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8.044 Lecture Notes Chapter 6: Statistical Mechanics at ...

Lecture NotesChapter 6: Statistical Mechanics at Fixed Temperature(Canonical Ensemble)Lecturer: Derivation of the Canonical Ensemble .. Monatomic, classical, ideal gas, at fixedT.. Two-level systems, re-revisited .. Classical harmonic oscillators and equipartition of energy .. Quantum harmonic oscillators .. Heat capacity of a diatomic ideal gas .. Paramagnetism .. by adiabatic demagnetization .. The Third Law of Thermodynamics .. 6-42 Reading:Greytak, Notes on the Canonical Ensemble;Baierlein, Chapters 5, 13, Reading for :Greytak, Notes on (Raman Spectroscopy of) Derivation of the Canonical EnsembleIn Chapter 4, we studied the Statistical Mechanics of anisolatedsystem.

To recap, our answer for the equilibrium probability distribution at xed temperature is: p(fp 1;q 1g) = 1 Z e H 1(fp 1;q 1g)=(k BT) Boltzmann distribution This is the probability that system 1 is in the microstate labelled by fp 1;q 1gwhen it is in contact with a heat bath at temperature T (and in equilibrium). We derived this by

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