Gibbs' Entropic Paradox and Problems of Separation Processes

Eugene Barsky

• Publisher: Elsevier
• Year: 2017
• Print ISBN: 9780444639196
• eBook ISBN: 9780444639202
• Topic: Technology & Engineering
• Subtopic: Chemical & Biochemical Engineering
• Index: Technology & Engineering

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. - 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

Chapter 1

Peculiarities of Thermodynamic Regularities Formation

Abstract

The notion of entropy has arisen in thermodynamics, which occupies a special place in the system of natural sciences and in the development of engineering and technology.

The science of heat transformations was developing on the basis of empirical data. This gave rise to different interpretation of the same facts, which led to the affirmation of disputable ideas. Despite that, two main thermodynamic laws were formulated correctly—the law of energy conservation and transformation and the law of heat and work equivalence. The latter substantiated the principle of entropy and its permanent growth. Main controversies and discussions flared up around the entropy parameter. They continue until now. A certain group of scientists demand a refusal from the entropy parameter thinking that it is a “cancerous tumor” of natural science. The reason being the appearance of a number of paradoxes and misunderstandings connected with this parameter. The main of these in modern physics is the Gibbs paradox, whose generally accepted solution has not been found as yet, although many outstanding scientists have devoted their works to this paradox.

Keywords

Entropy; Entropy jump; Informational entropy; Irreversibility; Mass process; Mixture of gases; Paradox; Probability; Quantum physics; Reversibility; Statistical physics; Thermodynamics

Chapter Outline

1. Character of the Development of Heat Conversion Science

2. Substantiation of the Validity of Boltzmann's Theory

1. Character of the Development of Heat Conversion Science

Thermodynamics occupies a special place among natural sciences due to both the general character of its basic principles and importance for engineering and technology.

The history of thermodynamics development is rather instructive, since this science was characterized by the greatest number of controversial assertions and conclusions made and ambiguous ideas suggested. Discussions of some of them continue up to our time.

This book is devoted to the Gibbs paradox solution. We can show that this paradox was formed in the atmosphere of numerous controversial ideas suggested. Not always were they wrong, but they usually induced heated debates. In the context of the problem under study, it is useful to look back and to discuss, at least superficially, some of the subjects of disputes and controversies for a deeper insight into the methodology of overcoming them.

Obviously, the point is that thermodynamics developed much later than classical mechanics, where everything logically followed from accepted axioms and hypotheses. Results obtained by classical mechanics methods did not excite serious disputes and had a high prestige.

The science of heat conversions arose on the basis of comprehension and generalization of empirical data based initially on rather rough experiments. This gave occasion to different interpretations of the same facts. The necessity of thermodynamics development was insistently dictated by the arising social need for correct design, construction, and operation of steam boilers, heat engines, and, later, diesel and petrol engines and turbines of various types.

The first experiments were successfully interpreted by equating heat to a certain material substance—a caloristic fluid called phlogiston. It was assumed that this fluid is transferred from one body to another in the process of heat transfer, its quantity being conserved.

This standpoint was shared by many top-level scientists of their time, such as Lavoisier, Fourier, Laplace, Poisson, etc. With the expansion of experiments and development of scientific notions, this theory was rejected, but it was accompanied by heated disputes.

Modern monographs and manuals of physics express an opinion that no progress was attained on the basis of phlogiston theory. However, it is not true. On the basis of these ideas, Poisson derived equations of adiabatic process, the problem of sound velocity in gases was solved, Sadi Carnot's outstanding theory, Fourier's analytical theory of heat conductivity, and Prevost's theory of dynamic equilibrium were developed. Thus, it was far from being simple to overcome these notions. Phlogiston theory was a historically necessary stage in the development of the theory of heat. This stage lasted for at least 150 years. Its positive role consisted of a combination of a great amount of facts and particular theories, their systematization and interpretation from a unified standpoint. Phlogiston theory reflected, to a certain extent, some regularities of heat phenomena and, in a number of special cases, led to correct results (the Poisson equation, quasistatic Carnot cycle, Hess law, etc.).

In these cases, consistent results were obtained owing to the fact that the original prerequisites contained conditions in which the quantity of heat in a specific system could be considered as unchanged. In this period of time, no convincing experiments were made proving the inconsistency of phlogiston theory. The principal notion of the phlogiston theory, the quantity of heat, was visual enough, measurable, and could be numerically calculated. Thermal balance equation could be easily written, which made it possible to perform various calculations.

A research constituting a starting point in the development of thermodynamics as a science was accomplished on the basis of phlogiston theory. We imply the work of a French engineer Sadi Carnot. He described the sequence of heat engine operation forming, on the whole, a cyclic process. He was the first to suggest this brilliant analytical method that exerted a decisive influence on the development of classical thermodynamics. It served as the basis for further formation of such fundamental notions as absolute temperature and entropy. However, these ideas of cyclic heat conversion in a thermal engine also remained questionable for a long time.

As known, many University professors refuted Carnot's ideas for a long time, but he finally proved to be right.

Experiments demonstrating a release of a large quantity of heat in the process of drilling gun barrels and proved that heat is not a substance. The theory of heat as a concept of weightless fluids was finally refuted after Mayer's and Joule's studies.

Recall that the second law of thermodynamics was openly ignored for a long time. It probably happened because by the 1980s of the XIX century, thermodynamics obviously started getting beyond the scope of not only the theory of heat and work correlation, but even of physics. It became clear that these methods could be successfully applied to other theoretical fields of natural science, and the two laws of thermodynamics pretended to the role of the most general laws of nature. As for the first law—law of energy conservation and conversion—its general character and universality were beyond any doubt by that time. It was successfully applied in chemistry and biology. The value of the results obtained by Clausius and based on the principle of heat and work equivalence is that they allowed formulating the second law of thermodynamics. These results can be summarized as follows:

▪ The method of cyclic processes initially developed by Carnot played the principal role in the substantiation of the second law and its application to specific thermodynamic systems.

▪ The substantiation of the second law was connected with a high enough degree of idealization of real physical systems, in particular, gases.

▪ Classical wordings of the second law combine two different principles—those of entropy existence and growth.

▪ The results obtained by Clausius allowed the introduction of such fundamental notions as absolute temperature and entropy into thermodynamics. Initially, these parameters were formulated on the basis of assumptions characteristic of ideal gases. However, the ideas of Clausius were not accepted at once and caused violent objections. His contemporaries, such as Rankin, Dekher, Gurie, Preston, Tem, and others, were proving the inconsistency of the second law of thermodynamics in their publications. They even asserted that the works of Clausius were “harmful for science”. After that, the consistency of the second law was proved for a broad range of processes (electrical, diffusive, chemical, biological, thermotechnical, etc.) in the works of Schiller, Ehrenfest spouses, Caratheodory, Born, Minde, Planck, and others. This definitely points to the fact that Clausius discovered one of the most general principles related to all laws of nature. As Michelson noted, the second law of thermodynamics is one of the most incomprehensible and difficult-to-master laws of nature.

Here is another example. Clausius introd...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Introduction
• Chapter 1. Peculiarities of Thermodynamic Regularities Formation
• Chapter 2. Brief Review of Thermodynamic Regularities
• Chapter 3. The Gibbs Paradox and Attempts of Its Solution
• Chapter 4. Solution of the Gibbs Paradox and Related Problems
• Chapter 5. Available Quality Criteria for Separation Processes
• Chapter 6. Generalized Optimization Criterion for Separation Processes
• Chapter 7. Multistage Separation Mechanism
• Chapter 8. Practical Application of the Obtained Results
• Chapter 9. Analysis of the Obtained Results and Summing-up
• Bibliography
• Index