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Physics Course, edited by Academician N. D. Papaleksi, Vol. I. Mechanics. Acoustics. Heat and Molecular Physics. State Publishing House of Technical and Theoretical Literature, 1948, 600 pp., 418 figs., with index.
Following the second volume of the course, a review of which appeared in the June issue of this journal, the first volume has now also been published. Familiarity with it allows us to generalize the judgment expressed regarding the second volume to the entire book. The reviewed Physics Course* is an exposition of physics that is interesting in a number of chapters and useful for a certain category of readers (teachers, senior students), but one that can in no way claim the role of a textbook for students in the lower semesters taking a general physics course. As in the second volume, a number of specific shortcomings—such as unevenness of presentation, excessive repetition, etc.—arise from collective authorship. Some of these shortcomings will be pointed out below; here the reviewer can only note his disagreement with the authors, who state in the preface that the unevenness of the exposition is an inevitable consequence of collective authorship, while collective authorship is a necessary condition for writing the best textbook. It seems that both a collective of authors and a single author can cope with the task of writing a good textbook; but unevenness of exposition does not permit such an assessment to be given to a textbook.
In the preface the authors state that they wish to take into account students’ lack of familiarity with higher mathematics in the first semester of study. To this end they undertake to introduce the necessary mathematical concepts along with the exposition of mechanics. How, then, does this look on the pages of the main text? Indeed, on p. 31 the concept of the derivative is introduced; on p. 32 the derivative of a square is even derived (as an example); the second derivative is introduced on p. 33; and the integral on p. 37. On p. 43 we are already differentiating composite functions, and we begin to solve differential equations on p. 64. I am no longer speaking of the fact that all vector concepts, including the vector product, are likewise explained “in passing” together with the exposition of the physical material on the first 60 pages. Thus, in only 2–3 lectures (more is never allotted to the exposition of the physical material on these pages) all the mathematics has been presented. Thereafter one may make full use of differential and integral calculus, solve differential equations, and use vector algebra, as N. N. Andreev does in the first part of the course—Mechanics.
I cannot imagine that the authors seriously believed such a pace and style of exposition to be possible. If that were so, then the course of higher mathematics in universities would become superfluous. It is well known how gradually a student develops a proper understanding of “function” in place of thinking in terms of “algebraic numbers.” This is a serious and substantial transition, which is accomplished not in a single day, nor even in a single semester. If lec-
* A. I. Kitaigorodskii, UFN, 35, 282 (1948).
...lectures in physics begin simultaneously with lectures in mathematics, then the only complication in the mathematical exposition that the lecturer in physical mechanics, taught in the first year, can allow himself is the writing of formulas in finite differences and the use of differential calculus only in one case—when calculating the formulas for velocity and acceleration in rectilinear motion—and that only on the condition that in the mathematics course these formulas have already been derived. Such is the reviewer’s opinion, and he believes that all lecturers of physics in the first year will agree with him.
There arises, further, the question whether the exposition of mechanics need be so strongly “permeated” with mathematics, and where this has led the author of this part of the course, N. N. Andreev. It seems to us that in most cases the mathematization of mechanics has led only to the fact that this part of the course has come to resemble very much the course in “theoretical mechanics” taught in all higher technical schools, while at the same time all the elements of so-called physical mechanics have dropped out of it, the aim of which is—to show the student, by means of a very large number of examples, through a consistent and logical exposition, the interrelation between mechanical concepts and mechanical phenomena. How dryly, for example, chapter 6 begins—Mechanics of a rigid body: definition of a concept, theorem... another theorem, and so on in the same spirit. Or on p. 125: the formal definition of the moment of a force, then of the moment of momentum, then the transformation (purely mathematical, with no remarks except mathematical ones) of Newton’s law, from which the basic law of rotation for a point is derived. On these pages we find neither a description of experiments, nor an analysis of these two new concepts, nor an indication of the reasons that made their introduction expedient, nor analogies, nor physical examples. In the overwhelming majority of cases, in our opinion, this apparent mathematical rigor is completely unnecessary, and in most cases it is harmful in this course, preventing the student from thinking through the empirical relationship of one concept or another.
In almost all chapters we find a striving for unnecessary generality and a fascination with the formal side of the matter. For example, the chapter devoted to relative motion could be divided into two equal parts—in the first, the rule for vector addition of velocities and accelerations is strictly proved, while in the second the forces of inertia are considered; it is doubtful that this is the proper distribution of the material by volume. The indicated excessively rigorous exposition did not guarantee the author against logical gaps. Thus, for example, on p. 130 it is proved that the change in the kinetic energy of an isolated system does not depend on the choice of the coordinate system. And immediately thereafter, “how important is the fact, if the system is not isolated. But in this case too one can prove the theorem—the kinetic energy of the system is the sum... etc.” Why the theorem proved below should have significance for the case of a non-isolated system remains unclear. One could point out several such places.
The striving for maximal rigor did not protect the author from errors either. For example, on p. 50 we read with surprise that in the case of nonplanar motion a third component is added to the tangential and normal acceleration. It is unclear what the author had in mind: as is known, acceleration always lies in the osculating plane, and its projection on the binormal is equal to zero.
It is completely incomprehensible how a gross error was made on p. 97, where it is repeated twice that unstable equilibrium corresponds to the least possible potential energy. In a number of cases one can find inconsistency of notation in the text and in the figure (p. 45).
As was to be expected, the fascination with the formal side of the matter and the approximation of physical mechanics to theoretical mechanics also led to the disappearance of a clear and profound consideration of basic physical concepts. The concepts of potential energy of a point (p. 94) and potential energy of a system of points
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(p. 131) are only defined; there are no examples that would show the reader what a potential well is, what a potential barrier is. Using the derivative, one could have discussed such a fundamental formula as the equality of force to the derivative of potential energy. This formula, however, is absent. The axiomatization of mechanics is set forth carelessly. The law of conservation of energy for systems is neither illustrated by a single example, and its entire exposition takes half a page. One can, it is true, imagine a category of readers for whom it would be useful to read the mechanics of N. N. Andreev—persons who know physics fairly well but are not acquainted with theoretical mechanics. Apparently these are not the readers the authors had in mind.
Turning to the consideration of the next part of the book—Acoustics—we at once draw attention to the absence of interconnection between the parts. In mechanics the vibrational motion of two bodies was presented (Kinematics, p. 41, and Dynamics, p. 64). Now the same material is presented for the third time in Chapter 11 under the title “Oscillations and Waves” (S. N. Rzhevkin). The same formulas are derived and discussed, the same arguments are repeated... though the authors use different notations. Still more important is the fact that S. N. Rzhevkin conducts the exposition without making use of higher mathematics. It should be acknowledged, therefore, that there is a certain lack of logic on the part of the authors in the use of mathematical tools. If on p. 252 of the course (i.e., by the end of the semester) one can get by without derivatives, then it was hardly worth using them on p. 40 for the exposition of the very same material.
Acoustics is presented considerably more simply and more “physically” than mechanics. It should only be regretted that it has expanded in comparison with the corresponding chapter (written by the same author) in the last edition of Michelson’s physics course. Perhaps the only additions which, from our point of view, deserve approval are the ultrasonic photographs and the corresponding text, as well as the final paragraphs. Theoretical additions, in our opinion, are superfluous. However, in the main, the material and style of exposition have remained the same. This part has undergone the least change in comparison with all the others, if one compares the present course with Michelson’s textbook of the 1939 edition.
An entirely new part of the book is “Molecular Physics and Thermodynamics,” written by G. S. Gorelik. The mathematical apparatus used by the author is in keeping with the students’ knowledge; it should be remembered that this part of the course is read as early as the second semester. Thus, the remarks we made in this respect concerning the mechanics part do not apply to molecular physics and thermodynamics.
In the exposition of thermodynamics and molecular physics there are many innovations on which one should dwell. The entirely noteworthy feature, which the author himself notes in the introduction to his part, consists in the fact that, following Carathéodory and T. A. Afanas’eva-Ehrenfest, he introduces heat as a derived concept, and it does not figure in his formulation of the first principle of thermodynamics.
On this point we do not agree with the author, and since this innovation seriously changes the character of the exposition of thermodynamics, we wish to dwell on it in more detail.
The author gives the following formulation of the first law of thermodynamics. “For an adiabatic transition of a system from a given initial state to a given final state, the same work is always required, regardless of how the adiabatic process is carried out” (p. 396). Thus, if it is required to find experimentally the difference in internal energy between its values in two different states, then for this it is necessary to carry out an adiabatic transition from the first state to the second. The measurement of the change in internal energy in an arbitrary process has no physical content. If such a process occurs, then the difference in energies is not equal to the work and to the “quantity of heat” received
system is called the sum of the increment of the internal energy of the system and the work it produces” (p. 423).
As we see, the author considers it necessary to avoid the usual method of defining heat in calories. This idea is also emphasized on p. 414, where it is said that “the numbers expressing the ratio of the calorie to the kilogram-meter are only, for historical reasons, called the mechanical equivalent” (italics ours). Thus, the calorie is only the name of a certain convenient unit of energy, and it stands in the same relation to the kilogram-meter as, say, the erg.
Consequently, it is insistently emphasized that there is no independent method, independent of energy, for measuring the quantity of heat. If so, what physical content will there be in the general formula of the first law \(Q = V_2 - V_1 + A\)? What does the first law tell us, when the heat passes by any method from state (1) to state (2)? As we see, nothing. Indeed, the difference \(V_2 - V_1\) has been measured by us once and for all for an adiabatic transition; therefore the only measurement that we can make is the measurement of the work performed by the system in various transitions from the first state to the second. Is there or is there not, then, some experimental content in the general formulation of the first law? It seems to us that this is not so. Leaving the author’s definition for the difference of energy \(V_2 - V_1\), and carrying out various transitions from state (1) to (2), we can verify the first law by measuring the quantity of heat \(Q\) in the usual way, which the author rejects. We see no objection that could be formulated here. Of course, in this case the nature of the process must be stipulated, and by comparison the heat capacities at different temperatures must be established in advance. All this, in principle, can be done. We have a way of comparing quantities of heat with one another without recourse to the first law. We can therefore put into the first law of thermodynamics the following experimental meaning: when a system in contact with a medium passes from one state to another, then the sum \(V_2 - V_1 + A\) is not equal to zero; calculating for different transitions the magnitude of this sum, we find from experience that the values of this sum will be connected with the character of the cooling of the medium in which the system is located, namely, the sum \(V_2 - V_1 + A\) will be proportional to the quantity \(Q\), the method of measuring which is contained in the formula \(\Delta Q = m\Delta T\). The proportionality coefficient found by experiment will be a universal constant.
It is quite understandable to the reviewer that the striving for a new method of exposition is caused by the desire to abolish such incorrect terms as thermal energy and to move away from the historical exposition, whose spirit was inspired by the theory of caloric. Such fine paragraphs as, for example, §§ 16, 17, serve this purpose perfectly. However, it seems to us that the author’s very interesting exposition would benefit from, in general, a slight restructuring, in accordance with which the quantity of heat would be granted its “rights”—its method of measurement independent of the law of conservation of energy.
It should further be noted that the description of physical facts in the new language sometimes becomes so cumbersome that the author is not even able himself consistently to maintain his point of view. An example of this is p. 427, where it is said that in a cyclic process the working substance receives heat and performs work. If heat at \(\Delta V = 0\) is by definition equal to work, then such language is inadmissible. The author realizes this, since in the heading he puts the words “transformation of heat into work” in quotation marks; in the text, however, the quotation marks are omitted, and cyclic processes are described clearly and comprehensibly in ordinary language.
If one does not speak of the indicated shortcoming, then the part written by G. S. Gorelik possesses high merits. The author’s great pedagogical experience and skill are evident. The paragraphs on the first principles in mechanics are very interesting and successful, although perhaps somewhat deliberately
lines, §§ 7–10, devoted to the qualitative definition of temperature and temperature scales.
The chapter following the first law of thermodynamics is devoted to information on heat transfer. The simplest cases of temperature equalization, periodic processes, are analyzed in mathematical terms. § 6 of this chapter is very good, where in general form and by four clear examples the concept of stationary temperature in the absence of thermal equilibrium is given.
In Chapter XV the elements of molecular physics are set forth. On the whole the chapter is very successful and clear. I should like to note as especially successful the paragraphs on statistical distribution laws, on the measurement of Avogadro’s number, and on internal friction.
The question of phase equilibria and transformations is presented very freshly and interestingly (Chapter XVI).
In presenting the second law of thermodynamics the author devotes almost the entire text to the consideration of reversible processes. This is connected with the accepted definition of the second law of thermodynamics: “for a reversible transition of an arbitrary system of bodies from a definite initial state to a definite final state, the same reduced quantity of heat is required, independent of the path by which the reversible transition is carried out” (p. 574). As we see, the second law of thermodynamics—as the author himself emphasizes in the introduction to his part—is a principle of the existence of entropy. Consideration of entropy is given only in the last three subsections of the page. It seems to us that, as a result of this exposition, the material has not been distributed in accordance with the physical significance of the problems, and that a very important idea has remained insufficiently emphasized—namely, that the second law is a law summarizing facts relating to the directedness of physical processes in nature. The author, on the other hand, mentions the physical content, for this last side of the principle (which is indeed very important), only in connection with the question of the symmetry of reversible processes. It should be noted that this aspect of the matter is excellently clarified in § 17 and the following sections, which show how, using the second law, one may derive a number of essential physical dependencies.
In concluding the consideration of the whole course of physics edited by Acad. Papaleksi, it should be noted once again that in some of its parts the book is of undoubted interest and will find readers, but in any case not among first-year students of technical higher educational institutions, for whom it was intended. For this purpose the book under review is too difficult, and in a number of places, moreover, dry and abstract.
A. Kitaigorodskii
The presentation of the section “Thermodynamics and Molecular Physics” (author—G. S. Gorelik) in the Course of Physics edited by N. D. Papaleksi *) is, in my opinion, of great interest; it has been deeply thought out both from the scientific and from the pedagogical side, is in a certain sense a novelty in the educational literature on physics (both Soviet and foreign), and represents a great success of the author.
The principal defects of the usual traditional exposition of thermodynamics in physics courses are, from my point of view, the following:
- The lack of clarity in the physical definitions of the concepts of temperature (and its scale), thermodynamic equilibrium, and quantity of heat. The encumbrance of the exposition with survivals of caloric conceptions or with such
) In view of the novelty and originality of the exposition in this section, alongside the review by A. I. Kitaigorodskii we are also printing the comment, received by the editors, by M. A. Leontovich. Editors.*
contentless concepts such as “heat energy,” and hence the lack of clarity in explaining the meaning of the principles of thermodynamics*).
- The juxtaposition of phenomenological thermodynamics with molecular-kinetic conceptions, or an insufficiently clear indication of their connection.
In G. S. Gorelik’s exposition both of these defects have been overcome. As is known, questions concerning a logically satisfactory definition of the basic thermodynamic concepts and the formulation of the principles of thermodynamics were discussed long ago in the scientific literature and found their resolution in a number of works**).
Since this revision, while bringing clarity to the logical structure of thermodynamics, concerned only the form of its exposition, it did not provide, for the solution of concrete physical problems, anything essentially new. Nevertheless, the fundamental explanatory value of these works must in no case be underestimated. It is clear that this aspect of the matter is especially important in the teaching of this branch of physics. Unfortunately, however, owing to the abstractness and mathematical form of exposition, these works have so far had almost no influence on the presentation of thermodynamics in elementary physics textbooks.
G. S. Gorelik has succeeded, in my opinion, in singling out the physically important ideas of these works and, by organically incorporating them into an elementary exposition of thermodynamics, giving a logically rigorous yet at the same time unnecessary rigorism-free, elementary in form and quite accessible presentation of this section. Such a new exposition of these questions is one of the chief merits of this section.
Special mention should be made of the exposition of the first law, the question of temperature and of the temperature scale in general, and of the absolute thermodynamic scale in particular, the clear exposition of the second law with a precise distinction of what the complex of assertions contained in it amounts to for reversible and for irreversible processes.
Following the exposition of the first law is a chapter devoted to molecular-kinetic conceptions. Here, in a clear elementary form, the basic ideas of statistical physics and kinetic theory are given (including the concept of the quantum theory of heat capacity). The chapter on phase transformations is extremely interesting. In particular, the mechanism of boiling of a liquid is analyzed here very clearly and vividly.
The exposition of molecular-kinetic questions is closely connected with the exposition of thermodynamic ones. In this way, the author has to a considerable extent succeeded (see, for example, § 3, Ch. XV, §§ 5 and 6, Ch. XVI) in avoiding the second defect indicated at the beginning, which is characteristic of many expositions of this branch of physics. One may hope that a student who has worked through these questions in the book under review will not be inclined to commit the often encountered mistake of trying to solve problems that are simply solved by applying phenomenological laws by means of the molecular mechanism (or, what is less frequent, to make the opposite mistake).
It should be said in this connection that one of the requirements imposed on a good exposition of a textbook in general (and on a textbook for a higher educational institution in particular) is the requirement that the material be presented so concretely that, on its basis, students can solve at least simple physi—
*) In this connection one should mention, as an illustration, the recently published illiterate article by Prof. Naumov in Vestnik Vysshei Shkoly, No. 8, 1948.
**) N. N. Schiller, Reports and Proceedings of the Physico-Mathematical Society. Kiev, 1897, pp. 1—12; 1900, pp. 1—14. C. Caratheodory, Math. Ann. 67, 3, 355, 1909; T. A. Afanas’eva-Ehrenfest, Journal of Applied Physics, vol. 5, 1928, issue 3, p. 3.
ical and practical problems. In the present case I regard this condition as fulfilled for the most essential parts of the section (the first beginning, the second beginning, reversible processes, heat transfer, phase transformations).
The author’s style is clear and vivid; the language is concise and precise. One feels that the entire exposition has undergone a thorough test in lecture teaching.
One should wish this section of the book wide circulation among both students and teachers.
M. Leontovich