Abstract
Thermodynamics is an axiomatic part of Theoretical Physics, which is presented as a set of phenomenological axioms or principles. Any investigation into the reasons why the principles are true and how they are related to micro-Physics belongs to the domain of Statistical Mechanics, while Thermodynamics gives guidelines that are never contradicted by experiments, at least for macroscopic objects. Actually, the principles are simple and part of the common wisdom by now, but Thermodynamics deduces profound consequences.
Any macroscopic object in thermal equilibrium contains so many particles in chaotic motion that the methods of Mechanics are totally useless. This chapter is a simple introduction to Thermodynamics and classical Statistical Mechanics.
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Notes
- 1.
A piece of diamond is out of equilibrium under normal conditions, because Graphite is the equilibrium form of Carbon; however since the kinetics of the transformation is extremely slow, one can do reversible transformations on diamond as well. Actually, the seemingly simple concepts on which Thermodynamics is based are far from obvious.
- 2.
Gustav Kirchhoff was a German physicist (Königsberg (now Kaliningrad, Russia), 1824- Berlin, 1887). He established the well-known laws on linear electric circuits, and, together with Bunsen, invented the spectroscope; he also discovered Cesium and Rubidium. He wrote “Vorlesungen \(\ddot{u}\)ber mathematische Physik”.
- 3.
Ludwig Boltzmann (Vienna 1844- Duino (near Trieste) 1906, Austria (now Italy(suicide))) pioneered Statistical mechanics with Gibbs.
- 4.
Note that \( \int _{0}^{\infty } \sqrt{x} e ^{- x} dx = \frac{\sqrt{\pi }}{2}, \) and so \( \int dN = N \).
- 5.
The great theoretician Josiah Willard Gibbs (New Haven, Connecticut, U.S.A., 1839 - Yale 1903) was the first professor of Mathematical Physics in U.S.A.
- 6.
If the system is the Universe, it is quite clear that it is not in thermal equilibrium, however, who knows if it evolves towards an equilibrium of some kind?
- 7.
Plack’s quantum h had not yet been discovered.
- 8.
A system at a fixed temperature exchanges energy with a heat bath, therefore its energy fluctuates; in the microcanonical ensemble the energy is fixed, and therefore the temperature fluctuates. However for a macroscopic sample such fluctuations are relatively unimportant. Therefore both schemes should lead to the same results for large systems.
- 9.
C.P. Williams, Explorations in Quantum Computing, Springer (2011).
- 10.
\( \left( \begin{array}{r} N\\ n \end{array} \right) = {N! \over n! (N-n)!}\) is the number of different choices of n objects from N, regardless the order of the selected objects.
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Cini, M. (2018). Thermal Physics. In: Elements of Classical and Quantum Physics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-71330-4_5
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DOI: https://doi.org/10.1007/978-3-319-71330-4_5
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