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