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This chapter gives an account of the statistical thermodynamics of pure fluids composed of non-spherical molecules. The early part of the chapter gives the derivation of equations for the various thermodynamic functions in terms of correlation functions and intermolecular forces, and includes discussion of quantum corrections and virial coefficients. The later parts of the chapter describe the application of molecular theory (perturbation theory, theory of hard non-spherical bodies, associating fluid theory) to the calculation of these properties, and compares these results with those from molecular simulations and experiments. The thermodynamics of nano-scale systems, in which some macroscopic laws and concepts may break down, are discussed at the end of the chapter. The mathematics of convex body geometry is given in an appendix.

Efforts to verify or invalidate hypotheses on the structure of liquid water have been hampered by the lack of a general theory of the liquid state. In the absence of such a theory, conclusions about the structure of water have been based on two approaches. The first involves formulating a model for liquid water, treating the model in a particular fashion — involving massive approximations — using methods of statistical mechanics, and comparing the calculated values of macroscopic properties with those that are observed. This chapter focuses on the second approach, which is to deduce aspects of the structure of the liquid from the macroscopic properties of water.

The properties of the real vapour, like those of ice and liquid water, are affected by the forces acting between the molecules. Studies of water in the vapour state have contributed to what is known about the interactions between water molecules. This chapter first considers the origin of these forces and their relation to the second and third virial coefficients of steam. It then discusses the thermodynamic properties of real vapour in detail.

This chapter describes the structure of ordinary ice and what is known of the structures of its polymorphs. It then outlines the thermodynamic, electrical, and spectroscopic properties of ice, and relates them to its crystal structure and to characteristics of the water molecule. The chapter closes with a discussion of hydrogen bonding and its role in determining the nature of ice.

The random energy model is probably the simplest statistical physics model of a disordered system which exhibits a phase transition. This chapter studies its thermodynamic properties and its phase transition, and describes in detail the condensation phenomenon at work in the low temperature phase. The same mathematical structure and techniques appear in a large number of contexts. This is witnessed by the examples from information theory and combinatorial optimization presented in the next two chapters.

This chapter discusses theoretical equations and models for analysing the velocity of sound in liquid metallic elements. It looks at the thermodynamic relationship between sound velocity and compressibility. It provides theoretical equations for sound velocity in liquid metallic elements; semi-empirical models for the velocity of sound in liquid metallic elements; and equations for the velocity of sound in terms of dimensionless new parameters. Finally, it offers an assessment of sound velocity models and experimental sound velocity data.

Sound velocity is one of the most basic thermodynamic properties of liquid metallic elements. Sound velocity also provides valuable information on transport, or dynamic, properties. This chapter predicts the melting point sound velocities in various liquid metals. These predicted sound velocities are then used to determine the common parameters for these liquid metals.

This chapter discusses the thermal properties of solids. A fundamental thermodynamic property of a body is its heat capacity, C ≡ dQ/dT, where dQ is an increment of heat transferred to the body and dT is the associated temperature change. When measured at constant volume (where no work is done by the sample on its environment), the heat added goes directly into increasing the internal energy, E. The internal energy is computed using the methods of statistical physics; which is briefly summarized. The remainder of the chapter analyzes the equipartition law for free and bound particles; the lattice heat capacity at low temperatures or the Einstein model; and the Debye model. Sample problems are also provided at the end of the chapter.