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Thermodynamics TREATISE ON THERMODYNAMICS BY DR. MAX PLANCK PROFESSOR OF THEORETICAL PHYSICS IN THE UNIVERSITY OF BERLIN TRANSLATED WITH THE AUTHOR'S SANCTION BY ALEXANDER OGG, M.A., B.Sc., PH.D., F.INST.P. PROFESSOR OF PHYSICS, UNIVERSITY OF CAPETOWN, SOUTH AFRICA THIRD EDITION TRANSLATED FROM THE SEVENTH GERMAN EDITION DOVER PUBLICATIONS, INC. FROM THE PREFACE TO THE FIRST EDITION. THE oft-repeated requests either to publish my collected papers on Thermodynamics, or to work them up into a comprehensive treatise, first suggested the writing of this book. Although the first plan would have been the simpler, especially as I found no occasion to make any important changes in the line of thought of my original papers, yet I decided to rewrite the whole subject-matter, with the inten- tion of giving at greater length, and with more detail, certain general considerations and demonstrations too concisely expressed in these papers. My chief reason, however, was that an opportunity was thus offered of presenting the entire field of Thermodynamics from a uniform point of view. This, to be sure, deprives the work of the character of an original contribution to science, and stamps it rather as an introductory text-book on Thermodynamics for students who have taken elementary courses in Physics and Chemistry, and are familiar with the elements of the Differential and Integral Calculus. The numerical values in the examples, which have been worked as applications of the theory, have, almost all of them, been taken from the original papers; only a few, that have been determined by frequent measurement, have been " taken from the tables in Kohlrausch's Leitfaden der prak- tischen Physik." It should be emphasized, however, that the numbers used, notwithstanding the care taken, have not vii x PREFACE. basis of the theory. Since this book is chiefly concerned with the exposition of these fundamental principles, and the applications are given more as illustrative examples, I have not aimed at a new treatment of the subject, but have limited myself to corrections of some numerical data, and to a careful revision of the general ideas. I have thereby found it advis- able to make a number of changes and additions. Many of these have been suggested by scientific acquaintances and colleagues. With regard to the concluding paragraph of the preface to the first edition, I may be permitted to remark that the theory of heat has in the interval made remarkable progress along the path there indicated. Just as the first law of Thermodynamics forms only one side of the universal principle of the conservation of energy, so also the second law, or the principle of the increase of the Entropy, possesses no inde- pendent meaning. The new results of the investigations in the subject of heat radiation have made this still clearer. In this connection, I may mention the names of W. Wien, F. Paschen, 0. Lummer and E. Pringsheim, H. Rubens, and F. Kurlbaum. The full content of the second law can only be understood if we look for its foundation in the known laws of the theory of probability as they were laid down by Clausius and Maxwell, and further extended by Boltzmann. According to this, the entropy of a natural state is in general equal to the logarithm of the probability of the corresponding state multiplied by a universal constant of the dimensions of energy divided by temperature. A closer discussion of this relation, which penetrates deeper than hitherto into a know- ledge of molecular processes, as also of the laws of radiation, would overstep the limits which have been expressly laid down for this work. This discussion will therefore not be undertaken here, especially as I propose to deal with this subject in a separate book. BERLIN, January, 1905. PREFACE. xi PREFACE TO THE THIRD EDITION. THE plan of the presentation and the arrangement of the material is maintained in the new edition. Nevertheless, there is to be found in this edition, apart from a further revision of all the numerical data, a number of explanations and additions, which, one way or another, have been sug- gested. These are to be found scattered throughout the whole book. Of such I may mention, for example, the law of corresponding states, the definition of molecular weight, the proof of the second law, the characteristic thermodynamic function, the theory of the Joule-Thomson effect, and the evaporation of liquid mixtures. Further suggestions will always be very thankfully received. A real extension of fundamental importance is the heat theorem, which was introduced by W. Nernst in 1906. Should this theorem, as at present appears likely, be found to hold good in all directions, then Thermodynamics will be enriched by a principle whose range, not only from the practical, but also from the theoretical point of view, cannot as yet be foreseen. In order to present the true import of this new theorem in a form suitable for experimental test, it is, in my opinion, necessary to leave out of account its bearing on the atomic theory, which to-day is by no means clear. The methods, which have otherwise been adopted in this book, also depend on this point of view. On the other hand, I have made the theorem, I believe, as general as possible, in order that its applications may be simple and comprehensive. Accordingly, Nernst's theorem has been extended both in form and in content. I mention this here as there is the possibility of the extended theorem not being confirmed, while Nernst's original theorem may still be true. BERLIN, November, 1910. xii PREFACE. PREFACE TO THE FIFTH EDITION. FOB the fifth edition, I have once more worked through the whole material of the book, in particular the section on Nernst's heat theorem. The theorem in its extended form has in the interval received abundant confirmation and may now be regarded as well established. Its atomic significance, which finds expression in the restricted relations of the quantum hypothesis, cannot, of course, be estimated in the present work. BERLIN, March, 1917. CONTENTS. PART I. FUNDAMENTAL FACTS AND DEFINITIONS. CHAP. PAGE I. TEMPERATURE ....... 1 II. MOLECULAR WEIGHT ...... 23 III. QUANTITY OF HEAT ...... 34 PART II. THE FIRST FUNDAMENTAL PRINCIPLE OF THERMODYNAMICS. I. GENERAL EXPOSITION ..... 40 II. APPLICATIONS TO HOMOGENEOUS SYSTEMS . 48 III. APPLICATIONS TO NON-HOMOGENEOUS SYSTEMS . 69 PART III. THE SECOND FUNDAMENTAL PRINCIPLE OF THERMODYNAMICS. I. INTRODUCTION . ..... 78 II. PROOF ........ 89 III. GENERAL DEDUCTIONS ..... 108 xiv CONTENTS PART IV. APPLICATIONS TO SPECIAL STATES OF EQUILIBRIUM. CHAP. [PAGE T. HOMOGENEOUS SYSTEMS ..... 125 II. SYSTEM IN DIFFERENT STATES OF AGGREGATION . 139 III. SYSTEM OF ANY NUMBER OF INDEPENDENT CON- STITUENTS 179 IV. GASEOUS SYSTEM . ..... 215 V. DILUTE SOLUTIONS ...... 229 VI. ABSOLUTE VALUE OF THE ENTROPY. NERNST's THEOREM 272 INDEX ........ 293 TREATISE ON THERMODYNAMICS. PART I. FUNDAMENTAL FACTS AND DEFINITIONS. CHAPTER I. TEMPERATURE. " " 1. THE conception of heat arises from that particular sensation of warmth or coldness which is immediately experi- enced on touching a body. This direct sensation, however, furnishes no quantitative scientific measure of a body's state with to heat it which regard ; yields only qualitative results, vary according to external circumstances. For quantitative purposes we utilize the change of volume which takes place in all bodies when heated under constant pressure, for this admits of exact measurement. Heating produces in most substances an increase of volume, and thus we can tell whether a body gets hotter or colder, not merely by the sense of touch, but also by a purely mechanical observation affording a much greater degree of accuracy. We can also tell accurately when a body assumes a former state of heat. 2. If two bodies, one of which feels warmer than the other, be brought together (for example, a piece of heated metal and cold water), it is invariably found that the hotter body is cooled, and the colder one is heated up to a certain 2 THERMODYNAMICS. point, and then all change ceases. The two bodies are then said to be in thermal equilibrium. Experience shows that such a state of equilibrium finally sets in, not only when two, but also when any number of differently heated bodies are brought into mutual contact. From this follows the important proposition : // a body, A, be in thermal equili- brium with two other bodies, B and C, then B and C are in thermal equilibrium with one another. For, if we bring A, B, and C together so that each touches the other two, then, according to our supposition, there will be equilibrium at the points of contact AB and AC, and, therefore, also at the contact BC. If it were not so, no general thermal equili- brium would be possible, which is contrary to experience. 3. These facts enable us to compare the degree of heat of two bodies, B and C, without bringing them into contact with one another; namely, by bringing each body into contact with an arbitrarily selected standard body, A (for example, a mass of mercury enclosed in a vessel terminating in a fine capillary tube). By observing the volume of A in each case, it is possible to tell whether B and C are in thermal equilibrium or not. If they are not in thermal equilibrium, we can tell which of the two is the hotter. The degree of heat of A, or of any body in thermal equilibrium with A, can thus be very simply defined by the volume of A, or, as is usual, by the difference between the volume of A and an arbitrarily selected normal volume, namely, the volume of A when in thermal equilibrium with melting ice under atmospheric pressure.
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