Introduction

ANTHONY R. H. GOODWIN, JAN V. SENGERS AND CORNELIS J. PETERS

In the series Experimental Thermodynamics the first and only volume concerned with equations of state for fluids and fluid mixtures was Volume V.5 This volume, which was published during 2000 in two parts, provided descriptions of equations of state, over an entire range of approaches and range of variables for their wide use in science, engineering and industry. Reference 5 included methods required to develop equations of state, including their theoretical bases and practical uses along with their strengths and limitations. Furthermore, the volume contained not only equations of state for simple fluids and fluid mixtures, but also for and more important classes of complex fluids and mixtures. In particular, the volume included associating fluids, ionic fluids, poly-disperse systems, polymers, and micelle-forming and other self-organizing systems. However, some subject matter of importance to the practitioner was omitted including equations of state specifically for chemically reacting fluids and methods applicable to non-equilibrium thermodynamics.

Since the year 2000, there have been over 15,000 publications in the academic scientific and engineering archival literature that in some form or other are concerned with equations of state. In addition, equations of state for chemically reacting and non-equilibrium fluids have received additional theoretical and practical attention and now deserve more detailed explanations than hitherto provided.

Both developments in the field and the desire to provide the content omitted in the previous volume motivated this text entitled Applied Thermodynamics of Fluids. The change in title also reflects a greater emphasis that has been placed on the application of theory, without recourse to derivations of the constitutive equations, while retaining the fundamental aspects. The volume includes thermodynamics at the nano and meso scale in Chapter 7, chemically reacting systems in Chapter 13 and the application of non-equilibrium thermodynamics in Chapter 14. This volume is intended to address the needs of practitioners within academia, government and industry. However, chapters from reference 5 regarding self-assembled systems and analytical solvable integral equations have been omitted in this work and as have in both volumes the use of computer simulations for the calculation of thermodynamic properties. The latter would deserve an in-depth coverage of its own and because of size limitations along with a recent special issue of Fluid Phase Equilibria and other publications reporting the Industrial Fluid Property Simulation Challenges, it was decided not to include the topic in the present volume.

Some chapters from Volume V5 have been revised and updated and are included here because of their fundamental importance to the topic: these appear in this text as Chapter 2, regarding Fundamental Considerations that is essential to determine the validity of any method adopted, Chapter 3, entitled Virial Equation of State, Chapter 4 concerned with Cubic and Generalized van der Waals Equations, Chapter 5, Mixing and Combining Rules, Chapter 6 on Corresponding States. Significantly greater prominence has been is given to Statistical Associating Fluid Theory (SAFT) in Chapter 8, while Chapter 9 provides and update on Poly-disperse fluids, Chapter 10 is concerned with the more general topic of Critical Behaviour, Chapter 11 reports on Ionic Fluids and Chapter 12 on the Multi-parameter Equations of State.

Applied Thermodynamics is published under the auspices of the Physical and BioPhysical Division (I) of the International Union of Pure and Applied Chemistry as a project proposed by the International Association of Chemical Thermodynamics (IACT) in its capacity as an organization affiliated with IUPAC. Consequently, throughout the text we have adopted the quantities, units and symbols of physical chemistry defined by IUPAC in the text commonly known as the Green Book. We have also adopted the ISO guidelines for the expression of uncertainty and vocabulary in metrology. Values of the fundamental constants and atomic masses of the elements have been obtained from references 21 and 22, respectively.

Fundamental Considerations

ANGEL MARTÍN MARTÍNEZ AND COR J. PETERS

2.1 Introduction

This chapter provides a thermodynamic toolbox and contains most of the important basic relations that are used in other chapters. The scope is restricted almost exclusively to the second law of thermodynamics and its consequence, but the treatment is still intended to be exemplary rather than definitive. New results are not presented as befits a discussion of fundamentals which are necessarily invariant with time.

2.2 Basic Thermodynamics

The state of a system may be described in terms of a small number of variables. For a phase in the absence of any external field, the second law of thermodynamics may be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2.1)

This equation shows that the change dU in the energy U may be described in terms of simultaneous changes dS in the entropy S, dV in the volume V, and dni in the amount of substance ni of the i components. It is often convenient to eliminate the size of the phase by writing eq 2.1 in terms of intensive variables. For example, division by the total amount n

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2.2)

gives

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2.3)

where the subscript m denotes a molar quantity and the mole...