Lecture 2 : Canonical Ensemble and the Partition Function Dr. Ronald M. Levy [email protected]...
-
Upload
austin-parrish -
Category
Documents
-
view
239 -
download
4
Transcript of Lecture 2 : Canonical Ensemble and the Partition Function Dr. Ronald M. Levy [email protected]...
Lecture 2 : Canonical Ensemble and the Partition Function
Dr. Ronald M. Levy
Statistical Thermodynamics
Ensemble and Canonical Ensemble:Ensemble: An idealization consisting of a large number of similar systems
Canonical Ensemble:An ensemble with the same Number of molecules, Volume and Temperature, but different Energy per system. (N, V, T)Step 1: Ensemble placed in heat bath to
equilibrate at T.Step 2: Ensemble surrounded by
thermal insulation: Total energy fixed.
Ensemble and Canonical Ensemble
E1
E2 E1
(NVT)
E2
E1
In principal, these are energy
eigenvalues of quantum states
2
Constraints on the distribution
Most probable distribution
Total number of members of the ensemble fixed
Total energy of the ensemble fixed
Any distribution which satisfies constraints above is a possible distribution for the ensemble
If each energy level is distinctEliminating over counting
3
Canonical partition function
Average statistical mechanical energy
of the system
Stat Mech:Average statistical mechanical energy
ThermodynamicsInternal Energy
6
Supplementary material
Pressure on system
Work done on the system
Change of ensemble internal energy Work
9