Gibbs' Entropic Paradox and Problems of Separation Processes

Gibbs' Entropic Paradox and Problems of Separation Processes

1st Edition - March 22, 2017

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  • Author: Eugene Barsky
  • eBook ISBN: 9780444639202
  • Paperback ISBN: 9780444639196

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Gibbs' Entropic Paradox and Problems of Separation Processes reviews the so-called Gibb’s Paradox observed during the mixing of two systems. During the last 150 years, many physicists and specialists in thermodynamics, statistical and quantum mechanics been engaged in the solution of the Gibbs paradox. Many books and journal articles have written on this topic, but a widely accepted answer is still lacking. In this book, the author reviews and analyzes all this data. Based on findings, the book formulates a different approach to this paradox and substantiates it on the basis of physical and statistical principles. The book clearly shows that entropy consists of two parts, static and dynamic. Up to now, entropy has been connected only with the process dynamics. However, the Gibbs paradox is caused by the change in the static component of entropy. Finally, the book includes examples of separation processes and how to optimize them in various fields, including biology, cosmology, crystallography and the social sciences.

Key Features

  • Provides a precise definition of entropy and allows the formulation of criteria for optimization of separation processes
  • Explains the role of entropy in many processes, facilitating an in-depth analysis and understanding of complicated systems and processes
  • Provides solutions to scientific and applied problems in various scientific disciplines related to separation processes
  • Elucidates entropy’s role in many separation systems


Students, doctoral candidates and scientists and specialists in the fields of thermodynamics statistical physics; biology; crystallography; astronomy; all other fields using the entropy parameter; mining engineering; metallurgy; electronics; modern ceramics

Table of Contents

  • Chapter 1. Peculiarities of Thermodynamic Regularities Formation

    • 1. Character of the Development of Heat Conversion Science
    • 2. Substantiation of the Validity of Boltzmann's Theory

    Chapter 2. Brief Review of Thermodynamic Regularities

    • 1. Preliminary Notes
    • 2. The First Law—Energy Conservation Principle
    • 3. The Second Law of Thermodynamics
    • 4. Carnot Cycle
    • 5. Formulation of the Notion of Entropy
    • 6. Statistical Substantiation of Entropy

    Chapter 3. The Gibbs Paradox and Attempts of Its Solution

    • 1. Essence of the Paradox
    • 2. Analysis of Attempts to Solve the Gibbs Paradox
    • 3. Operational Approach to the Paradox Solution
    • 4. Informational Approach to the Gibbs Paradox Solution
    • 5. Problems of Industrial Separation of Gas Mixtures

    Chapter 4. Solution of the Gibbs Paradox and Related Problems

    • 1. Physical Substantiation of Entropy Jump
    • 2. Entropy Dimension
    • 3. Certain Properties of Entropy of a Mixture

    Chapter 5. Available Quality Criteria for Separation Processes

    • 1. Quality Criteria Generation
    • 2. Other Indices of the Process Completion
    • 3. Criteria Differing From Hancock's Method
    • 4. Criteria-Free Methods of Separation Processes Optimization
    • 5. Optimization of Separation Processes by Fractional Extraction Curves
    • 6. Properties of Fractional Separation Curves

    Chapter 6. Generalized Optimization Criterion for Separation Processes

    • 1. Probabilistic Interpretation of Mixture Components
    • 2. Uncertainty of Mixture Composition
    • 3. Separation Efficiency
    • 4. Optimality Condition for Binary Mixtures Separation by the Entropy Criterion

    Chapter 7. Multistage Separation Mechanism

    • 1. Fractions Over the Cascade Stages
    • 2. Proportional Model of Cascade Separation
    • 3. Discrete Model
    • 4. Principal Relationships of the Model
    • 5. Fractional Extraction into Fine Product
    • 6. Analysis of Mathematical Model of Regular Cascade
    • 7. Separation at Cyclic Feed of the Initial Material into a Cascade Apparatus
    • 8. Absorbing Markov's Chain in Cascade Separation of Bulk Materials
    • 9. Mathematical Model of Cascade Separation With Arbitrary Distribution Coefficients

    Chapter 8. Practical Application of the Obtained Results

    • 1. Separation of Binary Mixtures
    • 2. Multiproduct Separation
    • 3. Algorithms of Optimization of Separation into n Components
    • 4. Optimality Conditions for Multiproduct Separation

    Chapter 9. Analysis of the Obtained Results and Summing-up

    • 1. Extension of the Insight into Some Aspects of Entropy Parameter
    • 2. Some Fundamental Aspects of Entropy
    • 3. Conclusion

Product details

  • No. of pages: 202
  • Language: English
  • Copyright: © Elsevier 2017
  • Published: March 22, 2017
  • Imprint: Elsevier
  • eBook ISBN: 9780444639202
  • Paperback ISBN: 9780444639196

About the Author

Eugene Barsky

The author, Dr. Eugene Barsky, has been engaged in this subject for 18 years, since 1993. His M.Sc. thesis completed in 1998 was devoted to the development of models of cascade separation of solid materials in flows. His PhD thesis completed in 2001 was devoted to the development of entropy criterion of separation processes optimization. Among dozens of criteria applied, the entropy criterion has proved to be the most unbiased one. Since that time, the author has been developing these topics in depth. He created a number of industrial cascade apparatuses for powders separation and dust collection, wrote about 20 articles, published two books, participated in many scientific congresses and conferences. The material accumulated during 6 recent years is presented in the proposed book.

Affiliations and Expertise

Department of Industrial Engineering, Azrieli College of Engineering, Jerusalem, Israel

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