Kinetic theory of gases Quotes

“Thermodynamics”

“Boltzmann, Ludwig”

“Wikipedia: Kinetic theory of gases”

“Early Theories of Gases from Dave Livermore, University of Maryland, College Park”

“Hari Seldon devised psychohistory by modeling it upon the kinetic theory of gases. Each atom or molecule in a gas moves randomly so that we can't know the position or velocity of any one of them. Nevertheless, using statistics, we can work out the rules governing their overall behavior with great precision. In the same way, Seldon intended to work out the overall behavior of human societies even though the solutions would not apply to the behavior of the individual human beings.”

“The influence of Quetelet's ideas spread throughout the sciences, even to the physical sciences. The two primary founders of the modern kinetic theory of gases, based on considerations of probability, were James Clerk Maxwell and Ludwig Boltzmann. Both acknowledged their debt to Quetelet. ...[H]istorians generally consider the influence of the natural sciences on the social sciences, whereas in the case of Maxwell and Boltzmann, there is an influence of the social sciences on the natural sciences, as Theodore Porter has shown.”

“YouTube videos
• 7. Kinetic Theory of Gases Part 1, MIT OpenCourseWare
• Kinetic molecular theory of gases, Khan Academy
• Kinetic molecular theory of gases, Khan Academy
• The kinetic molecular theory of gases, Khan Academy
• Kinetic Theory of Gases, Chemistry by Sudhakar AVC”

“The idea of a Kinetic Theory of Gases originated with J. Bernouilli about the middle of the last century, but the first establishment of the theory on a scientific basis is due to Professor Clausius.
During the last few years the theory has been greatly developed by many physicists, especially by Professor Clerk Maxwell in England and Professor Clausius and Dr. Ludwig Boltzmann... and although still beset by formidable difficulties, it has succeeded in explaining most of the established laws of gases in so remarkable a manner as to render it well worthy of the attentive consideration of scientific men. ...For the most part I have followed the method of treatment adopted by Dr. Ludwig Boltzmann in some very interesting memoirs ...”

“The science of Thermodynamics, founded by the labors of these three illustrious men [Nicolas Léonard Sadi Carnot, William Thomson & Rudolf Clausius], has led to the most important developments in all departments of physical science. It has pointed out relations among the properties of bodies which could scarcely have been anticipated in any other way; it has laid the foundation for the Science of Chemical Physics; and, taken in connection with the kinetic theory of gases, as developed by Maxwell and Boltzmann, it has furnished a general view of the operations of the universe which is far in advance of any that could have been reached by purely dynamical reasoning.”

“The first constant... is connected with the definition of temperature. If temperature were defined as the mean kinetic energy of a molecule in a perfect gas, which is a minute energy indeed, this constant would have the value ⅔. But in the conventional scale of temperature the constant ...[instead] assumes an extremely small value... intimately connected with the energy of a single molecule... [I]ts accurate determination would lead to the calculation of the mass of a molecule and... associated magnitudes. This constant is frequently termed Boltzmann's constant, although to the best of my knowledge Boltzmann... never introduced it (...he, as appears from... his statements, never believed it would be possible to determine this constant accurately)...”

“It will be shown in this paper that, according to the molecular-kinetic theory of heat, bodies of microscopically visible size suspended in liquids must, as a result of thermal molecular motions, perform motions of such magnitude that these motions can easily be detected by a microscope. It is possible that the motions to be discussed here are identical with the so-called "Brownian molecular motion"; however, the data available to me on the latter are so imprecise that I could not form a definite opinion on this matter.
If it is really possible to observe the motion to be discussed here, along with the laws it is expected to obey, then classical thermodynamics can no longer be viewed as strictly valid even for microscopically distinguishable spaces, and an exact determination of the real size of atoms becomes possible. Conversely, if the prediction of this motion were to be proved wrong, this fact would provide a weighty argument against the molecular-kinetic conception of heat.”

“One of the most important and interesting aims of physical chemistry is to explain the properties of matter in terms of the motions and spatial arrangements of atoms and molecules. This aim has been more nearly achieved in the physical chemical study of gases at low pressures [below a few atmospheres at ordinary temperatures] than the study of matter in any other conditions. ... The structure of gases at these pressures is particularly simple: such gases are collections of molecules which move randomly in space and which collide with each other relatively infrequently—that is, the molecules are so far apart that much of the time they exert little influence on each other. ...[T]he properties of the gaseous state play a role in many important practical processes, such as [in]... the internal combustion engine, the function of the lungs, the motions of the winds across the earth and the flight of airplanes. Gases... provide a useful and pedagogically attractive starting point for the introduction of students to physical chemistry.”

“The last thirty years have seen the beginning and development of a new period in physics and chemistry, namely the atomic period. In contrast to the period preceding it where nature's processes were described in terms of continua, recent developments have emphasized the discrete structure of the submicroscopic universe. Thus, today one hears of the atoms of matter, the atoms of electricity, and even the atoms of energy, the quanta. ...[T]he atomic theory of matter is the oldest and perhaps the most complete. ...[B]ecause of its relative simplicity the problem of the atomic theory of gases, in the form of the kinetic theory of gases, has attained the highest degree of perfection in this field. Its admirable methods of analysis are therefore indispensable... This book... endeavors to develop the various concepts... independently...Besides a simple introduction of each concept it gives derivations... elementary ones, using little or no calculus; more advanced classical derivations; and in some cases the most recent developments available. It also contains the comparison of the theoretical deductions with modern experiment and a critique of the theories.”

“In 1909 Perrin suspended particles of gamboge in a liquid of slightly lower density, and found that the heavy particles did not sink to the bottom of the lighter liquid; they were prevented from doing so by their own Brownian movements. If the liquid had been infinitely fine-grained, with molecules of infinitesimal size and weight, every solid particle would have had as many impacts from above as below; these impacts, coming in a continuous stream, would have just cancelled one another out, so that each particle would have been free to fall to the bottom under its own weight. But when they were bombarded by molecules of finite size and weight, the solid particles were hit, now in one direction and now in another, and so could not lie inertly on the bottom of the vessel. From the extent to which they failed to do this, Perrin was able to form an estimate of the weights of the molecules of the liquid... and this agreed so well with other estimates that there could be but little doubt felt as to the truth either of the kinetic theory of liquids, or of the associated explanation of the Brownian movements.”

“The first edition of this book appeared in 1877, at the time of the most rapid and beautiful development of the kinetic theory of gases. About twenty years before, the founders... Kronig and Clausius, had explained the expansive tendency of gases, and had calculated their pressure on the assumption that the smallest particles of gases do not repel each other, but are in rapid motion. From the theory based on this supposition not only were the laws of gases... deduced... but also new laws, hitherto undreamt of, were discovered... [and] afterwards confirmed... by experiment. These results, which we owe to Maxwell and Clausius, quickly won to the theory many friends and adherents. ...I undertook ...to exhibit the ...theory ...such ...as to be more easily intelligible ...especially to chemists and other natural philosophers to whom mathematics are not congenial. ...I endeavoured ...not only to develop the theory by calculation, but ...to support it by observation and found it on experiment. I... collected... and summarised, the observations by which the admissibility of the theory might be tested and its correctness proved. ...The mathematical discussions form ...an Appendix which ...need not be studied by every reader ...”

“If we study the history of science we see happen two inverse phenomena, so to speak. Sometimes simplicity hides under complex appearances; sometimes it is the simplicity which is apparent, and which disguises extremely complicated realities.
...What is more complicated than the confused movements of the planets? What simpler than Newton's law?
...In the kinetic theory of gases, one deals with molecules moving with great velocities, whose paths, altered by incessant collisions, have the most capricious forms... The observable result is Mariotte's simple law. ...The law of great numbers has reestablished simplicity in the average.
...No doubt, if our means of investigation should become more and more penetrating, we should discover the simple under the complex, then the complex under the simple, then again the simple under the complex, and so on, without our being able to foresee what will be the last term. We must stop somewhere, and that science may be possible, we must stop when we have found simplicity. This is the only ground on which we can rear the edifice of our generalizations.”

“Boltzmann decided to publish his lectures, in which the most important parts of the theory, including his ...contributions, were carefully explained. ...[H]e included his mature reflections and speculations on such questions as the nature of irreversibility and the justification for using statistical methods in physics. His Vorlesungen über Gastheorie was... the standard reference... for advanced researchers, ...[and] a popular textbook ...for the first quarter of the [20th] century ...The reason why the classical theory works is that, while the internal structure of molecules must be described by quantum mechanics, the interaction between two molecules can be fairly well described by a classical model which ignores this structure and simply uses a postulated force law whose parameters can be chosen to fit experimental data. ...Aside from phenomena at very high densities or very low temperatures, the only property that the classical theory fails to account for is the ratio of specific heats. ...Boltzmann ...simply concludes that for some unknown reason all the possible internal motions of a molecule do not have an equal share in the total energy, and takes this into account as an empirical fact.”

“Boyle... proposed a theoretical explanation for the elasticity of air... "a heap of little bodies, lying upon one another"... The atoms are said to behave like springs... Boyle also tried the "crucial experiment" which was to help overthrow his own theory in favor of the kinetic theory two centuries later, though he did not realize its significance... Experiment No. 26... places a pendulum in the evacuated chamber... [A]bsence of air makes hardly any difference to the period of the swings or the time... to come to rest. In 1859, James Clerk Maxwell deduced from the kinetic theory that the viscosity of a gas should be independent of its density... which would be very hard to explain on the basis of Boyle's theory. ...Neither Boyle nor Newton claimed that the hypothesis of repulsive forces between atoms is the only correct explanation for gas pressure; both were willing to leave the question open. Boyle mentions the Descartes theory of vortices (1644)... somewhat closer in spirit to the kinetic theory since it relies more heavily on the rapid motion of the parts of the atom as a cause of repulsion. (Though Descartes did not believe in "atoms" in the classical sense.) Nevertheless, the Boyle-Newton theory of gases was apparently accepted by most scientists until about the middle of the 19th century, when the kinetic theory finally managed to overcome Newton's authority.”

“Now, although the plans of the edifice of the electromagnetic theory of light were laid in 1880 by H. A. Lorentz, and even indicated much earlier by W. Weber, a full 10 years were required before the discoveries of Heinrich Hertz gave the impetus to collect the building stones and work them into shape. In the years 1890-93 a number of works appeared by F. Richarz, H. Ebert and G. Johnstone Stoney, mostly dealing with the mechanism of the emission of luminous vapours, and in which attempts are made, on the basis of the kinetic theory of gases, to determine the magnitude of the elementary electrical quantity, called by Stoney by the now universally accepted name of electron. ...H. Ebert proved that the amplitude of an electron in luminous sodium vapour need only be a small fraction of a molecular diameter in order to excite a radiation of the absolute intensity determined by E. Wiedemann. The way of determining the amount of electricity contained in the electron is very simple. The quantity of electricity required for the electrolytic evolution of 1 cubic cm. of any monatomic gas is divided by Loschmidt's number—i.e., the number of gas molecules contained in 1 cubic cm.”

“The kinetic theory of gases is a small branch of physics which has passed from the stage of excitement and novelty into staid maturity. ...Formerly it was hoped that the subject of gases would ultimately merge into a general kinetic theory of matter; but the theory of condensed phases... today, involves an elaborate and technical use of wave mechanics, and for this reason it is best treated as a subject in itself.
The scope of the present book is, therefore, the traditional kinetic theory of gases. ...[A]n account has been included of the wave-mechanical theory, and especially of the degenerate Fermi-Dirac case... There is also a concise chapter on statistical mechanics, which... may be of use as an introduction... [T]he discussion of electrical phenomena has been abbreviated... the latter voluminous subject is best treated separately. ...[F]undamental parts have been explained... [as] to be within the reach of college juniors and seniors. The... wave mechanics and statistical mechanics... are of graduate grade. ...[A] number of carefully worded theorems have been inserted in the guise of problems, without proof... to give... a chance to apply... lines of attack exemplified in the text.
To facilitate use as a reference book, definitions have been repeated freely, I hope not ad nauseam. ...Ideas have been drawn freely from ...books such as ...of Jeans and Loeb...”