This textbook has been developed from 25 years of experience teaching seismology at the universities of Madrid and Barcelona. The text is at an introductory level for students in the last years of European licentiate or American upper-division undergraduate courses and at similar levels in other countries. As a first book, no previous knowledge of seismology, as such, is assumed of the student. The book's emphasis is on fundamental concepts and basic developments and for this reason a selection of topics has been made. It has been noticed that sometimes even graduate students lack a true grasp of the very fundamental ideas underlying some aspects of seismology. The most fundamental concepts are developed in detail. Simple cases such as one-dimensional problems and those in liquid media are used as introductory topics. Mathematical developments are worked out in complete detail for the most fundamental problems. Sometimes more difficult subjects are introduced, but not fully developed. In these cases references to more advanced books are given.

The book presupposes a certain amount of knowledge of mathematics and physics. Knowledge of mathematics at the level of calculus and ordinary and partial differential equations as well as a certain facility for vector and tensor analysis are assumed. Cartesian, spherical, and cylindrical coordinates and some functions such as Legendre and Bessel functions are used. Tensor index notation is used preferentially throughout the book. Fundamental ideas about certain mathematical subjects are given briefly in Appendixes 1–4.

There are many important systems that exhibit nonequilibrium or noncontinuum behavior. This final chapter examines some important examples of such systems. In doing so, we have two objectives. The first is to understand how, and under what conditions, the system behavior may deviate from the idealizations embodied in equilibrium theory or continuum theory. The second is to demonstrate theories and methods that are commonly used to model nonequilibrium and noncontinuum systems. Because they are commonly used to analyze such systems, kinetic theory and the Boltzmann transport equation are introduced. Nonequilibrium and noncontinuum phenomena associated with multiphase systems and electron transport in solids are examined in detail. The final section of Chapter 10 uses results from previous chapters to examine length scales and time scales at which classical and continuum theories become suspect. Doing so defines the range of conditions for which we expect classical and continuum theories to be accurate models of real physical systems. Although limited in its coverage, this chapter provides an introduction to microscale aspects of nonequilibrium and noncontinuum phenomena and serves to illustrate how they relate to the theoretical framework developed in the preceding chapters.

Basic Kinetic Theory

With increasing frequency engineers are dealing with microscale systems in which the applicability of classical macroscopic equilibrium thermodynamics becomes questionable. Generally, the applicability of classical equilibrium theory breaks down because the system is far from equilibrium and/or the system behavior deviates from a continuum model.

The statistical and classical thermodynamics framework developed in Chapters 1–8 of this text is based on analysis of systems at equilibrium. In Chapter 9 we explore the extension of this framework to systems that are not in equilibrium. This chapter focuses on systems that exhibit steady spatial variations of properties. Systems of this type are modeled as having local thermodynamic equilibrium and obeying a linear relation between fluxes and affinities. Analysis of microscale features of such linear systems is shown to link correlation moments and kinetic coefficients. The Onsager reciprocity relations are subsequently derived. Thermoelectric effects are examined as an example application of the nonequilibrium linear theory developed in this chapter.

Properties in Nonequilibrium Systems

The thermodynamic theoretical framework developed in previous chapters of this text is limited to analysis of equilibrium states. Often, however, it is the process that takes the system from one state to another that is of primary interest. Overall changes accomplished during the process can be determined by analyzing the initial and final states using equilibrium thermodynamics. If the process is very slow, it may be well approximated by a sequence of equilibrium states, and a quasistatic model may adequately predict the outcome of the process.

In many real processes, the departure from equilibrium is so severe that the quasistatic model is too inaccurate to be useful. The objective of this chapter is to develop thermodynamic tools that can be applied to irreversible processes in nonequilibrium systems.

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.

The structure of this book is designed to facilitate coherent development of classical and statistical thermodynamic principles. The book begins with coverage of microscale energy storage mechanisms from a modern quantum mechanics perspective. This information is then incorporated into a statistical thermodynamics analysis of many-particle systems with fixed internal energy, volume, and number of particles. From this analysis emerges the definitions of entropy and temperature, the extremum principle form of the second law, and the fundamental relation for the system properties. The third chapter takes the concepts derived from the statistical treatment and uses mathematical techniques to expand the macroscopic thermodynamics framework. By the end of the third chapter, the full framework of classical thermodynamics is established, including definitions of all commonly used thermodynamic properties, relations among properties, different forms of the second law, and the Maxwell relations.

In the fourth chapter, statistical ensemble theory is covered, building on the initial statistical treatment in Chapter 2 and the expanded macroscopic framework developed in Chapter 3. The canonical ensemble and grand canonical ensemble formalisms are developed, and the relations developed from these formalisms are used to explore the significance of fluctuations in thermodynamics systems. By the end of the fourth chapter all the fundamental elements of classical and statistical thermodynamics have been established. Chapters 5–7 deal with applications of equilibrium statistical thermodynamics to solid, liquid, and gas phase systems.

The final three chapters of the text cover thermal phenomena that involve nonequilibrium and/or noncontinuum effects.

The basic elements of statistical thermodynamics were developed in Chapter 2. In this chapter, we digress briefly from development of the statistical theory to expand the theoretical framework using mathematical tools and macroscopic analysis. By doing so we more strongly link the statistical theory to classical thermodynamics and set the stage for alternative statistical viewpoints considered in Chapter 4.

Necessary Conditions for Thermodynamic Equilibrium

In the previous chapter, we have derived several important pieces of information about thermodynamic systems. The goal of this chapter is to expand the framework of macroscopic thermodynamic theory so that it can be applied effectively to a variety of system types. We will begin by summarizing the important ideas developed in the last chapter.

So far, we have taken the volume V, internal energy U, and particle numbers Na and Nb, to be intrinsic properties for any system we may consider. We subsequently defined the properties entropy S, temperature T, pressure P, and chemical potentials µa and µb. Our analysis of the statistical characteristics of thermodynamic systems has led to the conclusion that for a system with fixed U, V, Na, and Nb, equilibrium corresponds to a maximum value of the system entropy. This is referred to as the entropy maximum principle. The entropy of a composite system with an arbitrary number of subsystems is additive over the constituent subsystems. This is the additivity property of entropy.