Lectures on Gas Theory

Ludwig Boltzmann

• Publisher: Dover Publications
• Year: 2012
• Print ISBN: 9780486684550
• eBook ISBN: 9780486152332
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

One of the great masterpieces of theoretical physics, this classic work contains a comprehensive exposition of the kinetic theory of gases that is still relevant today, nearly 100 years after its first publication. Although the modifications of quantum mechanics have rendered some parts of the work obsolete, many of the topics dealt with still yield to the classical-mechanics approach outlined by Boltzmann; moreover, a variety of problems in aerodynamics, nuclear reactors, and thermonuclear power generation are best solved by Boltzmann's famous transport equation.
The work is divided into two parts: Part I deals with the theory of gases with monatomic particles, whose dimensions are negligible compared to the mean free path. Topics include molecules as elastic spheres and as centers of force, external forces and visible motions of the gas and the repelling force between molecules. Part II covers van der Waals' theory, the principles of general mechanics needed for a gas theory, gases with compound molecules, derivation of van der Waals' equation by means of the virial concept, theory of dissociation and supplements to the laws of thermal equilibrium in gases with compound molecules.
Combining rigorous mathematical analysis with pragmatic treatment of physical and chemical applications, Lectures on Gas Theory was the standard work on kinetic theory in the first quarter of the 20th century. It remains "one of the greatest books in the history of exact sciences." ― Mark Kac.

PART I

Theory of gases with monatomic molecules, whose dimensions are negligible compared to the mean free path.

NOTE ON LITERATURE CITATIONS

All the numbered footnotes correspond to Boltzmann’s notes in the original text, but the numbers start with 1 in each section rather than each page, and the form of citation of some journals has been changed for the sake of consistency with modern style. Footnotes indicated by asterisks, daggers, etc., have been added by the translator. More complete information including titles of articles cited will be found in the Bibliography at the end of the book.

NOTE ON GOTHIC LETTERS

To forestall possible difficulties in recognition, here are the alphabetical equivalents:

FOREWORD TO PART I

“Alles Vergängliche

Ist nur ein Gleichniss!”*

I have often before come close to writing a textbook on gas theory. I remember especially the enthusiastic request of Professor Wroblewski at the Vienna World’s Fair in 1873. When I showed little inclination to write a textbook, since I did not know how soon my eyes would fail me, he answered dryly: “All the more reason to hurry up!” At present, when I no longer have this reason, the time seems less appropriate for such a textbook than it was then. For, first, gas theory has gone out of fashion in Germany, as it were; second, the second edition of O. E. Meyer’s well-known text has appeared, and Kirchhoff has devoted a longer section of his lectures on the theory of heat to gas theory.† Yet Meyer’s book, though acknowledged to be excellent for chemists and students of physical chemistry, has a completely different purpose. Kirchhoff’s work shows the touch of a master in the selection and presentation of its topics, but it is only a posthumously published set of lecture notes on the theory of heat, which treats gas theory as an appendix, not a comprehensive textbook. Indeed, I freely confess that the interest, on the one hand, which Kirchhoff showed in gas theory, and on the other hand the many gaps in his presentation because of its brevity, have encouraged me to publish the present work, which likewise originated from lectures at the universities of Munich and Vienna.

In this book I have tried above all to make clearly comprehensible the path-breaking works of Clausius and Maxwell. The reader may not think badly of me for finding also a place for my own contributions. These were cited respectfully in Kirchhoff’s lectures and in Poincaré’s Thermodynamique* at the end, but were not utilized where they would have been relevant. From this I concluded that a brief presentation, as easily understood as possible, of some of the principal results of my efforts might not be superfluous. Of great influence on the content and presentation was what I have learned at the unforgettable meeting of the British Association in Oxford and the subsequent letters of numerous English scientists, some private and some published in Nature.†

I intend to follow Part I by a second part, where I will treat the van der Waals theory, gases with polyatomic molecules, and dissociation. An explicit proof of Equation (110a)—which is only indicated briefly in §16, in order to avoid repetition—will also be included.

Unfortunately it was often impossible to avoid the use of long formulas to express complicated trains of thought, and I can well imagine that to many who do not read over the whole work, the results will perhaps not seem to justify the effort expended. Aside from many results of pure mathematics which, though likewise apparently fruitless at first, later become useful in practical science as soon as our mental horizon has been broadened, even the complicated formulas of Maxwell’s theory of electromagnetism were oft...

Table of contents

• Cover
• Title Page
• Copyright Page
• Contents
• Translator’s Introduction
• Part I: Theory of Gases With Monatomic Molecules, Whose Dimensions are Negligible Compared to the Mean Free Path.
• Part II: Van Der Waals’ Theory; Gases with Compound Molecules; Gas Dissociation; Concluding Remarks.
• Bibliography
• Index