Prof. N. V. Kashin. The Doctrine of Energy. An Introduction to Thermodynamics. Leningrad. Vokrug-Éfron Publishing House, 1925. Pp. 396. Price 3 rubles.

This interesting and talentedly written book was compiled from courses taught by the author in several higher educational institutions. The author regards his course as an introduction to technical thermodynamics, enriched with physics. The exposition everywhere begins with very elementary considerations; then it rises to as complete an interpretation as possible of the complex constructions of modern theory.

Prof. Kashin has set himself the aim of presenting the principal laws of physics, proceeding from the concept of “energy,” which is “something” that exists alongside constant mass and remains constant in quantity in all processes in a given closed system (H. Helmholtz).

From this point of view, Prof. Kashin’s book sets forth methods for measuring mechanical, thermal, electrical and magnetic, radiant, and chemical energies. In the chapter on the measurement of electrical energy, Maxwell’s and Poynting’s formulas concerning the flow of electromagnetic energy are taken as the basis; the concept of the “Poynting vector” is given; all this is presented without derivation, in ready-made form. I believe that in some cases such use of ready-made formulas without their derivation may be useful, if the real meaning of the formulas cited and of the quantities entering into them is clear to the reader; in many cases the author employs this device quite successfully; but sometimes it also happens that the content of such extracts from broad scientific investigations can give nothing to the unprepared reader.

In deriving the law of conservation of energy for the case of central forces depending only on distances, the author touches upon Einstein’s theory of relativity, using the ready-made formula for the dependence of mass on velocity, and from this derives the relation between mass and energy, establishing the equivalence of energy and mass and introducing the concept of an enormous store of energy hidden in the bowels of matter. I doubt how useful such a broad and bold generalization is for the reader without an exposition and critique of the fundamental principles of Einstein’s doctrine.

In the exposition of the first law of thermodynamics, the concept of internal energy is introduced at once as something comprehensible from the molecular point of view, and it is asserted that internal energy is a function of state. In fact, the concept of internal energy arises as a consequence of the principle of the equivalence of heat and work, as is also evident from the later paragraphs of the book. Speaking of the parameters determining the state of a body, the author limits himself to three, forgetting to say that the remaining parameters are omitted from consideration because the discussion will proceed further about slow changes of the system, identical at all its points.

In all formulas connected with the first law of thermodynamics, the author uses the value of the mechanical equivalent of heat, denoted by him as Э; in formulas one usually uses the reciprocal quantity \(1/Э\), the thermal equivalent of a unit of work. Therefore it would have been more convenient to follow the custom of foreign technical books and to introduce everywhere into the formulas the quantity \(A = 1/Э\). This would have made it easier to read foreign books on heat engineering, in the sense of uniformity of formulas.

The thermodynamics of the perfect gas is presented in the usual way, as is its application to the analysis of simplified cycles of gas engines.

BIBLIOGRAPHY

The second law of thermodynamics in its various forms, the concept of entropy, the degradation of energy, and the thermodynamic temperature scale constitute the subject of the following sections of the book. It is doubtful whether the bold extrapolations placed at the end of the chapter—concerning the end of the world, the necessity of its beginning, and the dissipation not only of energy but also of matter as the equivalent of energy—will prove useful to the reader. All these considerations about the “world” and its properties on the basis of experiments in a limited corner, although presented under the banner of hypothesis, may give unprepared readers occasion for metaphysical discussions about propositions supposedly proved by science. The author himself, of course, does not attribute a metaphysical character to these considerations, but the danger for the reader nevertheless exists.

The molecular theory of matter, in connection with the theory of Mendeleev’s periodic law and Moseley’s theory of ordinal numbers, and with radioactive phenomena, has found a place in Chapter V. There too are given the concepts of the theory of the structure of the atom, of the divisibility of energy, of the quantum, of the disintegration of atoms, and of stores of intra-atomic energy.

Chapter VI contains the kinetic theory of gases with additions from Maxwell (without derivation) and Perrin’s experiments; there is a derivation of the coefficients of internal friction and diffusion, and of the Van der Waals formula from the point of view of kinetic theory. Of very great interest is the most recent theory of the heat capacity not only of gases, but of liquids and solids, in connection with the investigations of Einstein, Lindemann, and Nernst.

Chapter VII, on vapors, is set forth insufficiently for the technical purposes which the author nevertheless had in view in compiling the book; the application of entropy diagrams to the solution of problems is not shown, and in particular nothing at all is said about the Mollier \(J—S\) diagram, so often used now in heat engineering.

The first table of saturated (the author uses the term “satiated”) steam is now not used, since it was compiled by taking as the unit of pressure the pressure of a column of mercury 760 mm high, and not the international atmosphere \(\left(1 \frac{\text{kg}}{\text{m}^2}\right)\). The second table is sufficient. It would not hurt to make use of new investigations, bringing the table up to the critical temperature. The Clapeyron–Clausius equation, although derived, is used insufficiently; it should also have been justified for the case of melting, with all the applications that follow from this.

In Chapter VIII, on the general problem of thermodynamics, definitions are given of functions called thermodynamic potentials at constant pressure and at constant volume, and applications of these functions are shown to the theory of the galvanic cell, to perfect gases, and in general to the conditions of equilibrium of systems. Although the author introduced the terms phase and component, he refrained from presenting Gibbs’ phase rule, although even without proof, in the same spirit as he did in many places, and did not touch upon the application of the phase rule in physical chemistry. Without this, the thermodynamic potentials turn out to be perhaps unnecessary, since they are applied by the author only to the solution of questions previously examined without thermodynamic potentials. One can do without them also in the further approach to Nernst’s heat theorem. The latter theorem, with its consequences concerning the properties of bodies at low temperatures, is very instructive and appropriate in the book under consideration.

The last section concerns the interpretation of entropy as a quantity proportional to the logarithm of the probability of a given state of a system. The statistical method on which this interpretation of entropy is based is in itself very valuable, since it has led to significant results in the investigation of a number of phenomena in the kinetic theory of matter, the theory of turbid media, radiant energy, and others.

Despite the objections I have made regarding Prof. Kashin’s book, I consider it extremely interesting and vividly written.

Bibliography

The book is accessible to a reader acquainted with elementary physics and with the fundamentals of mathematical analysis to only a very limited extent. Therefore not only the engineer, but also the ordinary technician, may take an interest in this book, in order to view the knowledge and skills they employ from a broader point of view. A student of the natural sciences with modest mathematical preparation, after reading this book, will have an opportunity to systematize his knowledge and find his bearings in it. The book by Prof. Kashin will be read with particular interest by teachers of physics in schools who do not have the opportunity to follow the new journal literature on physics.

The book may serve as a useful introduction to such courses in heat engineering as those of Schüle, Oshurkov, and others.

A. L. Korolkov.