# Physics 3400: Thermal Physics

**3400 Thermal Physics** covers central concepts in thermodynamics and statistical mechanics, including temperature, entropy, the laws of thermodynamics, the Einstein model of solids, paramagnetism, Helmholtz and Gibbs free energies, chemical potential, thermodynamic identities, Boltzmann statistics, the partition function, and quantum statistics.

PR: Mathematics 2000, PHYS 2053 and PHYS 2750 (or 2056)

“*A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.*”

– A. Einstein

“*But although, as a matter of history, statistical mechanics owes its origins to investigations in thermodynamics, it seems eminently worthy of an independent development, both on account of the elegance and simplicity of its principles, and because it yields new results and places old truths in a new light in departments quite outside of thermodynamics.*”

– J.W. Gibbs

Thermodynamics and statistical mechanics, together comprising thermal physics, are all-encompassing fields of physics. Their applications span an enormous range of subjects, including oceanography, atmospheric science, chemistry, materials physics, biological physics, and astrophysics, and the tools of thermodynamics are used to understand phenomena as diverse as black holes and the self-assembly of biomolecules.

This course covers fundamental concepts and tools of thermodynamics and statistical mechanics. In the course, we discuss, in some depth, central concepts such as heat, work, entropy, temperature and the laws and assumptions of thermodynamics, as well as a range of applications. Some books and courses on thermodynamics take a type of ‘purist’ approach, presenting the topic without any reference to underlying microscopic details - as the subject of thermodynamics was developed historically by scientists like Rudolf Clausius and J. Willard Gibbs. By contrast, we will switch back and forth between thermodynamic (macroscopic) and statistical mechanical (microscopic) viewpoints. This intermediate approach makes it easier to illustrate some of the key thermodynamic concepts.

In more detail, the course starts with a review of basic concepts that you have encountered before, such as heat, work, enthalpy, first and second laws of thermodynamics, and heat capacities. Thereafter, we will use simple models (Einstein model of solids, ideal two-state paramagnets, and the ideal gas) to carefully illustrate the microscopic picture that underlies some fundamental ideas in thermodynamics, e.g., what temperature and entropy really are. Using these models, we will also encounter the exotic phenomenon of negative temperatures. You will be introduced to the thermodynamic potentials, which include Gibbs and Helmholtz free energies. The usefulness of these quantities is demonstrated in the analyses of phase transitions and chemical reactions.

Moving beyond what can be termed classical thermodynamics, we will turn to the basic elements of statistical mechanics. These include the Boltzmann factor, the partition function and thermodynamic averages. Armed with these tools, we will discuss the thermal excitation of atoms and the Maxwell speed distribution. The final part of the course is the application of statistical mechanics to quantum systems. Highlights in this final part include the Fermi-Dirac distribution, degenerate Fermi gases, and the ultraviolet catastrophe of black-body radiation.