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 original papers, yet I decided to rewrite the whole subject-matter, with the inten- my tion of giving at greater length, and with more detail, certain general considerations and demonstrations too concisely chief reason, however, was expressed in these papers My 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 praktischen Physik." It should be emphasized, however, that the numbers used, notwithstanding the care taken, have not vii PREFACE x basis of the theory Since this book is chiefly concerned with the exposition of these fundamental principles, and the applications are given not aimed at a more as new treatment have but have limited illustrative examples, I of the subject, myself to corrections of some numerical data, and to a careful revision of the general ideas I have thereby found it advisable to make a number of changes and additions Many of these have been suggested by scientific acquaintances and colleagues With regard to the to the concluding paragraph of the preface I may be permitted to remark that the first edition, 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 independent meaning The new results of the investigations in the subject of heat radiation have made this still clearer In connection, may mention the names of W Wien, F Paschen, Lummer and E Pringsheim, H Rubens, and F Kurlbaum The full content of the second law can only I this 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 this, the entropy of a natural state is in general the to logarithm of the probability of the corresponding equal state multiplied by a universal constant of the dimensions of According to energy divided by temperature A closer discussion of this relation, which penetrates deeper than hitherto into a knowledge of molecular processes, as also of the laws of radiation, would overstep the limits which have been expressly laid down This discussion will therefore not be undertaken here, especially as I propose to deal with this subject in a separate book for this work BERLIN, January, 1905 PREFACE xi PREFACE TO THE THIRD EDITION THE material there plan of the presentation and the arrangement of the is maintained in the new edition Nevertheless, is to be found in this edition, apart from a further number of explanations revision of all the numerical data, a additions, which, one way or another, have been sugThese are to be found scattered throughout the gested whole book Of such I may mention, for example, the law and 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 also principle whose range, not only from the practical, but from the theoretical point of view, cannot as yet be foreseen In order to present the true import of this new theorem 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 in a general as possible, in order that simple and comprehensive applications may be Accordingly, Nernst's theorem its has been extended both in form and in content I mention extended theorem not being confirmed, while Nernst's original theorem may still be true this here as there is the possibility of the BERLIN, November, 1910 PREFACE xii 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 I II III TEMPERATURE PAGE MOLECULAR WEIGHT 23 QUANTITY OF HEAT 34 PART II THE FIRST FUNDAMENTAL PRINCIPLE OF THERMODYNAMICS I II III GENERAL EXPOSITION APPLICATIONS TO HOMOGENEOUS SYSTEMS APPLICATIONS TO NON-HOMOGENEOUS SYSTEMS PART 40 48 69 III THE SECOND FUNDAMENTAL PRINCIPLE OF THERMODYNAMICS I II III INTRODUCTION PROOF GENERAL DEDUCTIONS 78 89 108 CONTENTS xiv PART IV APPLICATIONS TO SPECIAL STATES OF EQUILIBRIUM CHAP T II III HOMOGENEOUS SYSTEMS SYSTEM IN DIFFERENT STATES OF AGGREGATION V VI [PAGE 125 139 SYSTEM OF ANY NUMBER OF INDEPENDENT CONSTITUENTS IV GASEOUS SYSTEM DILUTE SOLUTIONS ABSOLUTE VALUE OF THE ENTROPY 215 229 NERNST's THEOREM INDEX 179 272 293 TREATISE ON THERMODYNAMICS PART I FUNDAMENTAL FACTS AND DEFINITIONS CHAPTER I TEMPERATURE THE conception of sensation of warmth " heat " arises or coldness which from that particular immediately experi- is enced on touching a body This direct sensation, however, furnishes no quantitative scientific measure of a body's state with regard to heat it yields only qualitative results, which vary according to external circumstances For quantitative ; purposes we utilize the change of volume which takes place when heated under constant pressure, for this in all bodies 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 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 THERMODYNAMICS point, and then all change ceases said to be in thermal equilibrium The two bodies are then 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 // a body, A, be in thermal important proposition brium with two other bodies, : B and C, then B equili- 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 of two were not so, no general thermal equilipossible, which is contrary to experience If it brium would be These facts enable us to compare the degree of heat B and C, without bringing them into contact bodies, 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 A in a fine capillary tube) By observing the volume of in each case, it is possible to tell whether B and C are in thermal equilibrium or not If they are not in thermal we can which of the two is the hotter The 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 equilibrium, tell degree of heat of A, or of under atmospheric pressure This volumetric difference, which, by an appropriate choice of unit, is made to read 100 when A is in contact with steam under atmospheric pressure, is to called the temperature in degrees Centigrade with regard as thermometric substance Two bodies of equal tem- A perature are, therefore, in thermal equilibrium, and vice versa The temperature readings of no two thermometric Hubstances agree, in general, except at and 100 The TEMPERATURE definition of temperature is therefore somewhat arbitrary This we may remedy to a certain extent by taking gases, in particular those hard to condense, such as hydrogen, oxygen, nitrogen, and carbon monoxide, and all so-called permanent gases as thermometric substances They agree almost completely within a considerable range of temperature, and their readings are sufficiently in accordance for most purposes Besides, the coefficient of expansion of these different gases is the same, inasmuch as equal volumes of them expand under constant pressure by the same amount about ^lir of C to C volume when heated from Since, also, their the influence of the external pressure on the volume of these gases can be represented by a very simple law, we are led to the conclusion that these regularities are based on a re- markable simplicity in their constitution, and that, therefore, it is reasonable to define the common temperature given by them simply as temperature We must consequently reduce the readings of other thermometers to those of the gas thermometer The definition of temperature remains arbitrary in cases where the requirements of accuracy cannot be satisfied by the agreement between the readings of the different gas thermometers, for there is no sufficient reason for the preference of any one of these gases A definition of temperature completely independent of the properties of any individual substance, and applicable to all stages of heat and cold, becomes first dynamics peratures ( possible on the basis of the second law of thermo- In the mean time, only such tembe considered as are defined with sufficient 160, etc.) will accuracy by the gas thermometer In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout same temperature and density, and uniform to a pressure acting everywhere perpensubject dicular to the surface They, therefore, also exert the same their substance the pressure outwards Surface phenomena are thereby dis- ABSOLUTE VALVE OF THE ENTROPY 289 equation (282) with respect to T and p, remembering that the change of volume v of the system is given by the general formula (79g) -80 T 3T v "~ ' ' (285) Equation (282) gives the absolute value of the equilibrium constant K, while (284) leaves the integration constant still undetermined If, for example, L 0, then it follows from is of that the (284) independent temperature, but its value = K On the other hand, from (282), Therefore a solution of two enantiomorphic remains undetermined K = log forms of an optically active compound can be in stable equilibrium only if it forms a racemic, optically inactive mixture, a conclusion peculiar to the Nernst theorem Without this theorem we can only conclude that the composition of the mixture does not change with temperature of 295 Calculation of the Degree of Dissociation an Electrolyte from the Heat of Dissociation we take a solution of an electrolyte e.g., acetic acid in water, then the system, as in 262, is represented by If Wl The total H2 0, n CH3 COOH, n3H, n CH~COO number of molecules is The concentrations are c*1 The = Wo = w, -A, c n ^ n , c8 a = n* n , c* = nn dissociation of a molecule of acetic acid gives = 0, v = = = Therefore in equilibrium, by (283), since c3 = c Vi 1, vz 1, v4 4, THERMODYNAMICS 9o and C2 c3 can each be calculated from the total