L04 Canonical ensemble

Readings (reference material)

• Reading Kittel Ch. 3
• Reading Sethna Ch 6.1, 6.2

Notes

Lecture 03 class notes

Ensembles

• A statistical ensemble is a collection of all accessible microstates of a system with associated probabilities.
• Canonical ensembles are the collection of possible states of a mechanical system in thermal equilibrium with a heat bath (or reservoir) at a fixed temperature T
• A microcanonical ensemble is a completely closed/isolated system

Helmholtz free energy

$F=TS-E$

$=-kTln(Z)$

$dF=-SdT-PdV$

From which we have:

${\displaystyle S={-\left(\frac{\partial F}{\partial T}\right)|}_{V,N},P={-\left(\frac{\partial F}{\partial V}\right)|}_{T,N},\mu ={\left(\frac{\partial F}{\partial N}\right)|}_{T,V}.}$

Ideal gas partition function

https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Statistical_Mechanics/Boltzmann_Average/Ideal_Gas_Partition_Function

Partition function to get functions of state

• Using the partition function to obtain functions of state