13. How To Measure Disorder
THE STATISTICAL MEANING OF ENTROPY
 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.
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