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Classical Thermodynamics of Fluid Systems

Principles and Applications

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## Book Description

This text explores the connections between different thermodynamic subjects related to fluid systems. Emphasis is placed on the clarification of concepts by returning to the conceptual foundation of thermodynamics and special effort is directed to the use of a simple nomenclature and algebra. The book presents the structural elements of classical thermodynamics of fluid systems, covers the treatment of mixtures, and shows via examples and references both the usefulness and the limitations of classical thermodynamics for the treatment of practical problems related to fluid systems. It also includes diverse selected topics of interest to researchers and advanced students and four practical appendices, including an introduction to material balances and step-by-step procedures for using the Virial EOS and the PRSV EOS for fugacities and the ASOG-KT group method for activity coefficients. The Olivera-Fuentes table of PRSV parameters for more than 800 chemical compounds and the Gmehling-Tochigi tables of ASOG interaction parameters for 43 groups are included.

## Table of Contents

PART I. FUNDAMENTALS

Chapter 1. Basic Concepts and Definitions

The Concepts of System and Surroundings

The Thermodynamic Process, State and Path Functions

The Concept of a Reversible Process

Compressible and Incompressible Fluids

Chapter 2. The First and Second Laws of Thermodynamics

Principle of Conservation of Energy in a Closed System

Reversible or Quasi-static Processes

The Concept of Entropy, the Extremum Principle and Clausius Inequality

*Confirmation of agreement with the directional nature of heat flow.*

Refrigerators, Air-Conditioners and Heat Pumps

Heat Engines

Chapter 3. Conservation of Energy in an Open Flow System. Definition of enthalpy

Closed System Moving in Space

Open Flow System at Unsteady State

Definition of Enthalpy

Open Flow System at Steady State

Mechanical Energy Balance

Use of the Enthalpy Function in Closed Systems

Chapter 4. The Algebra of State Functions. The Helmholtz and Gibbs Functions

Thermodynamic Functions in Open Systems

The Chemical Potential

Maxwell’s Relations

Other Useful Mathematical Relations

Chapter 5. Calculation of Changes in the Value of Thermodynamic Properties

Measurable Properties

Calculation of Property Changes for Solid and Liquid Phases

Calculation of Property Changes for Phase Change of a Pure Compound

Use of Equations of State (EOS) for a Pure Compound or for a Mixture of Constant Composition

*Case of Independent Variables v and T, :*

*Case of Independent Variables P and T, :*

Changes in the Values of the Thermodynamic Properties of the Ideal Gas

Adiabatic Reversible Compression or Expansion of the Ideal Gas

Deviations from the Ideal Gas Behavior

Preparation of Tables and Plots of Thermodynamic Properties

PART II. MIXTURES

Chapter 6. Partial Molar Properties and Property Changes by Mixing

Partial Molar Properties and the Gibbs-Duhem Equation

Maxwell Relations Applied to Partial Molar Properties

Generality of the Relations between Thermodynamic Properties

Limiting Values of the Partial Molar Properties

Partial Molar Properties as a Function of Mole Fractions

Equations and Plots for Binary Mixtures

Property Changes by Mixing

Ideal Mixtures

Chapter 7. The Chemical Potential and the Gibbs-Helmholtz Equation

The Chemical Potential as Partial Molar Property

Chemical Potential Dependence on Temperature and Pressure

The Gibbs-Helmholtz Equation

The Gibbs-Duhem Equation in Terms of Chemical Potentials

Maxwell Relation in Terms of the Chemical Potential

Chapter 8. The Principles of Physical and Chemical Equilibrium

Extremum Principle for Functions Other than Entropy

Phase Equilibrium without Chemical Reactions

Chemical Equilibrium in a Single Phase Closed System

Phase and Chemical Equilibrium in a Closed System

Chapter 9. The Phase Rule and Duhem Theorem

The Phase Rule for Non Reacting Systems

The Phase Rule for Reacting Systems

Common Cases of Application of the Phase Rule

The Duhem Theorem

The Phase Rule with Additional Constraints

Chapter 10. Generality of the Thermodynamic Treatment

Equilibrium Involving Ions

Adsorption of Chemical Species on a Surface

Chapter 11. The Ideal Gas and Ideal Gas Mixtures

Chemical Potential of a Compound in an Ideal Gas Mixture

Property Changes in the Mixing of Ideal Gases

Chapter 12. The Use of Fugacity and Activity in Equilibrium Studies

Definition of Fugacity and Fugacity Coefficient

Phase Equilibrium in Terms of Fugacities

Definition of Activity

Chemical Equilibrium in Terms of Activity

Property Changes of Reaction

Chapter 13. Calculation of Fugacities from Equations of State (EOS)

Use of Volume Explicit EOS:

Use of Pressure Explicit EOS:

Chapter 14. Fugacity of a Mixture and of Its Components

Fugacity and Fugacity Coefficient of a Mixture

Fugacity Coefficients as Partial Properties

The Gibbs-Duhem Equation in Term of Fugacity Coefficients

The Gibbs-Duhem Equation in Terms of Fugacities

Chapter 15. Fugacities and Activities in Liquid Mixtures of Non Electrolytes

Lewis’ Convention for Activity Coefficients

Henry’s Convention for the Activity Coefficient of a Solute

Generalized Definition of Activity

Relations between the Activity Coefficients in Lewis’ and Henry’s Conventions

Generalized Equations for an Ideal Mixture

Properties of Ideal Mixtures in Lewis’ Convention

Use of Molality as a Measure of Concentration

Chapter 16. Activity Coefficients and Excess Properties

Evaluation of the Fugacity of a Pure Compound Liquid at *P* and *T* of the system

Evaluation of Activity Coefficients from Phase Equilibrium Studies

The Gibbs-Duhem Equation in Terms of Activity Coefficients in Lewis’ Convention

The Excess Gibbs Energy and Other Excess Functions in Any Convention

Activity Coefficients and their Relation to Excess Functions and in Any Convention

Thermodynamic Consistency of Activity Coefficients in Lewis’ Convention

Excess Gibbs Energy in Lewis’ Convention in Terms of Fugacity Coefficients

Chapter 17. Mixture Behavior, Stability and Azeotropy

Basic Relations

Positive and Negative Deviations from ideal Behavior in Lewis’ Sense.

Berg Classification of Liquids and Mixture Behavior

Partial Miscibility

Condition for Stability of Liquid Mixtures

Phase Equilibrium Diagrams

Chapter 18. The Thermodynamics of Aqueous Electrolyte Solutions

Basic Relations

Mean Ionic Activity Coefficient.

Osmotic Coefficient

The Need for Considering the Existence of Individual Ions

The Behavior of the Activity of Individual Ions

Debye-Hückel Theory for Dilute Aqueous Electrolyte Solutions

Limiting Values of the Mean Ionic Activity Coefficient and the Osmotic Coefficient at High Dilution

Indirect Measurement of the Mean Ionic Activity Coefficient

Direct Electrochemical Measurement of the Mean Ionic Activity Coefficient

Electrochemical Measurement of the Mean Ionic Activity Coefficient with Independent Measurements for the Cation and the Anion

The Activity of a Second Solute in an Aqueous Electrolyte Solution

Aqueous Solutions of Weak Electrolytes

Charged Organic Molecules

Experiment to Determine the Charge of a Protein

Conclusions

PART III. APPLICATIONS

Chapter 19. The Thermodynamics of Chemical Reactions

Statement of the Problem and Basic Definitions

Determination of the Number of Independent Reactions

*Example 1. Catalytic Oxidation of Ammonia*

Example 2. Production of 1,3 Butadiene

Example 3. Isomerization of 1,3 Butadiene

The Thermodynamic Equilibrium Constant in Terms of the Equilibrium Compositions

The Solvay Process

Reactions in the Gas Phase

Reactions in the Liquid Phase

Reactions with Compounds in the Solid Phase

Calculation of the Thermodynamic Equilibrium Constant

Examples of Evaluation of the Thermodynamic Equilibrium Constant

*Example of a Heterogeneous Reaction*

*Example of a Reaction in the Gas Phase*

*Example of a Reaction in Liquid Phase*

Expression of *K _{x}* as a Function of the Conversion of One of the Reactants

Chemical Equilibrium with More than One Independent Reaction

Chapter 20. The Thermodynamics of Equilibrium Based Separation Processes

Distribution Coefficient and Selectivity

Azeotropic and Solvent Distillation

Vapor-Liquid Equilibrium

Bubble and Dew Point Calculations

Flash Calculations

Liquid-Liquid Equilibrium

Solid-Liquid Equilibrium

Phase Equilibrium through Membranes

Recapitulation of Concepts

Chapter 21. Heat Effects in Pure Compounds and Mixtures

Heat Effects in Pure Compounds

*Example 1. Determination of Steam Quality*

Heat Effects in Mixtures

*Heat of Mixing, *

Enthalpy-Concentration Diagrams

*Example 2. Calculation of a Heat of Dilution from Heats of Formation*

*Example 3. Calculation of the Enthalpy of a Solution*

Use of Enthalpy Concentration Information

Mixing of Two Solutions

Example 4. Mixing of Diluted and Concentrated H_{2}SO_{4}

Concentration of a Solution of a Nonvolatile Solute by Evaporation of Solvent

Example 5. Dilution of a Concentrated NaCl solution

Heat Effects in Reactive Systems

*Example 6. Calculation of the Heat of Formation*

*Example 7. Calculation of Standard Heats of Reaction*

Example 8. Heat Effects in Reacting Mixtures

Example 9. Production of Allyl chloride in an Adiabatic Continuous Stirred Tank Reactor

Chapter 22. Adsorption of Gases in Solids

A Two-dimensional Thermodynamic Approach

The Gibbs Treatment for the Isothermal Adsorption of a Pure Compound Gas at a Solid Surface

Isothermal Adsorption of a Gas Mixture

Example of the Gibbs Treatment for the Adsorption of a Gas Mixture

Thermal Effects on Adsorption

Heat Effects in "Ideal" Adsorption of a Mixture of Gases

PART IV. SELECTED TOPICS

Chapter 23. The Thermodynamics of Flow of Compressible Fluids

Subsonic, Sonic and Supersonic Flow

A Thermodynamic Understanding of the Limiting Speed

Enthalpy and Entropy Changes in Compressible Flow

Relation of Fluid Properties to Mach Number at Entrance Condition

Determination of Critical Length

Chapter 24. Elements of Statistical Thermodynamics

The Canonical Ensemble and Probability

The Internal Energy and the Partition Function

Entropy and Probability

Equation of State, Chemical Potential and Partition Function

Chapter 25. Statistical Thermodynamics Basis of Equations of State

Equation of State for the Ideal Gas

Virial Equations of State

Cubic Equations of State

Relation of Intermolecular Potentials to the Second Virial Coefficient

Second Virial Coefficients of Binary Mixtures

Mixing Rule for Cubic Equations of State

Non-cubic Equations of State of Theoretical Interest

Chapter 26. Statistical Thermodynamics Basis of Excess Gibbs Functions

The van Laar Model

The Regular Solution Theory

The Two-Suffix Margules Equation and the Redlich-Kister Polynomial

The Flory Huggins and the Guggenheim-Staverman’s Models for Athermal Mixtures

The Complete Regular Solutions and Flory-Huggins Expressions

Modern Times

The Quasi Chemical Theory

The Wilson Equation for the Excess Gibbs Energy

The Birth of the Solution of Groups Method to Calculate Activity Coefficients in Liquid Mixtures

The Analytical Solution of Groups, ASOG

The Non-Random-Two-Liquid Equation (NRTL) for the Excess Gibbs Energy

The UNIQUAC Equation

UNIFAC

Wang’s Renormalization of Guggenheim’s Partition Function

SAFT

Conclusions

Summary of Some Useful Equations for the Correlation of Activity Coefficients

Chapter 27. The Activity Coefficients of Individual Ions. Measurements and Modeling

The Crux of the Problem

Methods Used to Reduce the Experimental Data

*Indirect Electrochemical Approach*

Direct Electrochemical Approach

Effect of an Error in the Sign of the Junction Potential

Additional Experimental Studies

Henderson’s Approximation

New Equation to Calculate Liquid Junction Potentials

Use of the Activity of Individual Ions in Multi-ions Aqueous Solutions

Comparison of Experimental Results for the Activity of Individual Ions Obtained by Different Researchers

Emerging Theories of Electrolyte Solutions

*Fraenkel’s Smaller-ion Shell (SiS) Theory.*

*Liu and Eisenberg Poisson-Fermi (PF) Theory.*

PART V. APPENDICES

Appendix A. Material Balances in Open Flow Systems

Material Balances for Systems without Chemical Reactions

Material Balances for Systems with Chemical Reactions

Appendix B. Working with the Virial EOS

The Virial EOS Truncated After the Third Term

Fugacity Coefficient of a Pure Compound

The Virial EOS for Mixtures

Fugacity Coefficient of a Compound in a Mixture

Appendix C. Working with the PRSV EOS

The PRSV EOS

Exact Solution of a Cubic Equation

Volume roots for PRSV EOS at given *T* and *P*

How to Calculate the Saturation Pressure of a Pure Compound with PRSV EOS

How to Calculate Saturated Liquid Molar Volumes with the PRSV EOS

How to Calculate Enthalpies and Heats of Vaporization with the PRSV EOS

How to Calculate Fugacity Coefficients in Mixtures with PRSV

A ‘Two-Binary-Parameter’ Mixing Rule and its Extension to Multicomponent Mixtures

A Consistent Method to Combine the PRSV EOS with Excess Gibbs Energy Models

Tables of Parameters

Additional Table of PRSV Parameters Contributed by Professor Claudio Olivera Fuentes.

Appendix D. Working with ASOG-KT

Basic Equations

How to Read Parameters in Table D.2

The System Hexane-Methanol

Gmehling-Tochigi Complete Tables of Parameters

Abbreviations

Index

## Author(s)

### Biography

Juan H. Vera is Professor Emeritus, Department of Chemical Engineering, McGill University, Montreal, Canada. He received his Dr. Ing. (Ing. Quim.) from Universidad F. Santa Maria, Chile; M.Sc. (Chem. Eng.), University of California, Berkeley; Ing. Quim., U. Tecnica del Estado, Chile; and Lic. Quim. Ind., U. Tecnica del Estado, Chile. At McGill University, he served as Associate Dean (Research), Faculty of Engineering (2000–2004); Acting Dean, Faculty of Engineering (October–November 2003); President McGill Association of University Teachers, MAUT (1997–1998); Member of the Board of ResMIQ (2002–2004); Member of the Advisory Committee of Plasma Quebec (2002–2004); Engineering Faculty Representative to Plasturgie Quebec (2003); Engineering Faculty Representative to CRIAQ (2001–2004); and Associate Dean, Faculty of Graduate Studies and Research (1985–1988). He is coauthor of two textbooks, a manual on Copper Metallurgy (in Spanish) and over 190 refereed publications in international journals. He has an International Patent on Extraction of Proteins and a Canadian Patent on Extraction of Heavy Metals.

Grazyna Wilczek-Vera was Faculty Lecturer and Director of Undergraduate Studies in the Department of Chemistry and Research associate in the Department of Chemical Engineering at McGill University, Montreal, Canada, and Adjunct at the Department of Chemistry, University of Warsaw, Poland. She received the Principal’s Prize for Excellence in Teaching, 2008, at McGill University. She has authored 58 refereed publications, given 38 conference presentations, and coauthored two texts: Experimental Physical Chemistry for Biology Students, University of Warsaw, 1987 and Experimental Physical Chemistry for Chemistry Students, University of Warsaw, 1985. She also translated into Polish: R. A. Y. Jones, Physical and Mechanistic Organic Chemistry, Cambridge University Press, 1984. She received her Doctorate in Chemical Sciences (with Distinction), University of Warsaw and Master of Science in Chemistry (with Distinction), University of Warsaw, Poland.

## Reviews

"The book is written in an unfussy and approachable style. Concepts are clearly explained, equations do not pop out of thin air, and careful distinction is made between the proven principles and formal structure of classical thermodynamics and the tentative and possibly transient theories and models of fluid behavior. These subjects are of course covered in many textbooks on thermodynamics, but the strongest contribution of this new book is found in its later sections, which deal with special topics and contain illuminating and up to date accounts of subjects such as the statistical thermodynamic basis of solution models, and the behavior of ions in electrolyte solutions, where the authors allow their research expertise to come to the fore. Finally, some very useful appendices explain the practical use of several specific models for gaseous and liquid mixtures, including extensive tables of the necessary fluid-specific parameters. Throughout it all, the authors' absolute command and indeed love of their subject shines forth, and their many original contributions to the field are presented in lucid and unassuming fashion. This is a most enjoyable book, warmly recommended."

—Claudio Olivera-Fuentes, Simon Bolivar University, Caracas, Venezuela"

Classical Thermodynamics of Fluid Systems: Principles and Applicationsby Juan H. Vera and GrazynaWilczek-Vera is an excellent textbook written for an ample audience of undergraduate, and graduate students in Chemistry and Chemical engineering, as well as for professionals working in these fields. Drawing on their vast professional experience, the authors manage to present fundamental principles and complex subjects with simple, but at the same time rigorous approaches. In their convincing exposition of phase behavior, Vera and Wilczek-Vera consider the chemical nature of the molecules participating in the mixtures so as to clarify the conditions that lead to phase separation and azeotropy. They also present the basic principles of statistical thermodynamics in didactic fashion, to introduce the fundamentals of engineering models to predict thermodynamic properties. In another insightful chapter, the thermodynamics of electrolytes in aqueous solutions serves as a fitting introduction to the complex problem of solubility of proteins in aqueous media. The book’s rigorous treatment of the mathematics of thermodynamics, and its timely, thorough, and sophisticated discussion on the behavior of real systems are also to be commended. Without a doubt, Vera and Wilczek-Vera’s book is indispensable reading to anyone interested in the field of classical thermodynamics of fluid systems."

—Esteban Brignole, Universidad del Sur, Bahia Blanca, Argentina

..."the authors have shown that yes, there [is] a need for yet another textbook in applied thermodynamics and I think this book will be remembered by its brief—to the point, concise, rigorous but also, on times, rather personal way of presentation.... The authors recommend the book mostly for researchers and those already familiar with some of the thermodynamic principles."—Continuum Mech. Thermodyn (2017), 29:1415-1416