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Thermodynamics of Clouds LOUIS DUFOUR and RAYMOND DEFAY University of Brussels Brussels,. Belgium Royal Belgian Meteorological Institute Ucde, Belgium Translated by and M. Smyth A. Beer 1963 ACADEMIC PRESS New York and London COPYRIGHT © 1963, BY ACADEMIC PRESS INC. ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS, WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS. ACADEMIC PRESS INC. 111 Fifth Avenue, New York 3, New York United Kingdom Edition published by ACADEMIC PRESS INC. (LONDON) LTD. Berkeley Square House, London, W.l LIBRARY OF CONGRESS CATALOG CARD NUMBER: PRINTED IN THE UNITED STATES OF AMERICA 62.13089 Introduction Examining the treatment in meteorological works of thermodynamical problems involving the ideas of surface tension and of adsorption, one is struck by the fact that such questions are almost always dealt with in a fragmentary manner. The reader is referred to various works which he is recommended to study in order to understand the statements presented. The multiplicity of sources on which it is desirable to draw leads him to feel the need for a general treatment, and to wish for a single account uniting in a coherent manner the various problems of a similar nature involving the thermodynamics of capillarity. Only an account of this kind enables one to get to the root of problems, to perceive what physical hypotheses are required in the process, and to judge the consistency or inconsistency of various theories. For these reasons we considered it useful to present, under the title of Thermodynamics of Clouds, a coherent and rational account, requiring only a little knowledge of general thermodynamics, which takes up each idea from the beginning and allows the reader to appreciate the degree of rigor or of approximation at each stage, and which discusses each hypothesis and develops each theory with a clear statement of the basic physical concepts. We hope thus to have placed at the disposal of meteorologists a working tool which will allow them to master the problems encountered in this branch of meteorology. Finally, we have throughout this book given numerical applications of the formulas obtained. The results of these calculations are collected in the very numerous tables accompanying the text, in which we have evaluated the quantities which interest the meteorologist in this field. Thermodynamics of Clouds is divided into thirteen chapters, the first six of which, establishing the general formulas of the thermodynamics of surfaces, form in a sense the first part of the book. In this part we have followed the method used by Defay and Prigogine- (1951) of studying systems in a state of partial equilibrium. Mechanical and thermal equilibria are supposed to hold, whereas adsorption equilibria are not necessarily established. 1 The name of an author followed by a date in parentheses refers to a work listed in the Bibliography. v vi INTRODUCTION In Chapter I, devoted to ideas of capillarity, we have systematically used Young's concept of a strained surface. Both the position of this surface, called the surface of tension, and the value of the surface tension are fixed by making this simplified model mechanically equivalent to the complex layer which separates the two coexistent volume phases. An examination of the surface tension of crystalline faces has led us to the conclusion that the Wulff crystal seems to be the only one which can be described by the simple model of a phase of isotropic pressure surrounded by strained faces. In Chapter II, to define adsorption and surface thermodynamic properties we have systematically used the idea of the divid