Thermodynamics Enrico Fermi 1938 Nobel Laureate in Physics June 12, 2011
Copyright c 1936 by Enrico Fermi. Laura Fermi, Copyright Owner. All rights reserved under Pan American and International Copyright Conventions. Published in Canada by General Publishing Company, Ltd., 30 Lesmill Road, Don Mills, Toronto, Ontario. Published in the United Kingdom by Constable and Company, Ltd., 10 Orange Street, London WC 2. the This author (139 received + x)-page his LAT Nobel E X edition Prize. is written This edition in 2008, contains seventy some years minor after changes to fit the settings in LAT E X. ii
Preface THIS book originated in a course of lectures held at Columbia University, New York, during the summer session of 1936. It is an elementary treatise throughout, based entirely on pure thermo- dynamics; however, it is assumed that the reader is familiar with the fun- damental facts of thermometry and calorimetry. Here and there will be found short references to the statistical interpretation of thermodynamics. As a guide in writing this book, the author used notes of his lectures that were taken by Dr. Lloyd Motz, of Columbia University, who also revised the final manuscript critically. Thanks are due him for his willing and intelligent collaboration. E. FERMI
The Nobel Prize for Physics in 1938 was awarded to Enrico Fermi for his demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons. iii
Corrections Within this edition, certain parts of the original work were changed. This is especially in the cases whereby the error is obvious or in some conven- tions which are no longer used. A notable example is the unit for temper- ature, kelvin, which was written as ◦K by Enrico Fermi. Now, the conven- tion is to write the unit as just K.
Copyright As fifty or more years have passed since the death of the author, this book is now in the public domain of Malaysia. iv
Contents Contents vi Introduction ix
1 Thermodynamic Systems 1 1.1 The state of a system and its transformations. . . . . . . . . . 1 1.2 Ideal or perfect gases. . . . . . . . . . . . . . . . . . . . . . . . 8 2 The First Law of Thermodynamics 11 2.1 The statement of the first law of thermodynamics. . . . . . . 11 2.2 The application of the first law to systems whose states can be represented on a (V,p)diagram. . . . . . . . . . . . . . . . 17 2.3 The application of the first law to gases. . . . . . . . . . . . . 19 2.4 Adiabatictransformationofagas. . . . . . . . . . . . . . . . 23 3 The Second Law of Thermodynamics 27 3.1 The statement of the second law of thermodynamics. . . . . 27 3.2 TheCarnotcycle. . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Theabsolutethermodynamictemperature. . . . . . . . . . . 32 3.4 Thermalengines. . . . . . . . . . . . . . . . . . . . . . . . . . 39 4 The Entropy 41 4.1 Somepropertiesofcycles. . . . . . . . . . . . . . . . . . . . . 41 4.2 Theentropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.3 Some further properties of the entropy. . . . . . . . . . . . . . 48 4.4 The entropy of systems whose states can be represented on a (V,p)diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.5 The Clapeyron equation. . . . . . . . . . . . . . . . . . . . . . 56 4.6 The Van der Waals equation. . . . . . . . . . . . . . . . . . . . 61 v
5 Thermodynamic Potentials 69 5.1 Thefreeenergy. . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2 Thethermodynamicpotentialatconstantpressure. . . . . . 73 5.3 Thephaserule. . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.4 Thermodynamics of the reversible electric cell. . . . . . . . . 83 6 Gaseous Reactions 87 6.1 Chemical equilibria in gases. . . . . . . . . . . . . . . . . . . . 87 6.2 The Van’t Hoff reaction box. . . . . . . . . . . . . . . . . . . . 89 6.3 Another proof of the equation of gaseous equilibria. . . . . . 95 6.4 Discussion of gaseous equilibria; the principle of Le Chatelier. 97 7 The Thermodynamics of Dilute Solutions 101 7.1 Dilute solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . 101 7.2 Osmoticpressure. . . . . . . . . . . . . . . . . . . . . . . . . . 10 6 7.3 Chemicalequilibriainsolutions. . . . . . . . . . . . . . . . . 110 7.4 The distribution of a solute between two phases. . . . . . . . 113 7.5 The vapor pressure, the boiling point, and the freezing point ofasolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 8 The Entropy Constant 125 8.1 TheNernsttheorem. . . . . . . . . . . . . . . . . . . . . . . . 125 8.2 Nernst’s theorem applied to solids. . . . . . . . . . . . . . . . 128 8.3 The entropy constant of gases. . . . . . . . . . . . . . . . . . . 132 8.4 Thermal ionization of a gas: the thermionic effect. . . . . . . 135 vi
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List of Figures 1.1 Expansion of gas using a piston. . . . . . . . . . . . . . . . . 5 1.2 Expansion of gas in a irregular shape container. . . . . . . . . 6 1.3 Transformation on (V, p)diagram. . . . . . . . . . . . . . . . 6 1.4 Acyclicaltransformation. . . . . . . . . . . . . . . . . . . . . 7 2.1 Joule’sexperiment. . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Adiabaticchange. . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1 Carnotcycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Carnotprocess. . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.1 Different transformations from A to B. . . . . . . . . . . . . . 44 4.2 Two paths, I and II, from A to B.. . . . . . . . . . . . . . . . . 44 4.3 A reversible path R from A to B and an irreversible path I from B to A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.4 Two different paths, I and II, from state A to B on a (V, p) diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.5 Isotherms of a substance on a (V, p) diagram. . . . . . . . . . 56 4.6 Isotherms, according to Van der Waals equation, of a substance on a (V, p) diagram. . . . . . . . . . . . . . . . . . . . 62 4.7 An isotherm of a substance at supersaturated conditions on a (V, p) diagram. . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.1 Phase diagram for water. . . . . . . . . . . . . . . . . . . . . . 81 6.1 Van’tHoffreactionbox. . . . . . . . . . . . . . . . . . . . . . 90 6.2 Isothermal transformation in Van’t Hoff reaction box. . . . . 91 7.1 Osmoticpressure. . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.2 Determiningosmoticpressure. . . . . . . . . . . . . . . . . . 107 7.3 Colligative properties of a solution. . . . . . . . . . . . . . . . 117 8.1 Graph of C (T) against T forasolid. . . . . . . . . . . . . . . 128 vii
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Introduction THERMODYNAMICS is mainly concerned with the transformation of heat into mechanical work and the opposite transformation of mechanical work into heat. Only in comparatively recent times have physicists recognized that heat is a form of energy that can be changed into other forms of energy. Formerly, scientist had thought that heat was some sort of fluid whose to- tal amount was invariable, and had simply interpreted the heating of a body and analogous process as consisting of the transfer of this fluid from one body to another. It is, therefore, noteworthy that on the basis of this heat-fluid theory Carnot was able in the year 1824, to arrive at a compar- atively clear understanding of the limitations involved in the transforma- tion of heat into work, that is, of essentially what is now called the second law of thermodynamics (see Chapter 4). In 1842, only eighteen years later, R. J. Mayer discovered the equiva- lence of heat and mechanical work, and made the first announcement of the principle of conservation of energy (the first law of thermodynamics). We know today that the actual basis of the equivalence of heat and dy- namical energy is to be sought in the kinetic interpretation, which reduces all thermal phenomena to the disordered motions of atoms and molecules. From this point of view, the study of heat must be considered as a special branch of mechanics: the mechanics of an ensemble of such an enormous number of particles (atoms of molecules) that the detailed description of the state and the motion loses importance and only average properties of large numbers of particles are to be considered. This branch of mechan- ics, called statistical mechanics, which has been developed mainly through the work of Maxwell, Boltzmann, and Gibbs, has led to a very satisfactory understanding of the fundamental thermodynamical laws. But the approach in pure thermodynamics is different. Here the funda- mental laws are assumed as postulates based on experimental evidence, and conclusions are drawn from them without entering into the kinetic mechanism of the phenomena. This procedure has the advantage of being ix
