During the Fall 2018 semester, I took a course titled “Statistical Mechanics” at Mount Holyoke College, taught by Kerstin Nordstrom. This was an 300-level course that focuses on concepts in thermodynamics and statistical mechanics. Nearly all of our time in class was spent on lectures, where we discuss the fundamental concepts in statistical mechanics and solve some complex problems as a class.
Towards the end of the semester, we were assigned to come up with a project to do independently that further explores one of the topics we discussed in class. I was inspired by the lecture on quantum gases, which mentioned white dwarfs as an application of the Fermi gas, an example of a quantum ideal gas. Seeing this as an opportunity to merge my interests in physics and astronomy, I decided to do my project on white dwarfs, where I completed a problem that derives the relationship between the mass and the radius of a white dwarf star. The relationship between mass and radius is directly derived from the function for the total energy of the white dwarf. The function for total energy incorporates the Fermi Energy, which is an important property of a quantum gas.
This article walks through the derivation of the relationship between the mass and the radius of a white dwarf. It includes a detailed description of the process, as well as the equations used, calculations done, and some figures I created. Figure 1 in the article, the sketch showing the assembly of a sphere shell by shell was created in Adobe Illustrator, and Figures 2 and 3 in the article are graphs generated by Wolfram Mathematica.