PU-203 · Thermal & Statistical Physics I
From entropy and the second law to the statistical origin of temperature, and where classical counting fails.
Bring these before lecture 1
Assumes the variational machinery of PU-201 · Classical Mechanics (in particular Lagrange multipliers, used to maximise entropy under constraint) and the phase-space picture from PU-201. The multiplier argument leans on the stationary-action habit built in D-018.
Lectures
| L18 |
Carnot & the second law
cites D-015
|
26 min |
| L24 |
Maxwell relations from the potentials
cites D-016
|
21 min |
| L27 |
The Boltzmann factor
cites D-013
|
24 min |
| L31 |
Equipartition and the ultraviolet trouble
cites D-020
|
28 min |
Showing 4 of 32 · Wave 1
Derivations homed in this unit
The Boltzmann distribution from maximum entropy
Maximise Gibbs entropy under fixed mean energy; the Lagrange multiplier is temperature.
The Maxwell–Boltzmann speed distribution
From the Boltzmann factor to the distribution of molecular speeds in an ideal gas.
Carnot efficiency from the second law
A reversible cycle between two reservoirs bounds every engine; efficiency depends only on temperatures.
The four Maxwell relations
Equality of mixed second derivatives of the thermodynamic potentials.
Sackur–Tetrode entropy & the Gibbs paradox
Counting indistinguishable microstates fixes the additive constant and resolves the mixing paradox.
Equipartition, and the failure that demanded quanta
Where classical counting predicts infinite energy — the crack that opened quantum theory.