2 Basic ideas
- a smallnumber ofpairs ofthermodynamic co-ordinates – e.g. pressurePand
volumeV;magnetic fieldBand magnetizationM;surface tension and surface
area, etc.Eachofthese pairsis associatedwithawayofdoingworkon thesystem. For many
systems onlyP−Vwork is relevant, and (merelyfor brevity) we shall phrase what
follows in terms ofP−Vwork only. Magnetic systems will also appear later in the
book.
In practice the two co-ordinates specified, rather than beingPandV,will be those
appropriate to the external conditions. For instance, the lump of copper might be ata
specificpressureP(= 1 atm) andtemperatureT(= 450 K). In this case the macrostate
would be defined byPandT;and the volumeVand internal energyUandother
parameters would then all be determined in principle fromPandT.It is precisely
one oftheobjectives ofstatisticalphysics to obtainfromfirst principles what are
these values ofV,U, etc. (In fact, we need not set our sights as low as this. Statistical
physics also givesdetailedinsightsintodynamicalproperties, andan exampleofthis
isgiveninChapter 12.)
Now comes, by choice, an important limitation. In order to have a concrete situation
todiscussinthischapter (andindeedthroughout thefirst eightchapters ofthisbook),
we shallconcentrate on one particular type ofmacrostate,namelythat appropriate
to an isolated system.Therefore the macrostate will be defined by the nature of the
substance, the amount, andbyUandV. For theisolatedsysteminits energy-proof
enclosure, theinternalenergy isafixedconstant, andVisalso constant since nowork
is to be done on the system. The (fixed) amount of the substance we can characterize
bythe numberNofmicroscopic ‘particles’ making up the system.
Thislimitationis not too severein practice. For anisolatedsysteminwhich
Nis reasonably large, fluctuations in (say)Taresmallandonefinds thatTis
determinedreally rather preciselyby(N,U,V).Consequently one can use results
based onthe(N,U,V)macrostate in order to discuss equallywell the behaviour in
any other macrostate, such as the(N,P,T)macrostate appropriate to our piece of
copper.
Towards the end of the book (Chapters 12 and 13, inparticular), we shall return to
the question as to how to set up methods of statistical physics which correspond to
other macrostates.
1.2 Microstates
Let us now consider the mechanical microscopic properties of the system of inter-
est, which we are assuming to be an assembly ofNidentical microscopic particles.
For thegiven(N,U,V)macrostate there are an enormous number ofpossible
‘microstates’.
The wordmicrostate means the mostdetailedspecification ofthe assemblythat
canbeimagined. For example,intheclassicalkinetictheoryofgases, themicrostate