Using the basic features of microscale energy storage discussed in Chapter 1, in Chapter 2 we develop the foundations of statistical thermodynamics. In doing so, we introduce the concepts of microstates and macrostates and properly account for the fact that particles in fluid systems are generally indistinguishable. The development of the theoretical framework in this and subsequent chapters considers a binary mixture of two particle types. The statistical machinery is applied first to a microcanonical ensemble of systems, each having a specified volume, number of particles, and total internal energy. Definitions of entropy and temperature emerge from this development. Application of the results to a monatomic gas is discussed.

Microstates and Macrostates

In this chapter we will construct a general statistical mechanics foundation on which we will develop a full equilibrium thermodynamic theory for systems composed of a large number of particles. In doing so we will make use of the information about energy storage derived from quantum theory in the previous chapter.

In analyzing systems of particles, we can deal with the state of a system at two levels: the microstate of the system and the macrostate of the system. The system microstate is the detailed configuration of the system at a microscopic level. To specify the microstate we would have to specify the quantum state (including the position) of each particle in the system. If we observe a system at a macroscopic level, we can, at best, distinguish some of the gross characteristics of the system.