Lecture 34—Grand canonical ensembleLecture 34—Grand canonical ensembleChapter 9, Monday April 7Chapter 9, Monday April 7thth

•The Grand canonical ensemble

•The grand potential

•Some examples

•Quiz

Reading: Reading: All of chapter 9 (pages 188 - 207)All of chapter 9 (pages 188 - 207)Homework 9 due Wed. Apr. 9th at 5pmHomework 9 due Wed. Apr. 9th at 5pmAssigned problems, Assigned problems, Ch. 9Ch. 9: 2, 4, 6, 8, 10: 2, 4, 6, 8, 10Exam 3 next Friday (18th), Chs 8-10Exam 3 next Friday (18th), Chs 8-10Review next week (time/place TBA)Review next week (time/place TBA)

Microcanonical ensembleMicrocanonical ensembleE, V and N fixedS = kB lnW(E,V,N)

Canonical ensembleCanonical ensemble

T, V and N fixedF = kBT lnZ(T,V,N)

Grand canonical ensembleGrand canonical ensemble

T, V and fixed = kBT ln (T,V,)

Grand canonical ensembleGrand canonical ensembleGrand partition function:

/. .j j BE N k T

j j jj

e i e E E N

/ /

/

i i B i i B

j j B

E N k T E N k T

i E N k T

j

e ep

e

Grand canonical ensembleGrand canonical ensembleGrand potential:

lnG Bk T U N TS F N

Gd PdV Nd SdT

, ,

, ,

, ,

ln

ln

ln

BG

V V

BG

T T

BG

T V T V

k TS

T T

k TP

V V

k TN