Lecture 3: Other Ensembles and

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Lecture 3: Other Ensembles and Statistical Thermodynamics Lecture 3: Other Ensembles and Fluctuations Dr. Ronald M. Levy ronlevy@temple.edu

Thermodynamic connection Other ensembles Partition function Thermodynamic connection (1) (2) (3) Gibbs free energy (4) (5) (6) 1

Equivalent information Microcanonical entropy canonical entropy (7) (8) states energy (9) Rapidly increasing function of E Rapidly decreasing function of E Sharply peaked function 2

Equivalent information (10) (11) (12) (13) (14) 3

Energy fluctuation in canonical ensemble and CV 4

Energy fluctuation in canonical ensemble and CV (14) (15) (16) 5

(17) (18) (19) 6

Canonical distribution (20) (21) 7

Canonical distribution (22) (23) (24) 8

Canonical distribution In general, a canonical ensemble is a distribution over microcanonical ensembles, it “degenerates” to microcanonical ensemble. In the microcanonical ensemble, the energy of the system is fixed, there are no energy fluctuation. In canonical ensemble, only the average energy is fixed. 9

Grand canonical partition function (25) N: # molecules j: states (26) (27) 10