13. How To Measure Disorder   Previous PageNext Page

For crystals and gases, Wc = 4 and Wp = 122; thus a gas is more than 30 times as likely to occur as a crystal.

If we were to repeat the experiment with four atoms in a 4 x 4"universe" or box, we would find that

different arrangements would be possible, of which 9 would be crystals and 1811 would be gases (left). In that universe a gas would be more than 200 times as probable as a crystal. When we jump to the real world, with many times Avogadro's number of atoms and many, many places for atoms to be, W becomes astronomical. It is easier to use a logarithmic representation in which 10, 10,000,000, and 100,000,000,000,000 (or 101, 107, and 1014) are reduced to a more manageable 1, 7, and 14. The entropy, S, is simply the number of ways of obtaining a given state of matter, expressed logarithmically instead of linearly:

S = k ln W = 2.303 k log10 W

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