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any minor changes in apparatus or procedure are such as would probably seem necessary or desirable, in working a t the higher temperatures, to anyone familiar with the synthetic method and the relative ease of de,omposition of aqueous urea solutions a t these temperatures. Using the method of least averages, the equation loglo NP = -631.86/?' 1.5314 was obtained, but it is not perfectly satisfactory, since the points show- a slight but definite curvature. Several attempts to get a satisfactory equation with three terms proved unsuccessful; hence it sepms necessary to give the solubilities at rounded temperatures (table 1). The average departure of fourteen of the sixteen points from the: line as drawn is 0.11' (for all sixteen points it is 0.16'); the corresponding average departure for the four points of Miller and Dittmar is about 1.7". (At and above 104.4OC. their data agree quite well with nn extension of tht. present curve, especially if a slightly reversed S curvature is assumed.) In conclusion, then, the present results confirm the work of Shnidman and Sunier around 70°C. in a w r y satisfactory manner and further show that the log,,, Nzversus 1/T curve is not a straight line throughout the temperature interval 60 to 100OC. HARPERKAKINUMA. Departmcnt of Chemistry The University of Rochester Rochester, New York
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GLASSTONE.15 x 23 om.; xiii 1289 Tezt Book of Physical Cheniistry.1 By SAMUEL pp.; 267 figures. New York: D. Van Nostrand Company, Inc., 1940. Price: $10.00. This is a large book of over 1250 pages, about one-third of which is stated t o be i n fine type. I t is offered as a text book of intermediate character aa well as a book that may be used as reference. The book is very comprehensive, and, except for a rare lapse, is clearly written. I t is interesting and sufficiently up-todate t o make it useful t o any trained physical chemist. The suitability of the book for use in an intermediate course depends t o a considerable extent on the number and nature of the errors, particularly when the errors affect the explanations offered for the mathematics. Since this book presents thermodynamic theory and, when used aa a text of intermediate character, presents the theory for the first time t o students who have only the physical chemistry "such a8 might be gained in a normal course of general chemistry," any explanations for the thermodynamic reasoning, when offered, muat be relatively free from error, or more harm than good may easily be done t o the student. 1 .This review was prepared by Professor Gillespie shortly before his death in January, 1941.
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Some unimportant errors are the following: the referencr to L. H. (instead of E. Q.) Adams on page 977; the statement on page 688 that the weight of hydrogen sulfide dissolved by unit volunic is independent of (instead of proportional to) the pressure: and a misspelled word at the bottom of page 471. Of such errors the book seems unusually free. Some of the following are more important. The reviewer has rarefully esamined the hook with respect to the thermodynamics and the parts of physical chemistry that depend upon it. .is regards those parts that do not, the reviewer finds them interesting and probably excellent, but it is harder t o be sure of excellence than of fault, hence in the following W P deal mostly with the reviewer’s criticisms on his selected topics. The section “Partial Pressures of Real Gases,” page 299, appears pointless. Without a change in the definition of partial pressure, the answer is obviously wrong, and there seems no way to redefine partial pressure so as to make the discussion valid. (If equilibrium pressure is meant, then the assumption aboiit the interaction factors is known to be redundant.) In the virial equation of state (page 290), B, C, D,etr. w e not constants, as stated, but temperature functions. The virial coefficients are thus not determined by the equation of state constants, and the number of true constants exceeds the five that (on pagc 306) should make the Beattie-Hridgnian equation reproduce the behavior of a gas very closely (over a range of temperature). On page 305 I find objectionable the espression “they provide support for the view that gases behave ideally at very low pressures”in any book like this that treats of the Boyle temperature and the inversion temperature, since gases do not behave ideally in these respects even a t vanishing pressure. On page 442 I cannot find the statement, that the C‘lageyron equation applies t o any univariant system; instead, I find that i t applies to any change of state, and that Eq. 34 (illaxwell’s third relation) holds for a system of onecomponent irrespective of the number of phases, provided they are in equilibrium. On page 184 the Joule-Thomson effect is stated to be a heat change, and is identified with a small temperature change that occurs when a gas expands freely without doing ezlernal work. The second error (my italics) is the more serious for the student, as i t is t o be found in other hooks. The subject is taken up again on page 278. Here it is rather evident that the external work done need not be zero, but there are new difficulties. It is implied that throttling action is enough to keep the pressure constant oneachside of the plug. We are asked tosuppose the onemol of gas “streams through the plug very slowly, that is, reversibly . . . . ” At the foot of page 279, bothnumerator and denominator are taken outside the integration sign, though only the latter is stated to be assumed constant, and the result is treated as of considerable importance. Xone of this is in fine type, nor are thermodynamic subtleties in question. In discussing, on page 425, the behavior of a substance above the critical point, we read, “Nevertheless, the change from gas to liquid is gradual, and i t may be regarded a6 a continuous transition rather than as a discontinuous one.” But the diagram and discussion seem sufficient, so that n e may better conclude that there is no change of phase and no transition a t all, and that when a homogeneous fluid fills its container we arrive a t contradictions if we attempt to state whether i t is liquid or gas from the results of such methods of manipulation. In the definition of number of components, page 466, the words “composition of each phase present can be expressed, either directly or in the form of a chemical equation,” do not make good literal sense. A satisfactory definition requires more words, and a warning that only those equations are to be used that represent reactions with respect t o which the system remains a t equilibrium. Ionic systems are not included in the illustrative examples.
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On page 373 there is a difficulty of this same sort in interpreting literally “phenomenon,” one line before “order-disorder transformation.” On page 896, in the definition of transference number, “this fraction” can unfortunately refer to the word “fraction” (as i t ought) or to the mathematical fraction (as it can in special cases). There is too much in the definition, which is more clearly given a t the bottom of page 904. Special comment seems necessary on the thermodynamic treatment. In detail this often seems good, but the reasoning underlying the manipulation of the equations is on the whole unsatisfactory. If the reasoning were merely absent, the fact would not be mentioned here, since this is commonly the case in other books. But this book is a genuine book. The author has not in general been content with copying out treatments but has presented things in his own way with explanations that are in some cases incorrect. I must hasten to add that some of the errors that are common in other books do not appear in this one. The treatment of the first law begins with the energy, as in the majority of books, so t h a t we do not expect a very exact mathematical expression of the first law. The discussion is nevertheless, I think, satisfactory. But the discussion of Eq. 3 is not adequate; one needs t o add that one is permitted the use of all the operations in connection with dL’ that are taught in elementary calculus as legitimate for exact differentials. For i t is well known that the use of a similar equation for the lineintegral differential dq does not necessarily lead to contradictions if we avoid certain other operations allowed for dU. The words “always produces the same relative increase in the volume of a gas”, in the verbal statement of Charles’ law on page 185, are not strictly consistent with the correct equation for it, which shows the increase as relative to V O , not to v . The discussion of “Maximum Work’ (page 188) cannot of course be entirely satisfactory, as the word “expansion” is not defined narrowly enough t o make the integral of Eq. 37 a definite quantity, and we have to teach explicitly that when a gas expands from p , v , t o plus the integral is not in general defined in value. This is a difficult topic, and under the heading ‘Waximum Work” i t is especially difficult, sincein general there is no maximum work. A change from maximum work in expansion to maximum work ofexpansion would help a little, But i t appears that a clear discussion will require an exact and useful definition of reversible process, and subsequent emphasis on reversible rather than maximum. The discussion of the second law is less satisfactory. The definition of reversible process mentions changes in external bodies and I have complained of this before in connection with another bcok. I consider my complaint justified by the present author when, as stated above, he regards the slow passage of a gas through a porous plug as reversible. His definition did not protect him against this error noragainst others in the use of the word “reversible.” On page 208 the word “change” is used twice and the word “process” twice, interchangeably, Many like t o use the word “change” for change of state and the word “process” to refer to the manner in which the change of state is carried out. They are thus better able to discuss the maximum work of a constant-temperature change of state. (Quite a different thing from the maximum work mentioned above, which maximum, when there is one, is with respect t o the magnitude of the difference between the pressure of a gas and the external pressure,-a matter of little theoretical importance t o a chemist.) In the discussion of “thermodynamic equations of state” the quotation marks are , absent and so is the statement that they are not equations of state. There is plenty on the page to show that Eq.145 is not an equation of state, but the book says that it ip
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The section on “Spontaneous Processes” is interesting,-and too much so for the Rtudent, to whom it may easily (but, wrongly) appear that the second law can be derived from the mere fact that the definition of hot and rold ran be used in practice without experimental contradiction. In the development of thermodynamic theory, such discussions of spontaneous and irreversible processes are digressions. If they are interesting, that is unfortunate. What is essential is a clear statement of the same definition of reversible operation that is going to be used in the theory. In the present treatment this is needed on page 212, to justify the statement that under I1 the “Work done = -W’.” In the middle of page 224 is the statement “The increase in A is thus equal t o the ” maximum work done on the system, since reversibility has been assumed We usually say “minimum” in this connection. On page 217 the word “reversib1e”is correctly introduced (albeit in association with “change” instead of “proccss”), in connection with the equatiou ds = dq/T, but subsequently the word is frequently used in ronnection with equations that do not contain dq, and the usage is then not happy. For example, on page 232, Eq. 166 is written for a reversible change a t constant temperature and pressure, though the condition of reversibility is not necessary. On page 810, last paragraph, “a small reversible change dx is made fo occur . . . . ” The proress need not be reversible,-reversibility does not matter. (Only Gibbs discusses the change of stale that is not reversible; for example, the precipitate that cannot redissolve because i t has not yet been formed.) Except for occasional reference to dS = dq/T, a student of this book will do best t,o ignore altogether the words “reversible” and “reversibly” and any phrases in which they occur, and to proceed on the assumption that everything is all right. He had better also accept that (dG)T.pis zero when the author says it is as a matter cf principle and not t r y to justify the assertion. In general, the conditions under which various thermodynamic equations hold are not sufficiently well stated to allow of such justifications, as will now appear. On page 219 i t is stated that dq = d U pdu applies to any system, although i t need not, unless the system be treated in a special manner. At the bottom of page 227, under “Conditions of Equilibrium,” the first sentence of the last paragraph is based on a hopeless confusion of quantities with their delta variations, together with an apparent belief that the entropy is always a maximum for equilibrium. In the previous paragraph i t is, in fact, stated that the entropy is a maximum for equilibrium in a system kept a t constant temperature, which is wrong. (Otherwise a liquid and its vapor would not be in equilibrium at constant temperature, as the entropy per gram of the vapor is greater.) The answer the treatment appears to seek is that the free energy is therefore a minimum, and this answer is stated without qualification of constant temperature and pressure. The fact is that the free energy need not be a minimum in paths along which T or p vary. On page 232 Eq. 167 is given, as a consequence of (dG)p.p = 0, for equilibrium a t constant temperature and pressure. But if Eq. 167 be applied to a single phase, we see that it does not hold unless the phase is closed to entrance or exit of mass. (Otherwise the free energy would be independent of the mass of the system.) This shculd be stated, especially as the previous Eq. 166 is free of this restriction. It would appear that this discussion of the conditions of equilibrium does not give a very good basis for comprehending the applications, and this is proved on page 469 in the deduction of the phase rule. Here it is stated that, since the requirement &dn = 0 holds for each phase, i t must also apply to the whole systemin equilibrium. Now i t does apply to the whole system, but not for this reason. In fact, i t obviously does not apply t o each phase, since the free energy of each phase is affected in general by the virtual variation, though in such a way as t o leave stationary the total free
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energy of the system. The error here is a logical consequence of the failure noted above t o place a restriction upon Eq. 167. I t seems t o the reviewer that the book, while i t can be very useful t o students who have had a foundation in thermodynamics, should not be recommended for beginners or for students who have had only one year of general and physical chemistry. The typography of the book is excellent. The convenience of the book for reference purposes is lessened by t,wo faults for which the publishrr should share responsibility. The numbers of the chapters are not printed on every page or evory other page. In so large a book this causes delay in cross referencc. The journal references a t the ends of the chapters are listed serially, with aeveral refercnces to various authors under each number. The books are listed u7ithout theii dates. In the text the reference is only occasionally by serial number, more often by name and date. Hence the finding of a reference in a list sometimes three pages long is often tedious and sometimes uncertain. L. J. GILLESPIE. Coinparative Physiology of Respiratory Veckanisms. By luc;usr. KROQH.6 s 9 in.; vii 172 pp.; 84 figures. Philadelphia: University of Pennsylvania Fress, 1941. Price: $3.00. Dr. Krogh is Professor of Zoophysiology a t Copenhagen University, Denmark. His researches in the field of respiration have brought him international recognition and numerous honors, including the Sobel prize. Professor Krogh delivered the William J . Cooper Foundation lectures a t Swarthmore College in the spring of 1939. This book contains the substance of those leetimes. However, the delay in publication. caused by difficulties in communication, made numerous corrections and revisions of the literature necessary. The theme of the treatise is the adaptation of the respiratory mechanisms of animals t o the widely divergent differences in the “call for oxygen” and in the accessibility of oxygen encountered in nature. The subjects discussed, after a brief introduction, are: the call for oxygen; the access to oxygen; the forces acting in the transport of oxygen (and carbon dioxide) through living tissues; respiration in water; emergency respiration (the transition t o air breathing) ; respiration in air; the respiratory functions of blood; tracheal respiration; and a brief discussion of important problems yet to be solved. The discussions of the mechanisms employed by various diving vertebrates is of particular interest. Many readers will be surprised t o learn that diving animals cannot build up larger “oxygen debts” than other air-breathing forms. The failure of animal divers t o suffer from “caisson disease” is explained in detail. Physical chemists who are interested in problems of diffusion and membrane permeability will find much interesting factual and theoretical material in this monograph. Physiologists and biochemists will find an amazingly large compilation of data for so short a book, as well as numerous fruitful suggestions for future research. A11 scientists will appreciate the efficient manner in which Professor Krogh has applied physical and chemical laws t o one of the fundamental problems of biology. The book has an adequate index, and contains a list of nearly three hundred animals, together with the pages in the book on which their respiratory mechanisms are mentioned. Two hundred and eighty-seven references are included. The binding is black cloth with gold lettering. The paper used is of good quality and the type is clear and readable. Most of the eighty-four illustrations are excellent reproductions of ink drawings. L. EARLEARXOW.
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