Phase Modeling Tools

This book is part of a set of books which offers advanced students successive characterization tool phases, the study of all types of phase (liquid, gas and solid, pure or multi-component), process engineering, chemical and electrochemical equilibria, and the properties of surfaces and phases of small sizes. Macroscopic and microscopic models are in turn covered with a constant correlation between the two scales. Particular attention has been given to the rigor of mathematical developments.

Auteur

Michel SOUSTELLE is a chemical engineer and Emeritus Professor at Ecole des Mines de Saint-Etienne in France. He taught chemical kinetics from postgraduate to Master degree level while also carrying out research in this topic.

Contenu
PREFACE xiii

NOTATIONS xvii

SYMBOLS xix

CHAPTER 1. THERMODYNAMIC FUNCTIONS AND VARIABLES 1

1.1. State variables and characteristic functions of a phase 2

1.1.1. Intensive and extensive conjugate variables 2

1.1.2. Variations in internal energy during a transformation 3

1.1.3 Characteristic function associated with a canonical set of variables 5

1.2. Partial molar parameters 7

1.2.1. Definition 7

1.2.2. Properties of partial molar variables 8

1.3. Chemical potential and generalized chemical potentials 8

1.3.1. Chemical potential and partial molar free enthalpy 8

1.3.2. Definition of generalized chemical potential 9

1.3.3. Variations in the chemical potential and generalized chemical potential with variables 10

1.3.4. GibbsDuhem relation 10

1.3.5. Generalized Helmholtz relations 11

1.3.6. Chemical system associated with the general system 12

1.4. The two modeling scales 14

CHAPTER 2. MACROSCOPIC MODELING OF A PHASE 15

2.1. Thermodynamic coefficients and characteristic matrices 15

2.1.1. Thermodynamic coefficients and characteristic matrix associated with the internal energy 15

2.1.2. Symmetry of the characteristic matrix 17

2.1.3. The thermodynamic coefficients needed and required to thermodynamically define the phase 17

2.1.4. Choosing other variables: thermodynamic coefficients and characteristic matrix associated with a characteristic function 19

2.1.5. Change in variable from one characteristic matrix to another 22

2.1.6. Relations between thermodynamic coefficients and secondary derivatives of the characteristic function 26

2.1.7. Examples of thermodynamic coefficients: calorimetric coefficients 27

2.2. Partial molar variables and thermodynamic coefficients 27

2.3. Common variables and thermodynamic coefficients 28

2.3.1. State equation 29

2.3.2. Expansion coefficients 30

2.3.3. Molar heat capacities 32

2.3.4. Young's Modulus 34

2.3.5. Electric permittivity 34

2.3.6. Volumic and area densities of electric charge 34

2.4. Thermodynamic charts: justification of different types 35

2.4.1. Representation of a variable as a function of its conjugate 35

2.4.2. Representation of a characteristic function as a function of one of its natural variables 38

2.5. Stability of phases 39

2.5.1. Case of ensemble E0 of extensive variables 40

2.5.2. Coefficients associated with ensemble En 43

2.5.3. Case of other ensembles of variables 44

2.5.4. Conclusion: stability conditions of a phase in terms of thermodynamic coefficients 46

2.5.5. Example applying stability conditions 46

2.6. Consistency of thermodynamic data 48

2.7. Conclusion on the macroscopic modeling of phases 49

CHAPTER 3. MULTI-COMPOUND PHASES SOLUTIONS 51

3.1. Variables attached to solutions 51

3.1.1. Characterizing a solution 52

3.1.2. Composition of a solution 53

3.1.3. Peculiar variables and mixing variables 54

3.2. Recap of ideal solutions 57

3.2.1. Thermodynamic definition 57

3.2.2. Molar Gibbs energy of mixing of an ideal solution 57

3.2.3. Molar enthalpy of mixing of the ideal solution 57

3.2.4. Molar entropy of mixing of the ideal solution 58

3.2.5. Molar volume of mixing 58

3.2.6. Molar heat capacity of ideal solution: Kopp's law 58

3.3. Characterization imperfection of a real solution 59

3.3.1. Lewis activity coefficients 60

3.3.2. Characterizing the imperfection of a real solution by the excess Gibbs energy 71

3.3.3. Other ways to measure the imperfection of a solution 74

3.4. Activity of a component in any solution: Raoult's and Henry's laws 76

3.5. Ionic solutions 77

3.5.1. Chemical potential of an ion 78

3.5.2. Relation between the activities of ions and the overall activity of solutes 80 3.5.3. ...