4]

Molecules are like to many individuals, having the most various states of motion, and the properties of gases only remain unaltered because the number of these molecules which on average have a given state of motion is constant.”

American chemist Philip Ball claims that the theme of this quote traces to Boltzmann’s reading of English historian Henry Buckle’s 1861 History of Civilization. [5]

1. (a) Boltzmann, Ludwig. (1872). "Further Studies on the Thermal Equilibrium of Gas Molecules" (“Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen”) (abs), in Sitzungsberichte der Akademie der Wissenschaften, Mathematische-Naturwissenschaftliche Klasse (pgs. 275-370), Bd. 66, Dritte Heft, Zweite Abteilung, Vienna: Gerold.
(b) Reprinted in: Wisssenschaftliche Abhandlungen, ed. F. Hasenohrl, vol.1, pg. 317. J.A. Barth, Leipzig, 1909.
(c) Reprinted in: The Kinetic Theory of Gases (pgs. 262-349) by Stephen G. Brush, Nancy S. Hall. Imperial College Press, 2003.
2. Purrington, Robert D. (1997). Physics in the Nineteenth Century (pgs. 142-43). Rutgers University Press.
3. Flamm, Dieter. (1999). “Boltzmann: a Disordered Genius”, PhysicsWorld.com, 9 April.
4. Thims, Libb. (2008). The Human Molecule, (pg. 9) (preview). Morrisville, NC: LuLu.
5. Ball, Philip. (2004). Critical Mass: How One Thing Leads to Another (pgs. 65-69, 205). New York: Farrar, Straus and Giroux.

Further reading
● Cohen, E.G.D. and Thirring, W. (1973). The Boltzmann Equation: Theory and Applications. Proceedings of the International Symposium “100 Years Boltzmann Equation” in Vienna, 4th-8th September 1972 (Few-Body Systems). Springer.

External links
'Further Studies on the Thermal Equilibrium of Gas Molecules' ($3600) – ManhattenRareBooks-Science.com

TDics icon ns

More pages