The ideal gases considered in Chapter 5 are arguably the simplest fluids encountered in real systems. The behavior of dense gases, liquids, and quantum fluids deviates strongly from that of an ideal gas. In this chapter, we examine how the thermodynamic framework developed in earlier chapters can be applied to such fluids. The van der Waals model for dense gases and liquids is explored in detail for pure and binary mixture systems. In doing so, we demonstrate that the statistical thermodynamic framework provides a link between microscopic characteristics of the molecules or particles and the macroscopic behavior of these fluids.

Behavior of Gases in the Classical Limit

In Chapter 5, we observed that if the temperature is high enough, we can replace the summation in the definition of the partition function with an integral to obtain the limiting form the partition function at high temperature. This reflects one of the fundamental characteristics of quantum theory, which is that classical behavior is attained in the limit of large quantum number. At high temperature, the average energy per molecule increases and this implies that the average quantum number for each energy storage mode is higher. Thus at higher temperatures, the mean behavior of the system is classical in nature.

In the previous sections of this text we have attacked the problem of determining the partition function by considering the problem from a quantum perspective.