This preview shows page 1. Sign up to view the full content.
Unformatted text preview: e molecules are
) = (¼
not zero. So, we can o er
Perspectivelogic applies to H..,532*0if
the right-hand chamber; the probability of of 3 × (⅛) for Cases 3 and 4. is results in
on of spontaneity by saying ButOne same le and two in the right:
4. the in the
indistinguishable we have a probability nding
ess moves from states of
bothSuppose wein the le -the behavior)–( is (½)(½) =in¼). e probability of ndmolecules examine hand chamber AB )
( C of molecules ( a two-chamber apparatus,
tes of high probability. In this example, we see that the lowest probabilitythe histogram shown to the right for three indistinguishable molecules.
ing onein Figurethein the le chamber )–( AC )again, we note the pattern: (a) eis are n + 1 = 3 + 1 = 4 possible states
and one molecule in the right chamber re
that are relatively ordered, i.e. a large fraction of
gas molecules can B
½. and the states of high probability are(or)–( BC urations), and (b) the higher of two
( A con g )
he right or the left of the container; us, we construct our histogram accordingly. Notice that for our case probability cases are those for which there
The Case for 2 Molecules
e the system is relatively disordered.
identical molecules, there are three (n + 1) possible con gurations and that there L5/6763.308 Determination of Probability at the
Molecular Level 4.9 L5/6763.308 L5/6763.308 L5/6763.308 is the most balanced distribution between the two chambers.
But while each con g nding the molecules evenly has the same probability
is a higher probability ofuration of the three moleculesdistributed between the two
Spontaneity and Probability
if we distinguish the individual molecules
usion that we draw fromchambers. progression is of great prac- ((½)(½)(½) = ⅛), if the molecules are Molecules
The Case for 10
oceed to consider theimportant10 molecules in a illustrated for 3 Molecules
ndistinguishable we have probability we
cal) importance. It is icase for because we haveFigure 4.13,that3 × (⅛) for Cases 3 and 4. is results in
counting becomes rapidly moreparticular(or tedious!),between indistinguishable molecules. probFIGURE 4.12 c initial case of two but FIGURE f .13 As we continue to of high
the histogram heult to the right for the
f individual molecules seeking a di Tshowndistributionmol- three o4low probability to states add
mes spontaneous process based on a purely sso we will keep add- molecules to n + system, counting ossible states
more pronounced:eculeshistogram we note the pattern: (a) ere are the 1 = 3 + 1 = 4 p the states
e is straightforward, in the middle, corOnce again, peakstatistical treatment ability.
) is a
ing molecules the system and ndchambers,
molecules being distributedinvolvetobetween the energy, the en- assigning a probability to each arrange-there
(or con gurations), con guration changes.and
no point did we discuss or equallyof eachand (b)two higher probability cases are those for which
the probability the i...
View Full Document