The important physical quantity in the equation is the number of
ways of obtaining a given state, W. There is only one way of putting
together a perfect crystal, provided of course that the molecules
are indistinguishable from one another (lower right).
For a perfect crystal with motionless molecules at absolute zero,
W = 1 and S = k ln 1 = O. In contrast, if we were molecular architects
we would find that there are many ways of building a litre of gas
at a given temperature and pressure, all of which would look identical
to the outside world (upperright).
For example, the individual positions of molecules in a gas do
not have to be specified, nor do their individual speeds.
All that is required is that the total number of molecules of each
kind and the total energy per mole be known; all gases that satisfy
these conditions will appear alike to a macroscopic observer.
The number of ways of constructing a mole of gas is greater than
for a crystal; W is large, so ln W is a positive number, and S =
k ln W is greater than zero.
