
Entropy as disorder:
We worked through a thought experiment in which we defined a
property called "microstates." Microstates (W) are
experimentally indistinguishable configurations that all give the
same experimentally distinguishable result. Boltzmann
quantified the entropy of a system based on the number of available
microstates:
S = kb ln W
A system will move spontaneously in the direction of increasing
number of microstates:
deltaS = kb ln(Wf/Wi) > 0
This defines both the direction of entropy and provides a molecular
level reason for quantifying the magnitude of change in
entropy. This also implies entropy is a state function,
because the function is defined only by the number of microstates,
which is a property of a system that is independent of how it
acquired those microstates.
Entropy as heat: We also defined entropy in
terms of the heat released by a system that is not available to do
work. When this heat is divided by T, the result is
a state function.
deltaS = q/T.

