Help with Quantum Statistics

[PRodQuanta]

I'm a senior undergrad student and I am going to give a 50 minute lecture on Degenerate Fermi Gases to the Thermodynamics and Statistical Mechanics class. I was wondering if anybody could help me out with coming up with some interesting stories, factoids, thought experiments, history lessons, etc... on the subject of degenerate fermi gases. This topic includes: fermi energy and temperature, degeneracy pressure, bulk modulus, density of states, and the Sommerfeld expansion. More explicitly, if you have Daniel Schroeder's Thermal Physics, I'm covering section 7.3.

I have a basic outline of what I want to cover, including some problems to work in class, but I would like to spice it up with some quips if possible.

Thanks,
PRodQuanta

 

[NateD]

One interesting story related to degenerate Fermi gases is that of the discovery of the white dwarf star Sirius B. In 1844, Alvan Clark discovered a companion star to Sirius A, then known as "the Pup". After further observation, it was discovered that Sirius B was much dimmer than Sirius A and had a much lower temperature. This led to the realization that the Pup had to be a white dwarf star, made up of degenerate matter. This was the first observation of a star composed entirely of degenerate matter, and provided strong evidence for the existence of degenerate Fermi gases and their role in the structure of stars. Another interesting factoid to mention is that while the Fermi energy of a degenerate Fermi gas is proportional to the cube root of the density, the pressure of the gas is proportional to the square root of the density. This difference in power law dependence comes from the Pauli exclusion principle, which prevents particles from sharing the same quantum state and thus strongly reduces the available volume for new particles in a small system. You could also discuss the Sommerfeld expansion and its applications. The Sommerfeld expansion is an analytical tool used to calculate the thermodynamic quantities of a degenerate Fermi gas. It was developed by Arnold Sommerfeld in 1929 and is still used today to analyze the behavior of degenerate Fermi gases at low temperatures. Finally, it might be interesting to discuss some of the real-world applications of degenerate Fermi gases. Degenerate Fermi gases are used to model the behavior of neutron stars and white dwarf stars, as well as to study the properties of neutron-rich nuclei. They are also used to analyze the behavior of ultra-cold atomic gases, which are being studied for their potential applications in quantum computing.