Seminar to Statistical Thermodynamics Ludwig Boltzmann - Work and life

1

Ludwig Boltzmann - work and life 1. Biography Ludwig Boltzmann was born on 20th of February 1844. His grandfather, Gottfried Ludwig Boltzmann, was a maker of musical boxes. From him, Boltzmann got the talent and interest in mechanics. He applied the craftsmanship often during his lectures, by trying to explain experimental as well as theoretical physics with the help of well-designed experiments. Boltzmanns first education took place at home under a private teacher. His father died, when he was only 15 years old. At the age of 19, Boltzmann started his studies at the Institute of Physics in Vienna. Josef Stefan was the director of the institute. He introduced Boltzmann to Maxwells theories. Boltzmann appreciated the close contact, Stefan had to his students. In 1966, he got his PhD and became Assistant Professor. In 1868, Boltzmann decided to follow the call from Graz and obtained the Chair of Mathematical Physics. The fast development of this university of Graz and the chance of becoming head of a department appealed to Boltzmann. In Graz he published one of his most important papers called: Further investigations on the thermal equilibrium of gas molecules. During Boltzmanns first stay in Graz, he met his future wife Henriette von Aigentler. After meeting Boltzmann, Henriette decided to study mathematics. In 1873, Boltzmann obtains the Chair of Mathematics in Vienna. Being a Professor in Vienna was considered to be the highest part of an academic career. In 1876 the Chair of Experimental Physics in Graz was vacant. Boltzmann saw his time to return to the place, which he loved so much. He spent a lot of time with his kids and held many receptions at his house, among his quests were also his PhD students. The 14 years he spent in Graz during his second stay there were the happiest and most productive ones of his life. Boltzmann published another famous paper. He makes a mathematical description of the entropy as a well-defined measure of some kind of disorder of the atoms. He mentions, that entropy is nothing else than the level of probability of a macroscopic state, which can be related to the probability of the microscopic state. Boltzmann has become known around the whole world, by staying true to his believes, working as a Professor in different places and impressing both, personally and scientifically. However, rising reputation was connected to more publicity, more work and more criticism. The happy years in Graz were followed by a time of struggle. Boltzmann lost his mother when he was only 41. His son dies in 1889 from appendicitis. Additionally, he was elected to become the rector of the university of Graz. A lot of duties were bound to this position. Two years later, one of Boltzmann dearest friends – Gustav Kirchhoff – died in Berlin. At his funeral, Boltzmann was offered to become Kirchhoffs successor at the university of Berlin, He accepted immediately. The problem was, that the University of Graz did not know about the appointment in Graz officially. Boltzmann had to chose. Finally, he cancelled the appointment in Berlin. Boltzmann felt uncomfortable in Graz and leaves it finally heading to the university of Munich and occupying the Chair of Theoretical Physics there. The Department appealed to him, as he could teach theoretical physics. However, the University of Munich did not offer a high pension to university professors. In 1892, his great master Josef Stefan died. Boltzmann decided to move back to Vienna where he was promised a full pension. In Vienna however, there was still Ernst Mach who was still opposing the atomic picture of the nature.. Due to his uncomfortable surrounding, he went on many trips abroad and was unable to settle down in Vienna. So again, he decided to change universities and accepted an appointment as Professor of Theoretical Physics in Leipzig in 1900, facing opposition there as well. When Mach has a stroke in 1901, this was Boltzmanns chance to return to Vienna without Machs opposition. He was given a lot of work and subjects to teach, among them two hours of teaching philosophy. As it turns out, it was these lectures, which were attended the most. During the last years of Boltzmanns life, his manic depressive syndrome became stronger. On the one hand side, he is taking up many trips in order to lecture overseas and spent many evenings in bars, discussing his ideas with his fellow scientists. On the other hand, he suffered from asthma attacks and cancelled appointments. During a short holiday trip with his family in Duino, he hanged himself during a phase of acute depression in September 1906.

Abb. 2: Meeting in Graz, 1887: Working colleages and Boltzmann (front, middle) [2]

Abb. 1 Ludwig Boltzmann [1]

Bring vor, was wahr ist, schreib so, dass es klar ist. und verficht’s, bis es mit dir gar ist.

Seminar to Statistical Thermodynamics Ludwig Boltzmann - Work and life

2

2. Contacts

The first scientist influencing Boltzmann was Josef Stefan. He was working as a professor at the university of Vienna, supported Boltzmann during his studies and PhD and introduced him to Maxwells work. It took up quite a bit of work from Boltzmann, to prove the Maxwell equations. But it was not only Boltzmann who was influenced by others, but also the other way around. To start with, Max Planck (who was, before meeting Boltzmann, a defender of the atomism) put Boltzmanns thoughts about entropy in a well memorable equation. Finally, Paul Ehrenfest continued Boltzmanns work on the theory of thermodynamics. But not everyone was fund of Boltzmann. One of his strongest opponents was Ernst Mach, a professor in Vienna, who did not believe in the existence of atoms.

Furthermore there was Wilhelm Ostwald who strongly believed in energetics. Mach and Ostwald were opponents of Boltzmann on a scientific level, but good friends in everyday life. 3. Maxwell-Boltzmann distribution As mentioned before, Boltzmann dealt a lot with Maxwell's work, mostly in the field of kinetic gas theory. An ideal gas can be described with the model of a frictionless billard table. If you start pushing a couple of balls around they will achieve an equilibrium state after a while. All the speeds of the particles can be meassured at a given moment and plotted in a histogramm. The resulting plot will always look similar and is called a Maxwell-Boltzmann-distribution. It is useful to make statements on a random and thus normally unpredictable system with the help of statistical methodes. Values like the average speed of a particle in a gas, the kinetic energy or the most probable speed can be extracted from this concept. One might wonder why it is called the Maxwell-Boltzmann-distribution when these scientists actually never met or wrote to eachother in their entire lifes. The basic idea for this description came from Maxwell. Boltzmann later verified it and generalized it for real gases. 4. Boltzmann's philosophical views As Boltzmann grew older, his main focus changed from science to the philosophy of knowledge. He was convinced that it is not necessary to see something to assume its existence. In his time, the existence of atoms was highly discussed. Boltzmann was the biggest fighter for atomism in Europe. He believed it was important to stand up for this concept because otherwise his and the findings of others would get lost to the next generations. Mach and Ostwald were his most prominent opponents since they were both followers of phenomenology. This philosophical current states, that you can only know what you experience with your senses which means that a hypothesis isn't a legimit way of working. Boltzmann was discussing his opinions in public talks, where he was able to convince some known scientists like Planck of the atom idea which gives him an important role in the way we see the world today.            

Abb. 3: top: Stefan, Maxwell, Plank bottom: Ehrenfest, Mach, Ostenwald [3]

 

Abb. 4: Velocity distribution [4]

 

Seminar to Statistical Thermodynamics Ludwig Boltzmann - Work and life

3

References [1] http://de.wikipedia.org/wiki/Ludwig_Boltzmann [2] http://en.wikipedia.org/wiki/Ludwig_Boltzmann, 14.03.13 [3] www.wikipedia.org [4] http://www.tannerm.com/maxwell_boltzmann.htm