  The basic notions of statistical mechanics (microstates, multiplicities) are
quite simple, but understanding how the second law arises from these ideas
requires working with cumbersomely large numbers. To avoid getting bogged down
in mathematics, one can compute multiplicities numerically for a simple model
system such as an Einstein solid -- a collection of identical quantum harmonic
oscillators. A computer spreadsheet program or comparable software can compute
the required combinatoric functions for systems containing a few hundred
oscillators and units of energy. When two such systems can exchange energy, one
immediately sees that some configurations are overwhelmingly more probable than
others. Graphs of entropy vs. energy for the two systems can be used to
motivate the theoretical definition of temperature, $T= (\partial S/\partial
U)^{-1}$, thus bridging the gap between the classical and statistical
approaches to entropy. Further spreadsheet exercises can be used to compute the
heat capacity of an Einstein solid, study the Boltzmann distribution, and
explore the properties of a two-state paramagnetic system.
