Ludwig Boltzmann

Ludwig Boltzmann
Ludwig Eduard Boltzmann (1844-1906)
Born	February 20, 1844 Vienna, Austrian Empire
Died	September 5, 1906 Duino, Italy
Residence	Austria, Germany
Nationality	Austrian
Field	Physicist
Institutions	University of Graz University of Vienna University of Munich University of Leipzig
Alma mater	University of Vienna
Academic advisor	Josef Stefan
Notable students	Paul Ehrenfest Philipp Frank Gustav Herglotz
Known for	Boltzmann's constant Boltzmann equation Boltzmann distribution Stefan-Boltzmann law

Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist famous for his application of probability theory to the study of molecules in a gas. He used the results of his theoretical investigations to explain the thermodynamic properties of materials. He was one of the most important advocates for atomic theory when that scientific model was still highly controversial.

Biography

Childhood

Boltzmann was born in Vienna, then capital of the Austrian Empire. He was the eldest of three children of Ludwig Georg Boltzmann, a tax official, and Katarina Pauernfeind of Salzburg. He received his primary education from a private tutor at the home of his parents. Boltzmann attended high school in Linz, Upper Austria. As a his youth, his interests encompassed literature, butterfly collecting, and music. For a short time, he studied piano under the famous composer Anton Bruckner. At age 15, Boltzmann lost his father to tuberculosis.

University years

Boltzmann studied physics at the University of Vienna, starting in 1863. Among his teachers were Josef Loschmidt, who was the first to measure the size of a molecule, and Joseph Stefan, who discovered the law by which radiation depends on the temperature of a body. Stefan introduced Boltzmann to Maxwell's work by giving him some of Maxwell's papers on electricity, and an english grammar book to help him learn english. Loschmidt and Stefan, Boltzmann's chief mentors during this period, became his close friends. The laboratory in which they worked, in a private house separate from the university campus, was sparcely equipped. "We always had enough ideas," Boltzmann would later say. "Our only worry was the experimental apparatus." <<<Mehra, Jagdish and Helmut Rechenberg. 2001. The historical development of quantum theory. New York: Springer-Verlag. 50. ISBN 0387906428>>> Boltzmann published his first paper, on the electrical resistance between different points on a conducting sphere, in 1865. He received his doctorate in 1866 working under the supervision of Stefan.

Early research

In this same year, he published his first paper on the kinetic theory of gases, entitled "On the mechanical significance of the second law of thermodynamics." In 1867 he became a Privatdozent (lecturer). Boltzmann worked two more years as Stefan’s assistant. The following year, Boltzmann published a paper, Studies on the equipartition of thermal kinentic energy among material point masses, in which he attempted to express the manner in which energy was distributed among the trillions of molecules in a sample of gas.<<<Everdell, William R. 1997. The first moderns: profiles in the origins of twentieth-century thought. Chicago: University of Chicago Press. 51. ISBN 0226224805>>>

Academic career

In 1869, at age 25, he was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. In 1869 he spent several months in Heidelberg working with Robert Bunsen and Leo Königsberger and then in 1871 he was with Gustav Kirchhoff and Hermann von Helmholtz in Berlin. While working with Helmholtz, he experimentally verified an important relationship between the optical and electrical properties of materials. This relationship was seen as a confirmation of Maxwell's theory, of which Helmholtz was a staunch supporter. Boltzmann also made extensive use of the laboratory of a colleague at Ganz, August Toepler.

In 1872, Boltzmann, who had been working on his treatment of the kinetic theory, published a paper that took into consideration the dimensions of molecules in its calculations. In this paper, entitled "Further studies on the thermal equilibrium among gas molecules," he for the first time wrote an equation representing the mathematical conditions that must be satisfied by a function representing the velocity distribution among molecules in motion. It is today referred to as the Maxwell-Boltzmann distribution, since Maxwell had derived a similar equation. By applying this equation, Boltzmann could explain the properties of heat conduction, diffusion and viscocity in gases. In the same year, using his equations, he attempted to explain the second law of thermodynamics. His final expression of this thesis is called the H theorem.

Controversy over Boltzmann's theories

Loschmidt later objected to Boltzmann's findings because it basically showed that an irreversible process is the result of a reversible process, which violates conservation of energy. Boltzmann defended his theorem, saying that the apparent contradiction is due to the statistical probabilities involved. He also noted that Boltzmann's work did not take into consideration the effect of a gravitational field on the kinetic theory.

In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and where he stayed until 1876, when he succeeded Toepler as director of the Physics institute at Graz, winning the position over Ernst Mach. Among his students in Graz were Svante Arrhenius, and Walther Nernst. He spent 14 years in Graz.

Ludwig Boltzmann and co-workers in Graz, 1887. (standing, from the left) Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger.

Marriage

In 1872, long before women were admitted to Austrian universities, Boltzmann met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to unofficially audit lectures, and Boltzmann advised her to appeal; she did, successfully. She and Boltzmann were married On July 17, 1876; they had three daughters and two sons.

In 1877, Boltzmann tried to further clarify the relationship between probability and the second law of thermodynamics. He introduced an equation that showed the relationship between entropy and probability. Mechanics, he thought, could not account for a complete explanation of the laws of thermodynamics, and he introduced "the measurement of probability." These and similar concepts being explored by J. Willard Gibbs formed the foundation for the field of statistical mechanics. Between 1880 and 1883, Boltzmann continued to develop his statistical approach, and refined a theory to explain friction and diffusion in gases.

In 1885 he became member of the Imperial Austrian Academy of Sciences and in 1887 he became the President of the University of Graz. It was around this time that Heinrich Hertz discovered the electromagnetic waves predicted by Maxwell. Boltzman devised demonstrations that took into account the In 1889, Boltzmann's eldest son, Ludwig, suffered an attack of appendicitis, from which he died. This was a source of great sorrow to Boltzmann.

Boltzmann was appointed Chair of Theoretical Physics at the University of Munich in Bavaria, Germany in 1890. In 1893, he succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna.

Final years

Boltzman spent much of the next 15 years of his life defending the atomic theory. The scientific community of the time divided into two camps, one defending the actual existence of atoms, and the other opposing the theory. Boltzmann was a defender of the atomic theory, and in 1894, he attended a meeting of the British Association for the Advancement of Science during which the two different positions were debated.

At a meeting in 1895 in Lubeck, the two sides, represented by their respective proponents, debated the issue. Georg Helm and Wilhelm Ostwald presented his view of energetics, which saw energy, and not matter, as the chief reality. Boltzmann appeared to carry the day, later met with some serious objections to the program of statistical mechanics. Boltzmann attempted a defense against these challenges, coming mainly from the quarter of a student of Max Plank, who had supported Boltzmann in the debate. However, Boltzmann did not get along with some of his colleagues in Vienna, particularly Ernst Mach, who became a professor of philosophy and history of sciences in 1895. Thus in 1900 Boltzmann went to the University of Leipzig, on the invitation of Wilhelm Ostwald. After the retirement of Mach due to bad health, Boltzmann came back to Vienna in 1902. His students included Karl Przibram, Paul Ehrenfest and Lise Meitner.

Boltzmann’s 1898 I₂ molecule diagram showing atomic “sensitive region” (α, β) overlap.

Boltzmann as lecturer

In Vienna, Boltzmann not only taught physics but also lectured on philosophy. Boltzmann’s lectures on natural philosophy were very popular, and received a considerable attention at that time. His first lecture was an enormous success. Even though the largest lecture hall had been chosen for it, the people stood all the way down the staircase. Because of the great successes of Boltzmann’s philosophical lectures, the Emperor invited him for a reception at the Palace.

Boltzmann suffered from a number of infirmities. When he was a student, he often studied in dim candle light, and later blamed this sacrifice for damage to his sight, which he suffered more or less throughout his career. He also suffered increasingly from asthma, possibly triggered by heart problems. He also suffered from headaches.

Boltzmann was subject to rapid alternation of depressed moods with elevated, expansive or irritable moods. He himself jestingly attributed his rapid swings in temperament to the fact that he was born during the night between Mardi Gras and Ash Wednesday; he had, almost certainly, bipolar disorder [1]. Meitner relates that those who were close to Boltzmann were aware of his bouts of severe depression and his suicide attempts.

On September 5, 1906, while on a summer vacation with his wife and youngest daughter in Duino, near Trieste, Boltzmann committed suicide by hanging himself.

Physics

Boltzmann's most important scientific contributions were in kinetic theory, including the Maxwell-Boltzmann distribution for molecular speeds in a gas. In addition, Maxwell-Boltzmann statistics and the Boltzmann distribution over energies remain the foundations of classical statistical mechanics. They are applicable to the many phenomena that do not require quantum statistics and provide a remarkable insight into the meaning of temperature.

Much of the physics establishment rejected his thesis about the reality of atoms and molecules — a belief shared, however, by Maxwell in Scotland and Gibbs in the United States; and by most chemists since the discoveries of John Dalton in 1808. He had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient theoretical constructs. Only a couple of years after Boltzmann's death, Perrin's studies of colloidal suspensions (1908-1909) confirmed the values of Avogadro's number and Boltzmann's constant, and convinced the world that the tiny particles really exist.

The equation

$S=k\,\log W$

relating probability to entropy is engraved on Boltzmann's tombstone at the Vienna Zentralfriedhof.

The Boltzmann equation

Boltzmann's bust in the courtyard arcade of the main building, University of Vienna.

The Boltzmann equation was developed to describe the dynamics of an ideal gas.

${\frac {\partial f}{\partial t}}+v{\frac {\partial f}{\partial x}}+{\frac {F}{m}}{\frac {\partial f}{\partial v}}={\frac {\partial f}{\partial t}}\left.{\!\!{\frac {}{}}}\right|_{\mathrm {collision} }$

where $f$ represents the distribution function of single-particle position and momentum at a given time (see the Maxwell-Boltzmann distribution), $F$ is a force, $m$ is the mass of a particle, $t$ is the time and $v$ is an average velocity of particles.

Boltzmann's grave in the Zentralfriedhof, Vienna, with bust and entropy formula.

In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate limiting conditions. The Boltzmann equation is notoriously difficult to solve. David Hilbert spent years trying to solve it without any real success.

The form of the collision term assumed by Boltzmann was approximate. However for an ideal gas the standard solution of the Boltzmann equation is highly accurate.

Boltzmann tried for many years to "prove" the second law of thermodynamics using his gas-dynamical equation — his famous H-theorem. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with Loschmidt and others over Loschmidt's paradox ultimately ended in his failure.

Energetics of evolution

Boltzmann's views played an essential role in the development of energetics, the scientific study of energy flows under transformation. In 1922, for example, Alfred J. Lotka referred to Boltzmann as one of the first proponents of the proposition that available energy, also called exergy, can be understood as the fundamental object under contention in the biological, or life-struggle and therefore also in the evolution of the organic world. Lotka interpreted Boltzmann's view to imply that available energy could be the central concept that unified physics and biology as a quantitative physical principle of evolution. In the forward to Boltzmann's Theoretical Physics and Philosophical Problems, S.R. de Groot noted that

“

Boltzmann had a tremendous admiration for Darwin and he wished to extend Darwinism from biological to cultural evolution. In fact he considered biological and cultural evolution as one and the same things. ... In short, cultural evolution was a physical process taking place in the brain. Boltzmann included ethics in the ideas which developed in this fashion ...

”

Howard T. Odum later sought to develop these views when looking at the evolution of ecological systems, and suggested that the maximum power principle was an example of Darwin's law of natural selection.

Significant contributions

1872 - Boltzmann equation; H-theorem

1877 - Boltzmann distribution; relationship between thermodynamic entropy and probability.

1884 - Derivation of the Stefan-Boltzmann law

Legacy

Boltzmann refined the mathematics originally applied by James Clerk Maxwell to develop the kinetic theory of gases. In this he made great progress, and the body of work he left was extended by scientists searching for mathematical techniques to express what became known as quantum mechanics. In Boltzmann's personal life, he was subject to bouts of depression, which he may have repressed by keeping an arduous work schedule. This is what perhaps led to the mental instability that resulted in his suicide. It is the hazard of high-profile achievers that they may stray beyond the reach of their closest friends, and fall prey to the imbalances within their own psyches. Boltzmann's achievements will always be stained with the tragedy of the circumstances of his death.

See also

• Atom
• Gas
• Molecule
• Thermodynamics

References

ISBN links support NWE through referral fees

• Boltzmann, Ludwig. 1964. Lectures on gas theory. Berkeley: University of California Press.
• Brush, Stephen G. 1965. Kinetic theory. Oxford: Pergamon Press.
• Everdell, William R. 1988. The Problem of Continuity and the Origins of Modernism: 1870-1913. History of European Ideas 9 (5): 531-552.
• Tolman, Richard C. 1938. The Principles of Statistical Mechanics. Oxford University Press. Reprinted: Dover (1979). ISBN 0486638960
• Gibbs, J. Willard. 1960. Elementary principles in statistical mechanics, developed with especial reference to the rational foundation of thermodynamics. New York: Dover Publications. ISBN 0918024196.
• Lindley, David. 2001. Boltzmann's atom: the great debate that launched a revolution in physics. New York: Free Press. ISBN 0684851865.
• Lotka, A. J. 1922. Contribution to the energetics of evolution. Proc Nat Acad Sci USA 8 (6): 147.

External links

• Ruth Lewin Sime, Lise Meitner: A Life in Physics Chapter One: Girlhood in Vienna gives Lise Meitner's account of Boltzmann's life and career. Retrieved August 19, 2007.
• Ludwig Boltzmann, Universität Wien. Retrieved August 19, 2007.
• Ali Eftekhari, Ludwig Boltzmann (1844 – 1906). Retrieved August 19, 2007.
• John J. O'Connor and Edmund F. Robertson. Ludwig Boltzmann at the MacTutor archive. Retrieved August 19, 2007.
• Scienceworld biography. Retrieved August 19, 2007.
• Ludwig Boltzmann's Gravesite. Retrieved August 19, 2007.

Credits

New World Encyclopedia writers and editors rewrote and completed the Wikipedia article in accordance with New World Encyclopedia standards. This article abides by terms of the Creative Commons CC-by-sa 3.0 License (CC-by-sa), which may be used and disseminated with proper attribution. Credit is due under the terms of this license that can reference both the New World Encyclopedia contributors and the selfless volunteer contributors of the Wikimedia Foundation. To cite this article click here for a list of acceptable citing formats.The history of earlier contributions by wikipedians is accessible to researchers here:

• Ludwig Boltzmann  ^history

The history of this article since it was imported to New World Encyclopedia:

• History of "Ludwig Boltzmann"

Note: Some restrictions may apply to use of individual images which are separately licensed.