In this chapter, we make the connection between molecules and thermodynamics. Until this chapter, we have dealt only with macroscopic quantities, and the influence of molecular details has been discussed only qualitatively. Here, we make quantitative connections between molecules and much of the thermodynamics we have already seen. For example, we derive the fundamental relations for ideal gases (simple and general), molecular adsorption on solid surfaces, and the elasticity of polymer chains. The procedure is general, and may be used to derive fundamental relations for more complex systems, to relate macroscopic experimental results to molecular interactions, or to exploit computer simulations. Since statistical mechanics deals with more detailed information than does classical thermodynamics, we can also find how real systems fluctuate in time when at equilibrium. We will see that these fluctuations are important for all systems, and can even dominate the behavior of fluids near a critical point (or spinodal curve) or that of small systems.
This chapter is not essential for understanding most of the rest of the book. However, the remaining chapters will also have a few sections dealing with the statistical mechanics of mixtures and polymers, and the material in this chapter is essential for understanding those topics. Statistical mechanics is both beautiful and powerful, but often difficult to grasp the first time you see it. However, we believe that statistical mechanics, like thermodynamics, rewards the student who visits it repeatedly.