capacity of crystals is considered more successful. Once again, because absolute
temperature and Dalways appear together as a ratio, Debye’s model of crys-
tals implies a law of corresponding states. A plot of the heat capacity versus
T/Dshould (and does) look virtually identical for all materials.
Both Einstein’s and Debye’s treatment of crystals are approximations in the
sense that they assume some ideal behavior. Like real gases, real solids do not
behave ideally. Regardless, application of statistical thermodynamics gives us a
starting point for the thermodynamic understanding of these systems, much
as the ideal gas law gives us a starting point for understanding the properties
of real gases.18.11 Summary
We have seen how statistical thermodynamics can be applied to systems com-
posed of particles that are more than just a single atom. By applying the par-
tition function concept to electronic, nuclear, vibrational, and rotational en-
ergy levels, we were able to determine expressions for the thermodynamic
properties of molecules in the gas phase. We were also able to see how statis-
tical thermodynamics applies to chemical reactions, and we found that the
concept of an equilibrium constant presents itself in a natural way. Finally, we
saw how some statistical thermodynamics is applied to solid systems. Two sim-
ilar applications of statistical thermodynamics to crystals were presented. Of
the two, Einstein’s might be easier to follow and introduced some new concepts
(like the law of corresponding states), but Debye’s agrees better with experi-
mental data.
It was stated at the beginning of the previous chapter that thermodynamics
is one topic in which ideas can be developed from two completely different
perspectives and arrive at the same conclusions. What these different perspec-
tives guarantee is a wide applicability of thermodynamics to virtually every as-
pect of chemistry.648 CHAPTER 18 More Statistical Thermodynamics