PREFACE TO THE SECOND EDITION The present volume is an upgraded version of a reference text published by Elsevier under the same title in 1982. The goals of the presentation have re- mained unaltered: to provide a self-contained exposition of the main areas of thermodynamics and to demonstrate how from a few fundamental concepts one obtains a whole cornucopia of results through the consistent application of logic and mathematical operations. The book retains the same format. However, Section 1.16 has been com- pletely rewritten, and several new sections have been added to clarify concepts or to add further insights. Principal among these are the full use of thermody- namic information for characterizing the Joule-Thomson effect, a reformula- tion of the basic principles underlying the operation of electrochemical cells, and a brief derivation of the Onsager reciprocity conditions. Several short sections containing sample calculations have also been inserted at locations deemed to be particularly instructive in illustrating the application of basic principles to actual problems. A special effort has also been made to elimi- nate the typographical errors of the earlier edition. The author would appre- ciate comments from readers that pertain to remaining errors or to obscure presentations. It remains to thank those whose diligence and hard work have made it possible to bring this work to fruition: Ms. Virginia Burbrink, who undertook much of the enormous task of converting the typography of the earlier edition to the present word processor format; Ms. Gail Shively, who completed this onerous task and patiently dealt with all of the unexpected formatting prob- lems; and Ms. Sophia Onayo, who compiled the index and the table of contents. ix X ECAFERP TO THE SECOND EDITION Purdue University has provided a very comfortable milieu in which both the writing and the later revision of the book were undertaken. It is a pleasure to express my appreciation to various individuals at Aca- demic Press who encouraged me to prepare the revised text and who were most cooperative in getting the book to press. Last, this task could not have been completed without the support of my beloved wife, Josephine Vamos Honig, who gave me much moral support after the death of my first wife, as well as during the book revision process, and to whom I shall remain ever grateful. j. M. Honig Purdue University PREFACE TO THE FIRST EDITION The publication of yet another text on the well-explored topic of thermodynam- ics requires some commentary: such a venture may be justified on the grounds that as scientists our perceptions of any subject matter continually change; even as traditional and established an area as chemical thermodynamics si not ex- empt from such a subtle transmutation. Thus, there appears to be merit in a continuing series of expositions of the discipline of thermodynanics that differ perceptibly from linear combinations of discussions found in prior texts and monographs. In the present volume there occur several departures from conventional treatments, among them: )i( the presentation of the Second Law based on a simplified approach to Carath(~odory's method; (ii) a reasonably comprehensive treatment of thermodynamics of systems subjected to externally applied fields~ special emphasis has been placed on the systematics of electromagnetic fields and on gas adsorption processes, concerning which there has been much con- fusion; (iii) detailed investigations on the uniqueness of predictions of properties of solutions, in the face of a bewildering array of standard states, of methods for specifying composition, and of equilibrium constants; (iv) a rationalization scheme for the interpretation of phase diagrams; )v( a discussion of the ther- modynamics of irreversible processes, centered on the macroscopic equations. Most of the above topics are not covered in detail in existing texts. Throughout, emphasis has been placed on the logical structure of the the- ory and on the need to correlate every analysis with experimental operating conditions and constraints. This si coupled with an attempt to remove the mys- tery that seems so often to surround the basic concepts in thermodynamics. xi Xll oo ECAFERP TO THE FIRST EDITION Repeatedly, the attention of the reader si directed to the tremendous power inherent in the systematic development of the subject matter. Only the classical aspects of the problem are taken up; no attempt has been made to introduce the statistical approach, since the subject matter of classical thermodynamics is self- consistent and complete, and rests on an independent basis. The course of study si aimed at graduate students who have had prior expo- sure to the subject matter at a more elementary level. The author has had reason- able success in the presentation of these topics in a two-semester graduate class at Purdue University; in fact, the present book si an outgrowth of lecture notes for this course. No worked numerical examples have been provided, for there exist many excellent books in which different sets of problems have been worked out in detail. However, many problems are included as exercises at various levels of difficulty, which the student can use to become facile in numerical work. The author's indebtedness to other sources should be readily apparent. He profited greatly from fundamental insights offered in two slim volumes: -issalC lac Thermodynamics by H. A. Buchdahl and Methods of Thermodynamics by H. Reiss. Also, he found instructive the perusal of sources, texts, and mono- graphs on classical thermodynamics authored by C. J. Adkins, .I .V Bazarov, H. .B Callen, .S Glasstone, .E A. Guggenheim, G. N. Hatsopoulos and J. H. Keenan, .W Kauzmann, J. Kestin, R. Kubo, .P .T Landsberg, .F H. MacDougall, A. MOnster, A. .B Pippard, .I Prigogine, .P .A Rock, and M. .W Zemansky. Spe- cific sources that have been consulted are acknowledged in appropriate sections in the text. He si greatly indebted to Professor .L .L Van Zandt for assistance in formulating the thermodynamic characterization of electromagnetic fields. Most of all, he has enormously profited from the penetrating insight, unrelenting criticism, and incisive comments of his personal friend and colleague Professor J. .W Richardson. Obviously, the remaining errors are the author's responsibil- ity, concerning which any correspondence from readers would be appreciated. It si a pleasant duty to acknowledge the efforts of several secretaries, Jane Biddle, Cheryl Zachman, Nancy Holder, Susan Baker, and especially Konie Young and Barbara Rosenberg--all of whom cheerfully cooperated in trans- forming illegible sets of paper scraps into a rough draft. Special thanks go to Hali Myers, who undertook the Herculean task of typing the final version; without her persistence the manuscript could not have been readied for publi- cation. Dr. Madhuri iaP contributed greatly by assisting with the proofreading of the final manuscript. In a matter of personal experience, it si appropriate to acknowledge several meaningful discussions with my father, the late Richard M. Honig, who was an expert in jurisprudence and who readily saw the parallels between scientific methodology and the codification of law. He persisted with questions concern- ing the nature of thermodynamics that I could not readily answer and was thereby indirectly responsible for the tenor of the present volume. Last, it si important to thank my immediate family, particularly my beloved wife, Trudy, for much patient understanding and for many sacrifices, without which the work could have been neither undertaken nor completed. j. M. Honig July 1891 Chapter i FUNDAMENTALS .I 0 INTRODUCTORY COMMENTS In this chapter the fundamental concepts of thermodynamics are introduced in the form of the four basic laws. The procedure is reasonably axiomatic, so that one can deal with )i( the concept of temperature without initially having to refer to heat flow; (ii) the definition of energy as a function of state, after a general introduction to the concept of forces; (ill) the derivation of the entropy function by use of Carath~odory's Theorem, rather than by generalization of performance characteristics of heat engines. A variety of functions of state are then introduced and considerable emphasis is placed on systematically exploiting their mathematical properties. Lastly, the important concept of homogeneous functions is introduced, and used to provide a framework for analyzing the properties of open systems. We end with a discussion of stability problems. The reader should examine not only the individual steps in the derivation, but also the internal structure of every presentation, the exploitation of Maxwell's equations, and the relation between commonly used thermodynamic functions, and experimental information, such as equations of state. .i I INTRODUCTORY DEFINITIONS To understand the concepts of thermodynamics we must agree on the meaning of some basic terms discussed below: 2 I. FUNDAMENTALS )a( System" A region of the universe set apart from the remainder of the cosmos for special study. )b( Surroundings" Regions immediately outside of and contiguous to the system under study. )c( Boundaries" Partitions that separate the system from its surroundings. Commentary" It is of the utmost importance to delineate a system adequately and to distinguish it properly from its surroundings. Failure to do this leads to nonsensical and paradoxical results. The boundaries may represent either actual physical constraints such as walls, or conceptual designs such as geometric surfaces. )d( Body" The total physical contents of a specified region of the universe. Commentary" In order to be able to describe physical properties of the body or to carry out measurements that do not disturb the characteristics of the body, its volume must be large compared to the atomic scale, typically at least 10 51- cm 3 in s ize. )e( Homogeneous and Heterogeneous System" A homogeneous system is uniform throughout in all its physical properties. A heterogeneous system comprises several different homogeneous parts in close proximity. )f( Subsystem" A portion of a system, singled out for special study. )g( Continuous System" One whose physical properties vary continuously as a function of position within the system. )h( Open (Closed) Systems" Systems in which an exchange of matter with its surroundings is (is not) allowed to occur. )i( Permeable Boundaries" Boundaries that enclose an open system. )j( Semipermeable Boundaries" Boundaries that permit passage of certain chemical species, but that are impenetrable to others. )k( Diathermic Boundaries" Boundaries impermeable to matter flow but which permit other changes to occur inside the enclosed system through heating or cooling of the surroundings. YROTCUDORTNI SNOITINIFED 3 )I( Adiabatic Boundaries and Systems" Boundaries that are impervious to matter flow and that render the enclosed system totally unresponsive to processes in which the surroundings are heated or cooled. )m( Isolated System" One that is surrounded by boundaries which render the enclosed system totally unresponsive to any changes in the surroundings. Commentary" For a distinction between adiabatically isolated and completely isolated systems, see Exercise i.i.7. One should also note that systems may be perturbed through external manipulations of applied fields (e.g. , electric, magnetic, radiation, or gravitational fields). These perturbations can be achieved in all situations excepting the isolated system. Boundaries of a system may be physical, or, in some cases, imaginary ones. )n( Thermodynamic Properties" Physical attributes that are selected for a description of a system on a macroscopic scale. )o( Thermodynamic Equilibrium" A state of the system where, as a necessary condition, none of its properties changes measurably over a period of time exceedingly long compared to any possible observations on the system. Commentary" In each instance the system needs to be checked out, as a sufficiency condition, by subjecting it through external manipulations to all sorts of changes in properties. If the response is out of proportion to such applied deformations and the system cannot be returned to its earlier state on lifting the deformations, it could not have been at equilibrium" If the system is restored to its initial state on completion of the checking process, without incurring any other changes in the universe, the system is at equilibrium with respect to the tests that have been conducted. In practice it may be difficult to decide whether the equilibrium state has been achieved or not, especially if the system is subject to very sluggish processes. In particular, sufficient time must be allowed for a system to complete its response to external perturbations. Generally, it is 4 .I FUNDAMENTALS acceptable to ignore processes which are so slow as to produce no significant changes over time periods that are long compared to the observation interval. For example, one may usually ignore the effect of cosmological changes on everyday laboratory experiments. A reasonable rule of thumb involves the relaxation time of any process: where the latter is very large compared to the interval of the measurements on the system, one may regard a state of equilibrium or steady state to have prevailed during the experimentation. As an example of problems arising in connection with the sufficiency condition, consider the case of a mixture of H 2 and 02 in a balloon at room temperature. The fact that there is no important change in the content of the balloon over many hours does not establish that equilibrium prevails, as the introduction of platinum black as a catalyst shows: A small disturbance of the system in this manner leads to a large, irreversible change in its properties. On the other hand, once ,2H ,20 and H20 are formed in appropriate amounts, changes introduced by heating and cooling are reversible and lead to only small excursions of the system from its newly formed state. (p) Reservoir: A source or sink used for exchanging matter with the system or for altering the properties by suitable manipulations to be discussed later. A reservoir is always assumed to be of such large size that its physical characteristics remain essentially unaffected during any exchange process. (q) Coordinates, Variables (of State), Degrees of Freedom: All three refer to quantities needed to characterize the state of a system at any instant. Commentary: Ordinarily one selects a linearly independent set of variables for the above characterization. For systems at equilibrium this characterization is achieved with a minimum number of coordinates whose values are independent of the history by which the equilibrium state was reached. As examples one may cite variables such as temperature or pressure whose alteration will change the state of a system. INTRODUCTORY DEFINITIONS )r( Intensive (Extensive) Variables" Variables whose value is independent of (depends on) the size and the quantity of matter within the region which is being scrutinized. )s( Thermodynamic Function of State" A mathematical interrelation between several variables of state, which describes a property of the system. The suitable manipulation of such functions provides useful information to the observer of a system. Commentary" Generally, such functions are useful only where a system is at or very close to equilibrium, because only in these circumstances can a simple functional interrelation be anticipated. )t( State Space, Configuration Space, or Phase Space" An abstract space constructed as an aid in the visualization of processes. Each variable is assigned an axis on which any point represents a numerical value of the variable. A (hyper-) space is then formed by a mutually orthogonal disposition of these axes about a common origin. )u( Representative Point" Any point in phase space that reflects the physical properties of the system for which the phase space was constructed. )v( Macroscopic Process" Any change in the system that leads to an alteration of its large-scale properties. )w( Path" The succession of states traversed by the system in its passage from a specific initial state to a specific final state. )x( Quasistatic Process" One that consists of a succession of equilibrium states, each of which differs only infinitesimally from its predecessor. The surroundings may be irretrievably altered in such a transition, and in a return path, the universe may end up in a final state which differs from the initial state. )y( Reversible Process" One whose path may be exactly reversed by a succession of infinitesimal changes in operating conditions; the original state of a system undergoing such a process may be restored without incurring any other alterations in the universe. I. FUNDAMENTALS (z) Irreversible Process: One that occurs spontaneously, generally while the system exhibits severe departures from equilibrium. The original state of the system that has undergone an irreversible change can be restored only at the expense of other permanent changes in the universe. Commentary: Not all conceivable processes to which a system could in principle be subjected can actually be realized; we shall encounter such cases later. Operationally, the distinction between reversible and irreversible processes introduces an element of patience. Only if one waits a long time between successive steps that involve just infinitesimal alterations in the system can one hope to produce reversible changes. Clearly, all dissipative effects such as friction must be avoided also. The distinction between quasistatic and reversible processes may be illustrated by an example. In a paramagnetic material a slow increase and subsequent decrease of the applied magnetic field leads to a gradual magnetization and subsequent gradual restoration of the initial unmagnetlzed state. In a ferromagnetic medium, the gradual application of a magnetic field to a demagnetized specimen will lead to a progressive magnetization of the system, but on gradual removal of the applied field, hysteresis effects cause the system to go, in a succession of quaslstatic states, to a different final state, in which a degree of magnetization is preserved even in the absence of the field. Thus, a reversible process is necessarily quasistatic, but the converse may not hold. (aa) Steady State Process: Processes which induce no net alterations in the state of a system but which do alter the state of the surroundings. Commentary: Steady state conditions are distinguished from equilibrium by the occurrence of processes in which inputs and outputs for the systems remain in balance, so that no net alterations occur within the system. However, those processes do cause alterations in the surroundings. For example, in the passage of a constant electric current through a wire, which is the system, the number of electrons in any section of the wire