1 0 Entropyin other situations
Asthechartinthefront ofthebookshows, wehave now completedour elementary
studyofthethermalequilibrium properties ofidealsolidsandgases. However,it
would be a pity to stop here, since statistical physics has plenty more to say about
other types ofsystem also. In thischapter we shall lookagain at entropy, andshall
discuss the statistics ofasysteminwhichthe macrostate specifiesTratherthanU.
This generalization will help us to discuss vacancies in solids in this chapter, and
phase transitionsinthe next.
1 0.1 Entropy and disorder
InChapter 1, we tookas a statisticaldefinition ofentropytherelationS=kkkBln
(equation (1. 5 )). Since many verifiable results have followed, we may by now have
muchconfidenceinthe approach.Inthischapter we study somefurther consequences
oftherelation.10.1.1 IsotopicdisorderOne simpleform ofdisorderinasolid isisotopicdisorder. Forinstance ablockof
copper consists of a mixture of^63 Cuand^65 Cu isotopes. Therefore, if the isotopes
are randomly distributed on the lattice sites, there will be a large amount of disorder
associatedwithallthe possible arrangements oftheisotopes.
Consider a solid whoseNatoms have aproportionPLof isotope L. In other words,
there areNNNL=PLNatoms of isotope L, and∑
LNNNL=N,where the sum goes over
alltheisotopes. The number ofarrangements ofisotopes on theNsitesisgivenby
the well-trodden thirdproblem of Appendix A. It is=N!/
∏
L