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Once again we note the pattern a is a spontaneous

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Unformatted text preview: nt because we have illustrated that3 × (⅛) for Cases 3 and 4. is results in the histogram shown to the right for three f individual molecules seeking a particular distribution between indistinguishable molecules. Once again, we note the pattern: (a) ) is a spontaneous process based on a purely statistical treatment ere are n + 1 = 3 + 1 = 4 possible states (or or involve the internal energy, the encon gurations), and (b) the higher probability cases are those for which there no point did we discuss antity associated with is the most scale. So we now have between the two chambers. an energy balanced distribution another e concept of spontaneity: A spontaneous process moves from The Case for 10 bability to states of higher probability. We also notice something Molecules e: e states of lowest probability are characterized by a more FIGURE 4.13 As we continue to add ion—for example, if all the molecules are sequesteredstates molecules to the system, counting the in one more ordered con guration; just asa is the caseto each the clothes and assigning probability of all arrangeult, but we can g folded and placed in ment becomes more di isclink between proba single drawer! begin to see a general trend start processes Ten Molecules y, and order will loom large in our understanding of to emerge. in For example, we can see from the histograms Imagine now if we move from 100 molecules probability ofmole of for ten molecules that the to a single the 23 ber system. Now we have 6 × 10being distributed roughlyhistogram molecules molecules and the equally between each of the the center. cule distribution is a very narrow spike attwo sides is much more : 4.9 probable than the distribution being skewed to either the right or the left side. experience that when we place a hot object in contact with a al energy will ow spontaneously from the high temperature emperature body. But why is this? Does it have anything to do With order and disorder? 4.11 shown in Figure 4.11. ecules is straightforward, so we will keep addOnce again, we note the pattern: (a) ere are n + 1 = 3 + 1 = 4 possible states ing molecules to the system and nd out how (or conMolecules and (b) the higher probability cases are those for which there Chapter The Case the probability of each con guration changes. 4 for 2 gurations), isFor three identical molecules, eight di between the two chambers. the most balanced distribution erent L5/6763.308 L5/6763.308 L5/6763.308 Three Molecules arrangements are possible, but only four of Spontaneity and Probability these are distinct. For the arrangements of for 10 Molecules Case The Case for oceed to consider the case for 10 molecules in Figure 4.13, we3 Molecules the left and Themolecules two molecules on two counting becomes rapidly more di Theult (or tedious!), but the the of lowthe states can be realized by arc initial case of two mol- on right, probability to states of high probFIGURE 4.12 FIGURE 4.13 As we continue to add ranging the atoms in three di erent ways, so mes more pronounced:eculeshistogram peaks in the middle, cor- ability.the system, counting the states e is straightforward, so we will keep add- molecules to these ing molecules tobetween the twodchambers,...
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