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A KINETIC THEORY OF GASES AND LIQUIDS BY RICHARD D. KLEEMAN, D. Sc. Adelaide, B. A. Cantab. Associate Professor of Physics, Union College Consulting Physicist and Physical Chemist formerly 1851 Exhibition Scholar of the University of Adelaide, Research Student of Emmanuel College, Cambridge, Mackinnon Student of the Royal Society of London, and Clerk Maxwell Student of the University of Cambridge FIRST EDITION NEW YORK JOHN WILEY SONS, INC. LONDON CHAPMAN HALL, LIMITED 1920 Copyright, 1920 BY RICHARD D. KLEEMAN PRESS OF BRAUNWORTH CO. BOOK MANUFACTURERS BROOKLYN, H. Y. DEDICATED TO MY PARENTS PREFACE THE object of writing this book is to formulate a Kinetic Theory of certain properties of matter, which shall apply equally well to matter in any state. The desirability of such a development need not be emphasized. The difficulty hitherto experienced in applying the results obtained in the case of the Kinetic Theory of Gases in the well-known form to liquids and intermediary states of matter has been pri marily due to the difficulty of properly interpretating molec ular interaction. In the case of gases this difficulty is in most part overcome by the introduction of the assumption that a molecule consists of a perfectly elastic sphere not surrounded by any field of force. But since such a state of affairs does not exist, the results obtained in the case of gases hold only in a general way, and the numerical constants involved are therefore of an indefinite nature, while in the case of dense gases and liquids this procedure does not lead to anything that is of use in explaining the facts. Instead of an atom, or molecule, consisting of a per fectly elastic sphere, it is more likely that eachmay be regarded simply as a center of forces of attraction and repulsion. If the exact nature of the field of force sur rounding atoms and molecules were known, it would be a definite mathematical problem to determine the resulting properties of matter. But our knowledge in this connection is at present not sufficiently extensive to permit a develop ment of the subject along these lines. But in whatever vi PREFACE way the subject is developed fundamental progress will have been made only if molecular interaction is not, as is usually the case, represented by the collision of elastic spheres. It will be shown in this book that the subject may be developed to a considerable extent along sound mathe matical lines yielding important results without knowing the exact nature and immediate result of molecular interaction. Thus it will be found, for example, that the definition of the free path of a molecule in connection with viscosity, con duction of heat, diffusion, etc., may be given a form in each case not involving the exact nature of molecular interaction, which is mathematically quite definite, and which therefore applies equally well to the liquid and gaseous states. Since in the gaseous state each kind of path is proportional to the volume of the gas, its interest is then mainly associated with the characteristic factor of the volume which makes the product numerically equal to the path. A direct physical meaning may be given to this factor. In constructing a general Kinetic Theory the problem that presents itself first for investigation is the dependence of the velocity of translation of a molecule in a substance on its density and temperature. It is often assumed that this velocityis the same in the liquid as in the gaseous state at the same temperature. It can be shown, however, that this holds only for each molecule at the instant it passes through a point in the substance at which the forces of the surrounding molecules neutralize each other. The total average velocity corresponding to the whole path of a mole cule is usually much greater than the foregoing velocity in a liquid and dense gas on account of the effect of the molecular forces of attraction and repulsion...