NATURE 



73 



THURSDAY, NOVEMBER 23, 1899. 



T//E APPLICATIONS OF THERMODYNAMICS 



TO CHEMISTRY. 

 Traitd eUmentaire de Mecanique chimique, fondle sur la 



Thermodynamique. Par P. Duhem. 4 vols. \'ol. i. pp. 



viii + 299 ; vol. ii. pp. 378 ; vol. iii. pp. 380 ; vol. iv. pp. 381. 



(Paris : Librairie scientifique, A. Hermann, 1897-1899.) 



I^ROF. DUHEM'S treatise on the thermodynamic 

 potential is so well known that little or nothing 

 need be said in introducing another work from the pen 

 of the same writer dealing with thermodynamical 

 considerations. 



The study of the laws of combination and dissociation 

 is intimately connected with that of such physical pro- 

 cesses as evaporation, liquefaction and solution. To 

 this subject the not over-appropriate title of " chemical 

 mechanics " {mecanique chimique) has been given in 

 France. While Berthollet sought an explanation of the 

 fundamental phenomena in the laws of motion combined 

 with the Newtonian hypothesis of molecular attractions 

 and , repulsions, Sainte-Claire Deville referred the prin- 

 ciples of " chemical mechanics " to thermodynamical 

 considerations, and thanks to the labours of Hortsmann, 

 Moutier, Gibbs, Helmholtz and a large number of other 

 physicists, there has sprung up that wide field of in- 

 vestigation which has given the present book its title of 

 " chemical mechanics founded on thermodynamics," or 

 more briefly, chemical thermodynamics. 



It is not with special applications alone that Duhem 

 deals. The greater portion of the first volume and 

 part of the second are occupied with thermodynamics 

 proper, and constitute, to our mind, the best treatise on 

 thermodynamics that we have seen. An introductory 

 section contains a summary of the more important 

 mathematical and dynamical theorems and principles 

 required at the outset, and this should be helpful to 

 students. 



In his preface the author calls attention to the great 

 difficulty of giving a perfectly rigorous and logical ex- 

 position of the laws of thermodynamics, and claims only 

 to have attained the degree of precision usually adopted 

 in treatises on physics. A comparison of Duhem's 

 work with the heterogeneous mixtures of experimental 

 results, mathematical formulas and veiled assumptions 

 which commonly have to do duty as text-books on thermo- 

 dynamics, will show that the author has really advanced 

 a long way in making the subject clear and intelligible. 

 No better illustration of this can be cited than the careful 

 precautions taken to avoid premature assumptions with 

 regard to thermometric scales in the treatment of perfect 

 gases. In these days of widespread education in " general 

 elementary science " such terms as " a perfect gas " and 

 " absolute temperature " bid fair to become by-words ; 

 but how many B.Sc.'s either of London or of our provincial 

 universities can give correct definitions of them ? If this 

 point were tested, we venture to predict that in the vast 

 majority of cases the first term would be defined by 

 reference to the second, and the second by reference to 

 the first, and if the circular nature of this reasoning were 

 pointed out, the graduate under examination would have 

 NO. 1569, VOL. 61] 



to take refuge in considerations respecting molecules, 

 about whose nature an^ mode of motion he knew 

 nothing. Moreover, apart from Charles's law and the 

 difficulties connected with it, comes the question as to 

 whether or not the definition of a perfect gas is to include 

 Clausius's hypothesis as to the constancy of one (and 

 therefore both) of the specific heats. Here again the 

 question is considered most explicitly. 



Another feature of Duhem's treatment is that while 

 the old familiar /, v, t trio receives full consider- 

 ation, generalised coordinates are introduced from the 

 very outset, and the significance of such coordinates is 

 explained by illustrative examples as far as possible. 

 To one feature, however, we must take exception, 

 and that is the retention in Duhem's equations of 

 the useless E (synonymous with the English J) 

 standing for the "mechanical equivalent of heat," 

 as it was once, and unfortunately often still is, 

 called. This quantity is nothing more or less than 

 the work measure of the specific heat of water at a 

 certain temperature, and the equations of thermo- 

 dynamics in no way depend on the specific heat of water. 

 The absolute unit of heat is the unit of work, and with 

 this unit E must be replaced by unity. As Prof. 

 Poynting remarked in his address to Section A at Dover, 

 " the real superiority of the work measure of specific heat 

 lies in the fact that it is independent of any particular 

 substance, and there is nothing whatever hypothetical 

 about it." 



In this respect the work unit of heat stands on a much 

 more rational footing than the universally adopted dual 

 systems of so-called " absolute units " of electricity and 

 magnetism, which are not independent of the medium, 

 and whose dimensions moreover are incompatible. 



As regards Duhem's two chapters on stability, we 

 can only wish they had been before us when first learning 

 thermodynamics, as we should have been saved the 

 trouble of thinking out for ourselves conclusions similar 

 to those here expounded, after vainly attempting to 

 follow the arguments of the text-books and to apply 

 them to a Tripos rider ; now the whole matter appears 

 before us in a clearer light than it ever did previously. 



The last part (Book ii.) of volume i. deals with false 

 equilibria and explosions. By "false equilibria" {faux 

 dquilibres) are meant states of equilibrium which can 

 be realised experimentally, although the conditions of 

 equilibrium of conventional— or, as Duhem calls it, 

 " classical " — thermodynamics are not satisfied. They 

 are analogous to the equilibrium of rough bodies in 

 statics, in configurations which, in the absence of friction, 

 would have been impossible. This analogy has led, in 

 Duhem's hands, to the development of an extremely 

 elegant mathematical theory of false equilibria and ex- 

 plosions based on the introduction of a function which 

 the author calls the "friction" {le frottement) of the 

 system. This function is entirely distinct from that 

 which represents viscosity, but when it is introduced into 

 the equations of the system, along with the thermo- 

 dynamic potentials, Clausius's inequality for irreversible 

 cycles /</Q/T>0 is satisfied. In a diagrammatic repre- 

 sentation, the line of true equilibrium is bordered on 

 either side ;by a region of false equilibrium. When the 



E 



