Thermodynamics (statistical): Boltzmann distribution derivation

Derivation of the Boltzmann distribution from the canonical ensemble.
*NOTE:* I made a mistake at 11:30. Where I wrote Σ nj ! it should be Σ ln nj ! (I left out the "ln"). The correct value appears later at 17:30.

00:14 Introduction
00:30 Canonical ensemble
03:44 Two constraints
05:21 Number of ways to achieve distribution (Ω)
08:03 Stirling's approximation
09:36 ln Ω
11:30 See *NOTE* above; there is a omission here.
14:34 Lagrange's method of undetermined multipliers
16:15 Derivative of ln Ω
18:02 Apply Stirling's approximation twice
20:53 Derivative of N ln N
27:14 Full derivative equations
30:36 Use of definition of N
33:20 Canonical ensemble partition function Q
35:08 Boltzmann distribution

Don't forget to like, share, and subscribe!

Видео Thermodynamics (statistical): Boltzmann distribution derivation канала lseinjr1