Boltzmann made the crucial connection between thermodynamic entropy
and disorder. Any situation that is so definite that it can be put
together only in one or a small number of ways is recognized by
our minds as orderly. Any situation that could be reproduced
in thousands or millions of different but equivalent ways is disorderly.
Boltzmann's law tells us that the most perfect, orderly object
conceivable in the universe would be a perfect crystal at absolute
zero. Anything elsea crystal at any temperature above 0ēK, a liquid,
a gas, or a mixture of substancesis more disordered and has a positive
entropy. The higher the entropy, the greater the disorder.
When we combine Boltzmann's ideas with thermodynamics, we arrive
at one of the most important principles of science: In any real,
spontaneous processes, including chemical reactions, the disorder
of the universe always increases. In any isolated system, in which
the total energy does not change, a spontaneous reaction is one
in which entropy (and disorder) increases.

Any process that produces order, or lowers the entropy, cannot
occur without outside help. If we supply enough energy, we can make
a reaction occur even though the entropy decreases in the process.
If we do not supply enough energy, a reaction leading to increased
order will not take place.
The two ways of looking at entropythermodynamic and statisticalare
contrasted at the top of these two pages.
The thermodynamicist measures heats of processes, and calculates
from them a numerical value for the thirdlaw entropy, S^{0}_{298},
of the substance.
The theoretician can compute from the known amount of disorder
in a substance what its entropy should be. If his estimate of disorder
and his subsequent calculations are valid, he will arrive at a final
number that agrees with the value that was measured from heat experiments.
