Abstract
Book review: N. A. Izgaryshev. Chemical Thermodynamics.
Full Text
N. A. Izgaryshev. Chemical Thermodynamics. Scientific Chemical-Technical Publishing House (Scientific-Technical Administration of the Supreme Council of the National Economy). Leningrad, 19271.
In order to write a satisfactory textbook on any subject, it is not enough to know the subject and even to be able to apply it; one must know it as a specialist knows his subject. For example: many physicists, chemists, and engineers know infinitesimal analysis and use it as a tool. But if one of them were to write a textbook on differential and integral calculus, it is quite possible that the result would be so misshapen as to provoke the most negative reviews.
There is no need to say what may be expected in a case where a textbook is written by a person who quite simply does not know the subject.
It must be said that thermodynamics is, of all the physical disciplines, the most abstract; its axiomatics, apparently so simple, in fact presents considerable difficulties; the definition of its basic concepts is by no means easy. The quantities considered in thermodynamics are very numerous and are connected with one another by a multitude of equations. It is easy for the uninitiated to make mistakes in establishing the dependence between these equations. Of all the physical disciplines, thermodynamics is the most saturated with logic; in this respect it is akin to mathematics.
What difficulties may arise in considering the basic thermodynamic concepts is evident from the fact that two such scientific authorities as H. Poincaré and M. Planck diverged radically in defining the logical nature of the energy principle; according to Poincaré, this principle is something like a tautology or a disguised condition, whereas according to Planck it is an experimental law.
It is not surprising that although thermodynamics, like mathematics, is an instrument indispensable at every turn for the physicist, chemist, and engineer, by no means every chemist, physicist, or engineer can successfully expound its foundations.
The correctness of this proposition is confirmed, among other things, by the sad example of the author of the book named above. From this book several quotations will be given below. In doing so I shall leave aside various comparatively secondary defects, such as: minor errors; cases of unclear, confused, superficial, and generally unsuccessful exposition; vague, meaningless phrases; confused notation; stylistic improprieties. I shall draw the reader’s attention only to those cases in which the author makes major errors against logic, against methodological requirements, and against scientific truth (noting, moreover, that the list of major errors given here is not exhaustive).
P. 7. “There exists no sufficiently perfect, general definition of the concept of energy.”
This would be very sad, since it would undermine not only thermodynamics but all of physics! Fortunately, such a definition does exist; it may be found, for example, in Planck’s Thermodynamics, § 56.
P. 8. “Thermal energy is the product of temperature—the intensity factor—and heat capacity—the capacity factor.”
It is incomprehensible what Prof. Izgaryshev means by “thermal energy,” and it is unclear which “temperature” he is speaking of; in any case, the proposition expressed in such a general form is incorrect.
P. 9. In a short paragraph devoted to the first law of thermodynamics, Prof. Izgaryshev considers a certain process which he conducts “in a strictly reversible manner.” In doing so he gives neither a definition of a process, nor a definition of reversibility, and does not say what he understands by “strict reversibility.” The concept of reversibility is so fundamental and at the same time so delicate (moreover, this Russian term is, unfortunately, ambiguous, substituting
…especially since the French reversible is rendered as the French renversable, shows that such looseness in handling the basic terminology on the first pages of a textbook is quite inadmissible.
Pp. 9–10. In general, the paragraph devoted to the first law of thermodynamics is poorly presented: no precise verbal formulation of the first law is given1; it is expressed only by the indistinct (because of the double sign \(\pm\)) equality \(\Delta U = A \pm q\), and, moreover, it is not properly explained either what \(A\) is or what \(q\) is, and the most important thing is not said: that the internal energy of a thermodynamic system is determined by its state. The argument occupying the very end of p. 9 and the beginning of p. 10 (presented, it must be said, in an extremely confusing way) leads to the conclusion that the decrease in the internal energy of a system only in the case when one of the paths between the two given states is reversible probably does not depend on the path. Thus the applicability of the first law is made dependent on the reversibility of processes, which is fundamentally quite wrong.
P. 10. “In the case of an increase of temperature at constant volume, the pressure increases by a constant quantity, independent of the nature of the gas and equal to \(1/273\) of the pressure when the temperature changes by \(1^\circ\) C.” This formulation of the gas law is incorrect.
P. 12. Prof. Izgaryshev gives numerical values of the constant in Clapeyron’s equation: \(R = 0.0821\), etc. But since he has not said what quantity of gas he is considering, the unprepared reader will extract from these values of \(R\) nothing but great perplexities.
P. 13. “The gas laws have unconditional significance only for the so-called ideal gases; for nonideal gases certain deviations are observed, which in many cases must be taken into account, especially at temperatures only slightly exceeding the critical temperature of each gas or lying below the latter.”
This is erroneous. The point is not temperature, but density.
P. 13. “The basic property of internal energy is that it 1) depends on the temperature of the medium and 2) does not depend on volume or pressure.… Proposition 2) was proved experimentally by Joule and Thomson.”
These lines represent a completely distorted presentation of very important facts. The point is that, in order to characterize the state of the simplest thermodynamic systems, the variables \(T\), \(v\), \(p\) are most often used; but these variables are connected by the equation of state \(T = f(v,p)\), and consequently only two of them are independent. The internal energy \(U\) of the system will in general be a function of both these independent variables; ideal gases constitute an exception: for them \(U\) can indeed be determined by means of a single variable, namely by means of \(T\) (Joule’s law)2. As for real
\[ U = \frac{c_v}{R} vp + \mathrm{const.}, \]
and therefore as a function of volume and pressure, besides temperature; this is possible, of course, for other simple thermodynamic systems as well—only the functions will be more complex.
for gases, then for them, as has been proved by the experiments of Joule and Thomson, a more complicated relation \(U=\omega(T,r)\) holds. Prof. Izgaryshev’s errors consist in the following. First, he presents the matter as if all three variables \(T,v,p\) were independent of one another. Secondly, in his exposition it follows that for all thermodynamic systems (and not only for ideal gases) \(U\) is a function of \(T\) alone. Thirdly, his “proposition 2” (if this proposition is put into correct form) was not proved by Joule and Thomson, but, on the contrary, refuted by them.^1
P. 14. “Although gas particles move with different velocities, nevertheless, according to the statistical laws of large numbers, it may be assumed that in one or another system all particles are moving with some velocity \(u\), which is the mean of all the separate corresponding quantities.”
What, then, are the “statistical laws of large numbers”? And how many of them are there—these laws?
Pp. 14–15. “The mean living force (kinetic energy) of each particle will be equal to \(\frac{mu^2}{2}\), according to the doctrine of motion, kinematics.”
Comments, of course, are superfluous...
Pp. 15–16 are devoted to the derivation of the formula for gas pressure according to the kinetic theory. The arguments belonging here (which we do not write out in full for lack of space) are presented to the highest degree strangely. I shall point out only three errors in particular. First, Prof. Izgaryshev obtains the formula \(pv=\frac{mn^2N}{3}\), without referring to any general truth of mechanics. Secondly, the following passage is astonishing: “The quantity of motion parallel to the first edge before collision with the wall is represented by the product \(mu\), and therefore, upon impact with the opposite wall and upon the subsequent temporary stoppage, the particle gives up a quantity of motion equal to \(mu\), if it is assumed that it is directed perpendicular to the wall. Reflected back, the same particles receive an equal quantity of motion \(mu\), and thus the total value of this for each particle will be equal in sum to \(2mu\) for one impact.” Further on, Prof. Izgaryshev everywhere calls “quantity of motion” that which in fact is the increment of the quantity of motion per unit time. Thirdly, the velocity \(u\), the resultant of the components of velocity \(x,y,z\) (a very unfortunate notation), Prof. Izgaryshev considers to be “the velocity of the particle in all three directions.”
P. 17. For equal volumes of two gases, under the same pressure and at the same temperature, Prof. Izgaryshev writes the equality
\[ \frac{2}{3}N_1\frac{m_1u_1^2}{2} = \frac{2}{3}N_2\frac{m_2u_2^2}{2}, \]
and then says: “Since at the same temperature of both gases the living forces of their particles are equal
\[ \frac{m_1^2u_1^2}{2} = \frac{m_2^2u_2^2}{2} \quad (\text{sic! } A. B.), \]
therefore, consequently, \(N_1=N_2\).... Thus, proceeding from the principles of the kinetic theory, we have arrived at the derivation of the law known under the name of Avogadro–Gerard’s law.”
^1 The fourth error consists in the assertion that \(U\) supposedly “depends on the temperature of the medium.” But we shall think that “medium” is a slip of the pen instead of “system.”
The most essential point of the proof—the equality of the vis viva of the molecules of both gases—is in no way motivated. And therefore the “derivation of the law known as the Avogadro–Gerard law” amounts to an abuse of the reader’s trust.
P. 17. “If we take 1 cu. cm of hydrogen (under what conditions is not stated! A. B.), then its mass \(N_m\) will be equal to 0.000899 g, the pressure 1033.3 per 1 sq. cm, or \(1033.3 \times 980.6\) abs. units.”
What can be said here?
P. 20. “The part of the energy capable of being transformed into some kind of work is called free energy or the work of the process.”
This definition is entirely unsuitable; all the more so since, in essence, it does not differ from the definition of energy in general given by Prof. Izgaryshev on p. 7 (“everything that produces work”). The entire paragraph on free energy is a model of unclear exposition. It is impossible for a beginning reader to understand anything here.
P. 23. “Heat capacity is the heat perceived by a body during its heating.”
Having given this completely incorrect definition of heat capacity and having attached to it the (correct) definition of specific heat capacity, Prof. Izgaryshev says: “Consequently (!?), heat capacity characterizes the change of the total internal energy of a system with temperature, or
\[ c=\frac{du}{dT}=\frac{dQ}{dT}. \]
This is a gross error. The heat capacity \(c\) (if it is correctly defined) is equal to \(\frac{dQ}{dT}\), but in general \(c\) is not equal to \(\frac{dU}{dT}\), because in general \(dU \ne dQ\).
P. 24. Prof. Izgaryshev considers the heat capacities of gases, and throughout denotes the heat capacity at constant pressure by \(C_p\), and the heat capacity at constant volume by \(C_v\) (as if \(p\) and \(v\) here were factors). He says: “The quantity \(C_p\) is greater than \(C_v\), since a gas heated at constant pressure changes its volume, expands, and performs a certain external work requiring the expenditure of heat. Therefore \(C_p=C_v+a\), where \(a\) is the part of the heat that goes into work.”
Leaving aside the extreme lack of clarity of the exposition, I shall point only to the logical error that makes the conclusion illusory: Prof. Izgaryshev has forgotten to refer to Joule’s law, from which it follows that in both compared processes the gas undergoes the same change of internal energy.
Prof. Izgaryshev continues: “The work of a gas \(a\) is represented by the product of the pressure \(p\) by the volume \(v\) (sic!) and, being expressed in calories and referred to one degree, will be expressed by the quantity \(\frac{pv}{T}\), and therefore we obtain:
\[ C_p=C_v+\frac{pv}{T}\ldots\ldots\ldots\ldots\ldots\ldots\ldots (8). \]
Taking into account the Clapeyron equation \(pv=RT\), we determine the value
\[ \frac{pv}{T}=R \]
and substitute it into expression (8), which will take the form: \(C_p=C_v+R\).”
I shall dwell only on the crudest errors contained in this passage. The work of a gas is not equal to the product of pressure by volume, but to the product of (either constant or mean) pressure by the increment of volume, i.e. it is equal to
\(p\Delta v\). In order to “refer this work to one degree,” it must be divided not by \(T\) (which makes no sense), but by the temperature increment \(\Delta T\). The quotient obtained, as follows from Clapeyron’s equation, is equal to \(k\). If Prof. Izgaryshev has thus arrived, in the end, at the correct conclusion, this is because the two mistakes he made (and which have just been indicated) compensated for one another. Prof. Izgaryshev’s words concerning the work \(a\): “being expressed in calories,” oblige him to supply the expression for this work with the divisor \(J\) (the mechanical equivalent of heat), which he has not done.
Further on we find an entirely unfortunate definition of molecular heat capacity as “specific heat referred to one mole of substance.”
Next we read: “The analytical expression for the heat capacity \(Cv\) is the differential quotient (partial differential at constant volume)
\[ \left(\frac{du}{dT}\right)_v = c_v; \]
similarly, the heat capacity \(Cp\) will be expressed as:
\[ \left(\frac{du}{dT}\right)_p = c_p. \]
First, a partial differential and a quotient of differentials are not the same thing. Secondly, although the formula
\[ \left(\frac{dU}{dT}\right)_v = c_v \]
is correct, the formula
\[ \left(\frac{dU}{dT}\right)_p = c_p \]
is incorrect. In Prof. Izgaryshev these formulas, as one has to guess, arose on the basis of his manner of writing subscripts as factors: for if (see above)
\[ C = \frac{du}{dT}, \]
then indeed
\[ C.v = \left(\frac{du}{dT}\right)\cdot v \]
and
\[ C.p = \left(\frac{du}{dT}\right)\cdot p. \]
P. 25. “The determination of the quantities \(Cv\), and especially \(Cp\), by means of direct measurements presents rather considerable difficulties, and therefore has been carried out only for a relatively small number of gases and under an insufficiently great variety of temperature conditions. Therefore the interpolating empirical formula (10) is not sufficiently reliable.”
Here everything is confused, everything is wrong. It is precisely \(c_p\) that is determined experimentally without particular difficulty; this function has been determined for many gases (about fifty); \(Cv\) has also been determined approximately for half of the gases, sometimes over very considerable temperature intervals. Formula (10) would be quite reliable if by means of it \(c_p\) or \(c_v\) were expressed; but what the author understands by \(C\) is unknown, and therefore the formula has no definite meaning.
P. 29. Prof. Izgaryshev reduces the independence of the internal energy of an ideal gas from volume at constant temperature to “Joule–Thomson’s experiment.”
It was, however, precisely the experiments of Joule–Thomson that proved that the internal energy of gases depends also on the volume!
P. 42. “The most general characteristic of it (the second law of thermodynamics. A. B.) is the following proposition.
Natural, spontaneous processes can take place in any closed system only in the case when they are associated with a decrease of the factor of energy intensity1, i.e. when this factor at the end of the process assumes a smaller value than at its (?) beginning.”
In the preceding exposition Prof. I. Izgaryshev did not indicate the rule that would make it possible to determine which of the two energy factors is the factor of intensity. Since this is so, the given formula, even if it were correct, would not express a law of nature; it would only serve as a means for determining the “factor of intensity.”
But it is also incorrect. Prof. I. Izgaryshev illustrates the “law” he has stated by the example of the transfer of heat from one body to another, not noticing that by this example the proposed “law” is invalidated. For if heat is transferred between a warm body and a cold body, then although, on the one hand, we have a “decrease” of temperature (the factor of intensity), on the other hand (in the colder body) we have an increase of this factor! Moreover: how will Prof. I. Izgaryshev evaluate what the factor of intensity for the given system was equal to at the beginning of the process, when the temperatures of the two bodies were different? Let us take the simplest case: two given bodies have equal masses, consist of one and the same material, and have: one—the temperature \(t_1\), the other—the temperature \(t_2\). The final temperature, as is known, will be \(\frac{t_1+t_2}{2}\). How, here, is Prof. I. Izgaryshev’s proposition justified: “this factor at the end of the process assumes a smaller value than at the beginning”?
P. 43. It is a gross error to bring such a phenomenon as the flow of water from higher places to lower ones under the second law of thermodynamics, with which the indicated phenomenon has nothing in common.
P. 44. “The most valuable is free energy, i.e. energy capable of transformation”1.
All energy is capable of transformation. The important concept of “free energy” has a specific meaning, which Prof. I. Izgaryshev has not even touched upon.
P. 45. Prof. I. Izgaryshev formulates the second law in yet another way, and again quite incorrectly: “It is impossible to create such a machine which would continuously, without losses, transform energy from one form into another1, i.e. a perpetual mobile of the second kind is impossible.”
First, a perpetual mobile of the second kind is by no means “such a machine which continuously (?) without losses (what does that mean? A. B.) transforms energy from one form into another.” Secondly, there is nothing easier than to construct a machine which would operate in the sense the impossibility of which Prof. I. Izgaryshev asserts. One need only take, for example, an electric motor, clamp its shaft between brake shoes, and set the motor in motion. The motor will “continuously, without losses,” transform electrical energy into heat.
P. 45. Concerning the thermodynamic potential \(U - TS + Apv\), Prof. I. Izgaryshev expresses the following judgment: “In view of the great complexity of calculations with the aid of this function, it is of significance only for a limited number of scientific-technical calculations.”
First, the “complexity of calculations” with which Prof. I. Izgaryshev frightens the reader is not at all so great; secondly, the indicated thermodynamic potential
forms has a very wide sphere of application,—for example, to all reactions occurring at constant temperature and constant pressure.
P. 47. An error of a quite exceptional nature! Under the name of the Carnot cycle, Prof. Izgaryshev describes an entirely different process, namely the Stirling cycle (with two isotherms and two isochores).
P. 48. The second and fourth processes of the imaginary “Carnot cycle” take place, according to Prof. Izgaryshev, at constant volume. With regard to these processes Prof. Izgaryshev makes the following unexpected remark: “Strictly speaking, processes 2 and 4 (sic!) ought to have been represented in Fig. 6 by hyperbolas (these processes of constant volume are represented in the $vp$ diagram by hyperbolas! A. B.), but, taking into account that all changes of the system are very small, one may (!) introduce straight lines instead of hyperbolas.”
P. 58. Having written the equation
\[ \frac{d\lambda}{dT}=(a-a_0)+2T(\beta-\beta_0), \]
Prof. Izgaryshev says: “integrating this expression between $T_0$ and $T$, we have:
\[ \lambda=\lambda_0+(a-a_0)T+(\beta-\beta_0)T^2.” \]
As is evident, Prof. Izgaryshev has no correct conception of the difference between a definite and an indefinite integral!
P. 124. “The work performed by an evaporating liquid, when its initial volume is increased from $v_1$ to $v_2$, may be represented (according to equation 7) by the expression
\[ A=RT\ln\frac{v_2}{v_1}, \]
where, since $v_1$ is very small in comparison with $v_2$, and $v_2=\frac{1}{\pi}$ ($\pi$ being the vapor pressure), the equation assumes the form $A_v=-RT\ln \pi$.”
In these few lines there is an accumulation of gross errors. First, the work performed by an evaporating liquid is not expressed by the formula $RT\ln \frac{v_2}{v_1}$. Secondly, if in the indicated formula $v_1$ is very small in comparison with $v_2$, then on this basis the formula in no way turns into $RT\ln v_2$ (as Prof. Izgaryshev thinks). Finally, the relation $v_2=\frac{1}{\pi}$ is also erroneous.
And so on and so forth.
Need one say that this booklet is wholly unsuitable for the use for which it was intended (see the preface) by the author and the publishing house?
A. Bachinsky.