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The book is published under the auspices of the International Association of Chemical Thermodynamics (IACT) and is the third volume in our series published by The Royal Society of Chemistry, Cambridge; the previous three, published in 2010, 2015 and 2017, respectively, and all edited by Emmerich Wilhelm and Trevor M. Letcher are:

  • Heat Capacities: Liquids, Solutions and Vapours;1 

  • Volume Properties: Liquids, Solutions and Vapours;2 

  • Enthalpy and Internal Energy: Liquids, Solutions and Vapours.3 

Our four books follow a long tradition, started in 1956, of publishing reviews of important areas and topics in chemical thermodynamics (see details in the Preface to Volume Properties).2  As in previous books, we have looked to the world-wide international field of thermodynamics for our authors and our new book has authors from 13 countries: Austria, Canada, Germany, Greece, Israel, Japan, Russia, Slovenia, South Africa, Spain, Switzerland, the United Kingdom and the United States of America.

The objectives of our book are many. It includes the presentation of reviews for new researchers and for those who need to understand the origins and background of a topic and also to see where a topic is leading. Many of the topics discussed in this new volume have not been reviewed before as they have only recently been researched. The reviews published here also include copious references to the literature, including the latest publications (up to the end of 2020 in the case of this volume). Another objective is to bring together research from disparate disciplines that have a bearing on Gibbs energy and Helmholtz energy. We believe that cross-linking these chapters can lead to a synergistic effect, leading to news ways of looking at problems in physics, chemistry and engineering and expanding the horizons to which solutions can be applied. Another objective is linked to our philosophy that a book, be it in electronic or printed form, is an important vehicle for disseminating knowledge.

Where possible, the units, symbols and thermodynamic quantities have been checked against the rules laid down in the Green Book of the International Union of Pure and Applied Chemistry (IUPAC),4  and in most cases we have adhered to the nomenclature/symbols suggested by IUPAC. Deviations from a few of these suggestions are due to our desire to present a concise notation in compliance with usage preferred by the scientific community interested in thermodynamics, i.e. by physical chemists, physicists and chemical engineers. Such an approach is in accord with the spirit of the Green Book expressed so admirably by Martin Quack in his Historical Introduction on p. xii of its third edition, 2007: It is not the aim to present a list of recommendations in form of commandments. Rather we have always followed the principle that this manual should help the user in what may be called “good practice of scientific language”. The quantities, in particular, that we would like to single out to comment on are the Helmholtz energy F, the pressure P, the mechanical coefficients, i.e. the isobaric expansivity αP, the isothermal compressibility βT and the isochoric thermal pressure coefficient γV, and the Henry fugacity hi,j(T, P), also known as Henry's law constant.

The symbol F is used as an alternative symbol for the Helmholtz energy A and has a long tradition in (European) thermodynamics, as evidenced by the following classic, authoritative books:

  1. I. Prigogine and R. Defay, Chemical Thermodynamics (translated and revised by D. H. Everett), Longmans, Green and Co, London, 1967.

  2. R. Haase, Thermodynamik der Mischphasen, Springer-Verlag, Berlin, 1956.

  3. G. Kortüm and H. Lachmann, Einführung in die chemische Thermodynamik, Verlag Chemie, Weinheim and Vandenhoeck & Ruprecht, Göttingen, 7th edn, 1981.

  4. H. B. Callen, Thermodynamics and an Introduction to Thermostatics, John Wiley & Sons, New York, 2nd edn, 1985.

F is listed in the IUPAC Green Book4  (3rd edition, published 2007) in Table 2.11, p. 56, at the same level as A, and it is preferred by many physicists. In addition, A is commonly used for the affinity of a chemical reaction, that is, a state function introduced by de Donder in 1922 and heavily used in reaction chemistry and related fields. Affinity is defined by

graphic
where G denotes the molar Gibbs energy, n is the amount of substance, ξ is known as the extent of reaction, νi is called the stoichiometric number (for component i) and µi is its chemical potential. The chemical state of the system is thus defined by
graphic
and the necessary and sufficient condition for equilibrium in a chemical reaction is

A(T, P, ξ) = 0.

This symbol A, for the affinity of reaction, is listed in Table 2.11 on p. 56 of the Green Book (3rd edition).4  In addition, A is commonly used for area; hence, for surface thermodynamics, the use of F for the Helmholtz energy has obvious advantages.

The symbol P for pressure is now accepted by IUPAC as an alternative to p, as indicated in Tables 2.2 and 2.10 of the Green Book.4  The reason why we (and many others) prefer P is the following: temperature T and pressure P are both intensive quantities and, together with the composition expressed by the set of mole fractions {xi}, or by the set of extensive amounts of substance {ni}, they form a group of basic thermodynamic variables advantageously used in chemical thermodynamics. They are not perceived primarily as properties of the fluids but as conditions imposed on/exhibited by them with the valuable bonus of being (in principle) easily measured and controlled. In other words, temperature and pressure are quantities of “equal rank”, which fact should be reflected in the symbols we use, that is, capital T and capital P. For heterogeneous PVTx systems consisting of several phases in equilibrium with each other, temperature and pressure are identical in the coexisting phases. We note that Griffiths and Wheeler5  call such variables fields (in contradistinction to variables that are in general not equal in coexisting phases, such as molar volume, enthalpy and entropy, which they call densities). For the isothermal compressibility, Rowlinson and Swinton,6  among many others, use the symbol . Together with the isobaric expansivity and the isochoric thermal pressure coefficient , for a constant-composition fluid these mechanical coefficients form a mnemonic triple:

αP/βT = γV.

Writing them in this way, i.e. by indicating via a subscript what quantity is to be held constant, is advantageous in general and particularly when discussing the related isentropic and orthobaric quantities. The Henry fugacity hi,j(T, P) depends on T and P and also on the chemical identities of solute i and solvent j (the other component), hence the double subscript i, j has been added to the symbol h. In order to indicate visibly the close relationship of the Henry fugacity (Henry's law constant) to the pure-substance fugacity f*(T, P), it is thus consequently represented by a lower-case letter h instead of a capital letter H; h2,1(T, P) is a materials property, which fact is clearly indicated by the parenthetical information.

We wish to thank all 33 authors and co-authors for their cooperation, help and especially for writing their chapters. It has been a pleasure working with each and every one of the authors. We thank our wives, Olga and Valerie, for all the help they have given us over these long months of putting the book together. Finally, we wish to thank The Royal Society of Chemistry and in particular Janet Freshwater and Liv Towers for their help and patience in producing: Gibbs Energy and Helmholtz Energy: Liquids, Solutions and Vapours.

Emmerich Wilhelm

Vienna, Austria

Trevor M. Letcher

Stratton on the Fosse, United Kingdom

1.
E.
Wilhelm
and
T. M.
Letcher
,
Heat Capacities: Liquids, Solutions and Vapours
,
Royal Society of Chemistry
,
Cambridge
,
2010
2.
E.
Wilhelm
and
T. M.
Letcher
,
Volume Properties: Liquids Solutions and Vapours
,
Royal Society of Chemistry
,
Cambridge
,
2015
3.
E.
Wilhelm
and
T. M.
Letcher
,
Enthalpy and Internal Energy: Liquids, Solutions and Vapours
,
Royal Society of Chemistry
,
Cambridge
,
2017
4.
E. R.
Cohen
,
T.
Cvitas
,
J. G.
Frey
,
B.
Holstrom
,
K.
Kuchitsu
,
R.
Marquardt
,
I.
Mills
,
F.
Pavese
,
M.
Quack
,
J.
Stohner
,
H. L.
Strauss
,
M.
Takami
and
A. J.
Thor
,
International Union of Pure and Applied Chemistry: Quantities, Units and Symbols in Physical Chemistry
,
Royal Society of Chemistry
,
Cambridge
, 3rd edn,
2007
5.
Griffiths
 
R. B.
Wheeler
 
J. C.
Phys. Rev.
1970
, vol. 
A2
 (pg. 
1047
-
1064
)
6.
J. S.
Rowlinson
and
F. L.
Swinton
,
Liquids and Liquid Mixtures
,
Butterworth Scientific
,
London
, 3rd edn,
1982

Figures & Tables

Contents

References

1.
E.
Wilhelm
and
T. M.
Letcher
,
Heat Capacities: Liquids, Solutions and Vapours
,
Royal Society of Chemistry
,
Cambridge
,
2010
2.
E.
Wilhelm
and
T. M.
Letcher
,
Volume Properties: Liquids Solutions and Vapours
,
Royal Society of Chemistry
,
Cambridge
,
2015
3.
E.
Wilhelm
and
T. M.
Letcher
,
Enthalpy and Internal Energy: Liquids, Solutions and Vapours
,
Royal Society of Chemistry
,
Cambridge
,
2017
4.
E. R.
Cohen
,
T.
Cvitas
,
J. G.
Frey
,
B.
Holstrom
,
K.
Kuchitsu
,
R.
Marquardt
,
I.
Mills
,
F.
Pavese
,
M.
Quack
,
J.
Stohner
,
H. L.
Strauss
,
M.
Takami
and
A. J.
Thor
,
International Union of Pure and Applied Chemistry: Quantities, Units and Symbols in Physical Chemistry
,
Royal Society of Chemistry
,
Cambridge
, 3rd edn,
2007
5.
Griffiths
 
R. B.
Wheeler
 
J. C.
Phys. Rev.
1970
, vol. 
A2
 (pg. 
1047
-
1064
)
6.
J. S.
Rowlinson
and
F. L.
Swinton
,
Liquids and Liquid Mixtures
,
Butterworth Scientific
,
London
, 3rd edn,
1982
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