STATISTICAL PHYSICS PROBLEMS: MICROCANONICAL ENSEMBLE #1

Hi! Today we are going to be solving a problem on Statistical Physics. In this problem, we have an ultrarelativistic ideal gas contained in a volume V, with a number of particles N and a fixed energy E, and we will find its entropy, equation of state, ..., using the microcanonical ensemble!

This problem and many others that we will be doing on Statistical Physics can be found in the book "Problems on Statistical Mechanics", by Diego A. R. Dalvit, J. Frastai and Ian Lawrie. This book not only contains a lot of solved problems which are explained really clearly, it also gives a summary of the theory that will be used in the problems, which is great for when you want to revise the key concepts of the subject! So, if you are interested in learning about how to solve problems on Statistical Mechanics, give it a try!

As always, here are the time stamps of the video:
0:00 Statement of the Problem
1:28 Review of the Microcanonical Ensemble and previous results
1:45 Phase Space
3:10 Volume of the Phase Space
4:55 Gibbs factor
5:22 Planck's constant and degrees of freedom
6:55 Heaviside Step Function
7:30 Differentials
9:20 Extensive quantities/Homogeneous functions
10:35 Stirling's approximation for N!
11:30 Thermodynamic Relations
11:35 Beginning of the problem
11:37 1. Volumue of the phase space
36:30 2. Entropy
45:00 3. Temperature
46:30 4. Pressure/Equation of state
47:35 5. Heat capacities
54:40 Final results

If you want more problems on Statistical Physics, stay tuned to the channel, as I'll be uploading many problems on this playlist:

https://youtube.com/playlist?list=PLfYI1HSKgu4keuMWMCtE1W2cGt6cezYvD

Видео STATISTICAL PHYSICS PROBLEMS: MICROCANONICAL ENSEMBLE #1 канала Sandro’s Space