Summary 11betweenSandissuggested,andmoreover a monotonically increasingone,in
agreement with (1. 5 ).- For a composite assembly, madeupoftwo sub-assemblies1and2 say, wehave
shown in section 1. 6 .2 that the number of microstates of the whole assembly
is given by= 1 · 2 .The required behaviour of the thermodynamic entropy
isofcourseS=S 1 +S 2 , and the relation (1.5) is consistent with this; indeed
thelogarithmistheonly function whichwill give the result. (This was Planck’s
original ‘proof’ of (1. 5 ).)
3 .The correlationbetween entropyandthe number ofmicrostates accessible(i.e.
essentiallya measure of disorder) is a veryappealingone. It interprets the third
law of thermodynamics to suggest that all matter which comes to equilibrium will
orderat theabsolute zerointhe sense that onlyone microstate will be accessed
(= 1 correspondingtoS=0, a natural zero for entropy).
Later in the book, we shall see much more evidence in favour of (1.5), the final
testbeingthat the resultsderivedusingit are correct,for examplethe equation of
state of an ideal gas (Chapter 6), and the relation of entropy to temperature and heat
(Chapter 2).
1 .8 Summary
In thischapter, themainideas ofa statisticalapproachto understandingthermal
properties are introduced. These include:
Statisticalmethods are neededas abridgebetween thermodynamics (toogeneral)
and mechanics(too detailed).
Thisbridgeis readily accessibleifwe restrict ourselves to a system whichcanbe
consideredas an assemblyofweakly-interactingparticles.
Three ways of specifying such a system are used. The macrostate corresponds
to thethermodynamic specification, basedon afew externalconstraints. The
microstateisafullmechanicaldescription,givingallpossibleknowledgeofits
internal configuration. Between these is the statistical notion of a distribution of
particles whichgives moredetailthan the macrostate,butless than themicrostate.
4 .The numberofmicrostates whichdescribeagiven macrostate plays a central
role. The basic assumption is that all (accessible) microstates are equally probable.
If we define entropy asS =kkBln,then thisisagoodstartin our quest to
"understand" thermodynamics.