02. Kinetic theory, statistical mechanics

Slides and transcripts: drive.google.com/drive/folder...
At 1:31:05 I'm inconsistent with the use of E_sys and U_sys: apologies for that.
0:00:00 Recap of previous video
0:01:36 Ideal gas law
0:08:04 Equipartition theorem
0:13:43 Maxwell's velocity distribution
0:18:36 Boltzmann's combinatorics
0:42:14 Boltzmann entropy
0:49:47 Quasi-static processes
0:53:54 Exponential distributions
0:55:13 Lagrange multipliers
0:58:31 Distinguishability
1:02:21 Phase space, coarse graining
1:10:11 Gibbs paradox
1:17:44 Thermodynamic quantities from entropy
1:23:32 Fundamental thermodynamic relation, Lagrange multipliers
1:26:00 Chemical potential in chemical reactions
1:29:20 System interacting with reservoir
1:37:20 Gibbs entropy
1:43:06 Partition function
1:48:08 Statistical ensembles
1:50:25 Summary

[@JohnSmall314]

This is excellent content

[@StefanHoffmann84]

29:33 As far as I understand, the table does not match the shown configuration above? For example, in the picture slot one is occupied by partition one but not in the table where partition one occupies slot five. Is this intentional?

[@SanderKonijnenberg]

You are correct that the table does not represent the illustration above it, but rather another random configuration just to show a different example. I guess it's indeed debatable whether such an example is optimal from a didactic perspective.

[@NicolasSchmidMusic]

At 48:22 how does the 3/2 * ln(.../T) transform into 3/2 * ln (T) + Const ? isn't there a minus sign missing there?

[@SanderKonijnenberg]

The minus sign comes from the equation at the very top of the slide: ln(Omega)=C-integral. In the equation at the bottom of the slide, we calculate the integral, so we need to take its negative to find ln(Omega). That's also why ln(N/V) becomes ln(V/N) after the arrow.