Phase Modeling Tools E-Book

Michel Soustelle

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 258

Veröffentlichungsjahr: 2015

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Title

Copyright

Preface

Notations

Symbols

1: Thermodynamic Functions and Variables

1.1. State variables and characteristic functions of a phase

1.2. Partial molar parameters

1.3. Chemical potential and generalized chemical potentials

1.4. The two modeling scales

2: Macroscopic Modeling of a Phase

2.1. Thermodynamic coefficients and characteristic matrices

2.2. Partial molar variables and thermodynamic coefficients

2.3. Common variables and thermodynamic coefficients

2.4. Thermodynamic charts: justification of different types

2.5. Stability of phases

2.6. Consistency of thermodynamic data

2.7. Conclusion on the macroscopic modeling of phases

3: Multi-Compound Phases – Solutions

3.1. Variables attached to solutions

3.2. Recap of ideal solutions

3.3. Characterization imperfection of a real solution

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

3.5. Ionic solutions

3.6. Curves of molar variables as a function of the composition in binary systems of a solution with two components

4: Statistics of Object Collections

4.1. The need to statistically process a system

4.2. Statistical effects of distinguishable non-quantum elements

4.3. The quantum description and space of phases

4.4. Statistical effect of localized quantum objects

4.5. Collections of non-localized quantum objects

4.6. Systems composed of different particles without interactions

4.7. Unicity of coefficient

β

4.8. Determining coefficient

α

in quantum statistics

5: Canonical Ensembles and Thermodynamic Functions

5.1. An ensemble

5.2. Canonical ensemble

5.3. Molecular partition functions and canonical partition functions

5.4. Thermodynamic functions and the canonical partition function

5.5. Absolute activity of a constituent

5.6. Other ensembles of systems and associated characteristic functions

6: Molecular Partition Functions

6.1. Definition of the molecular partition function

6.2. Decomposition of the molecular partition function into partial partition functions

6.3. Energy level and thermal agitation

6.4. Translational partition functions

6.5. Maxwell distribution laws

6.6. Internal partition functions

6.7. Partition function of an ideal gas

6.8. Average energy and equipartition of energy

6.9. Translational partition function and quantum mechanics

6.10. Interactions between species

6.11. Equilibrium constants and molecular partition functions

6.12. Conclusion on the macroscopic modeling of phases

7: Pure Real Gases

7.1. The three states of the pure compound: critical point

7.2. Standard state of a molecular substance

7.3. Real gas – macroscopic description

7.4. Microscopic description of a real gas

7.5. Microscopic approach of the heat capacity of gases

8: Gas Mixtures

8.1. Macroscopic modeling of gas mixtures

8.2. Characterizing gas mixtures

8.3. Determining activity coefficients of a solution from an equation of state

Appendices

Appendix 1: The Method of Lagrange Multipliers

A1.1. An overview of the problem

A1.2. Solving the problem using the method of Lagrange multipliers

A1.3. Determining the multiplier values

Appendix 2: Moments of Inertia of Molecules

Appendix 3: Mathematical Complements

A3.1. Homogeneous functions and Euler functions

A3.2. Exact total differentials

A3.3. Cross partial derivatives

A3.4. Elements of combinatorial analysis

Appendix 4: Constants and Units

A4.1. The international system of units (SI)

A4.2. Electrostatic formulae

Appendix 5: Function Γ

A5.1. Definition

A5.2. Recurrence relation and table of values

A5.3. Extension to negative values

Bibliography

Index

End User License Agreement

List of Illustrations

2: Macroscopic Modeling of a Phase

Figure 2.2.

Mollier chart

3: Multi-Compound Phases – Solutions

Figure 3.1.

Activity of a constituent in a solution- a) with a positive deviation with regard to Raoult – b) with a negative deviation

Figure 3.2.

Gibbs energy of a binary solution according to the composition

4: Statistics of Object Collections

Figure 4.1.

Height distribution of gas molecules under the action of gravity

6: Molecular Partition Functions

Figure 6.1.

Interaction between two ions

Figure 6.2.

The hard sphere model without attraction

Figure 6.3.

Hard sphere model with force of attraction

Figure 6.4.

London molecular interaction potential

7: Pure Real Gases

Figure 7.1.

Main lines in the diagram of pure compound states

Figure 7.2.

Differences of real gases to the Boyle-Mariotte

Figure 7.4.

Compressibility chart

Figure 7.5.

Fugacity coefficient chart of pure gases

Figure 7.6.

Different configurations of paired molecules for the first four terms of the sum in relation [7.66]

Figure 7.7.

Variation in the second coefficient of the virial with temperature

Figure 7.9.

Hard-sphere model with force of attraction

Figure 7.10.

Variations in the second coefficient of the virial with temperature (according to Lennard-Jones)

Figure 7.11. V

ariation in the third coefficient of the virial with temperature according to Malijevsky et al.

8: Gas Mixtures

Figure 8.1.

Variations in the second coefficient of the virial with composition – I - H

2

/He, II - H

2

/Ar, III - He/Ar (from [GIB 29])

Figure 8.2. C

ritical temperature and pressure of a binary compound

Figure 8.3.

Liquid-vapor chart of binary cyclohexane – carbon dioxide, comparison of experimental points and calculated curves

Figure 8.4.

Comparison between experimental data, PSRK results (---) and VTPR results (

—

) for some liquid-vapor equilibria (from Ahler and Gmehling, 2001)

Figure 8.6.

Comparison of a liquid-vapor chart obtained experimentally, by VTPR and VTPR using UNIFAC (DO)data (according to Foster, Rarey, Ramjugernath, 2009)

Figure 8.7.

Comparison of coefficients of activity calculated using both models in the case of binary propane-benzene (according to Foster, Rarey, Ramjugernath, 2009)

Figure 8.8.

Comparison between experimental data and VTPR data using UNIFAC (Do) and with UNIFAC (Do) only (according to Foster, Rarey, Ramjugernath, 2009)

Figure 8.9.

Chart showing the iterations when calculating activity coefficients of transfer

Guide

Cover

Table of Contents

Begin Reading

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Chemical Thermodynamics Set

coordinated by MichelSoustelle

Phase Modeling Tools

Applications to Gases

Volume 1

Michel Soustelle

First published 2015 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd

27-37 St George’s Road

London SW19 4EU

UK

www.iste.co.uk

John Wiley & Sons, Inc.

111 River Street

Hoboken, NJ 07030

USA

www.wiley.com

© ISTE Ltd 2015

The rights of Michel Soustelle to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2015940031

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-84821-864-2

Preface

This book – an in-depth examination of chemical thermodynamics – is written for an audience of engineering undergraduates and Masters students in the disciplines of chemistry, physical chemistry, process engineering, materials, etc., and doctoral candidates in those disciplines. It will also be useful for researchers at fundamental- or applied-research labs, dealing with issues in thermodynamics during the course of their work.

These audiences will, during their undergraduate degree, have received a grounding in general thermodynamics and chemical thermodynamics, which all science students are normally taught, and will therefore be familiar with the fundamentals, such as the principles and the basic functions of thermodynamics, and the handling of phase- and chemical equilibrium states, essentially in an ideal medium, usually for fluid phases, in the absence of electrical fields and independently of any surface effects.

This set of books, which is positioned somewhere between an introduction to the subject and a research paper, offers a detailed examination of chemical thermodynamics that is necessary in the various disciplines relating to chemical- or material sciences. It lays the groundwork necessary for students to go and read specialized publications in their different areas. It constitutes a series of reference books that touch on all of the concepts and methods. It discusses both scales of modeling: microscopic (by statistical thermodynamics) and macroscopic, and illustrates the link between them at every step. These models are then used in the study of solid, liquid and gaseous phases, either of pure substances or comprising several components.

The various volumes of the set will deal with the following topics:

– phase modeling tools: application to gases;

– phase modeling of liquid phases;

– modeling of solid phases;

– chemical equilibrium states;

– phase transformations;

– electrolytes and electrochemical thermodynamics;

– thermodynamics of surfaces, capillary systems and phases of small dimensions.

Appendices in each volume give an introduction to the general methods used in the text, and offer additional mathematical tools and some data.

This series owes a great deal to the feedback, comments and questions from all my students at the École nationale supérieure des mines (engineering school) in Saint Etienne who have “endured” my lecturing in thermodynamics for many years. I am very grateful to them, and also thank them for their stimulating attitude. This work is also the fruit of numerous discussions with colleagues who teach thermodynamics in the largest establishments – particularly in the context of the group “Thermodic”, founded by Marc Onillion. My thanks go to all of them for their contributions and conviviality.

This volume is split into two parts. In the first part, Chapter 1 is dedicated to phase modeling tools and covers the modeling of a phase: constructing potential characteristic functions. Chapter 2 covers the microscopic approach and presents the characteristic matrices that group together thermodynamic coefficients, from different experimental data. Chapters 3, 4 and 5 cover tools used in the microscopic modeling of phases through the use of statistics of molecular objects and microcanonical and canonical spaces. The calculation of state functions from molecular data allow the characteristic functions of a phase to be calculated.

The second part covers the modeling of gaseous phases. In Chapter 7, we cover macroscopic and microscopic modeling of pure gases using state equations, generalized compressibility charts and the concept of fugacity. Microscopic modeling is an initial application of statistical thermodynamics by calculating the second virial coefficient. The eighth chapter describes the models of gaseous mixtures, macroscopic and microscopic. Mixed models from models of condensed solutions and state equations are covered.

Michel Soustelle Saint-Vallier, France April 2015

Notations

{gas} : pure gas

{{gas}} : gas in mixture

(liquid) : pure liquid

((liquid)) : liquid in solution

〈solid〉 : pure solid

〈〈solid〉〉 : solid in solution

Symbols

A : Area of a surface or interface

: Hamaker constant between two media 1 and 2