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269 



THURSDAY, JANUARY 17, 1901. 



MODERN THERMODYNAMICS. 



An Outline of the Theory of Thermodynamics. By 

 Edgar Buckingham, Ph.D. (Leipzig). Pp. xi + 205. 

 (New York : The Macmillan Company. London : 

 Macmillan and Co., Ltd., 1900.) 



THE study of thermodynamics is customarily 

 approached, in treatises and text-books, from a 

 point of view to a great extent the reverse of that which 

 is adopted in opening up the subject of dynamics. In 

 •dynamics, the usual treatment is essentially theoretical, 

 as opposed to experimental. Newton's laws of motion 

 are regarded as axiomatical ; the second and third laws 

 are employed to afford quantitative definitions of force 

 and mass respectively, the parallelogram of forces is 

 practically assumed, and all which follows is mere 

 mathematics. It is only quite recently that the possi- 

 bility of teaching dynamics from a more experimental 

 standpoint has been seriously considered. 



In thermodynamics it is usual to go to the other 

 extreme. Temperature is defined in the first place by a 

 common thermometer, calorimetry is treated largely in 

 its experimental aspect, and the first law of thermo- 

 dynamics thus becomes more closely associated in the 

 reader's mind with Joule's experiments on the "mechanical 

 equivalent of heat" than with its interpretation as afford- 

 ing a definition of "quantity of heat." The ordinary 

 treatment of the mechanical equivalent of heat would, in 

 fact, have an analogue in dynamics if we were to start 

 with the pound weight as unit of force, and to define the 

 constant^ as the "kinetical equivalent of force." 



Of recent years a great impetus has been given to the 

 study of higher thermodynamics by the development of 

 physical chemistry based on the theories first enunciated 

 by Willard Gibbs. The experimental study of what at 

 first was a purely mathematical investigation plays a part 

 in the history of science closely analogous with the 

 experimental verifications of Maxwell's theory by Hertz's 

 discovery of electromagnetic waves. This new develop- 

 ment has, to quote Mr. Buckingham's own words, caused 

 *' a considerable gap between the text-books available 

 and the modern memoirs." Mr. Baynes's treatise, so long 

 the favourite English introduction to thermodynamics, 

 does not deal with thermodynamic potentials, yet it is 

 with the study of these functions that modern thermo- 

 dynamics is primarily occupied. Several subsequent 

 attempts have been made to produce text-books on 

 thermodynamics, but their writers have generally intro- 

 duced long digressions on extraneous matter while 

 omitting many of the most important features of the 

 theory. 



What we have been wanting was, in the first place, an 

 application to thermodynamics of the same deductive 

 methods that have been used in building up other con- 

 nected theories, such as rational dynamics and hydro- 

 dynamics, and, in the second place, an introduction to the 

 study of the thermodynamic potential, the conditions of 

 thermodynamic equilibrium and stability for a generalised 

 system the state of which is defined by any number of 

 NO. 1629, VOL. 63] 



variables, and not merely by two of the pressure, volume 

 temperature triad, and, lastly, an exposition of the phase 

 rule. In compiling this book Mr. Buckingham is prac- 

 tically alone in the field, and the result of his efforts will 

 greatly remove the difficulties which most students 

 experience in acquiring a knowledge of thermodynamics. 

 In Chapter i. (Thermometry) the author defines equality 

 of temperature, and enunciates the axiom of equal tem- 

 peratures, according to which bodies which are of equal 

 temperature with a third body are themselves of equal 

 temperature. Absolute temperature cannot, of course, 

 be defined until the second law ; but in introducing the 

 so-called " absolute gas scale," the author is careful to 

 guard against misleading assumptions. In Chapter ii. 

 (Calorimetry) the various heat-units are discussed, and 

 the advantage of the dynamical unit explained. The 

 next chapter practically defines thermodynamic systems 

 and thermodynamic equilibrium ; while in Chapter iv. we 

 have the first law enunciated in the form of the statement 

 that for a cyclic process the integral of ^W+^Q is zero. 

 Chapters v. and vi. deal with the problem of thermo- 

 chemistry and the thermal properties o fluids, so far as 

 they can be deduced from the first law alone. A re- 

 capitulation of the first six chapters makes up the 

 seventh. 



Chapter viii. deals with the second law of thermo- 

 dynamics. The author, having previously defined abso- 

 lute temperature on the ideal gas scale, here expresses 

 the efficiency of an ideal gas engine in terms of the 

 temperatures, so defined, of the source and refrigerator. 

 In his proof, Boyle's and Joule's laws are assumed. We 

 do not altogether like this order of treatment. We should 

 prefer to see the second law treated somewhat earlier 

 and used to furni-sh a definition of absolute temperature 

 the properties of gases, as affording a measure of tem- 

 perature, being subsequently deduced from Boyle's and 

 Joule's law combined with the first and second laws. 

 This method would altogether obviate the necessity of 

 introducing the "gas scale of temperature." Still, the 

 author is so careful in pointing out what is assumed and 

 what is proved in his work that his order of treatment 

 cannot raise any serious objections. 



General Equations (Chapter ix.) introduce the thermo- 

 dynamic potentials. The next chapter deals with the 

 theory of the plug experiment for determination of 

 absolute temperature. Lord Kelvin's equation, application 

 of the laws of thermodynamics to the E.M.F. of a galvanic 

 cell, change of state, and change of osmotic pressure with 

 the temperature. 



In the next chapter we have a summary of the hypo- 

 theses and conditions involved in the criteria of thermo- 

 dynamic equilibrium, followed, in Chapter xii., by a concise 

 account of applications of these conditions involving the 

 use of the thermodynamic potentials, in which Duhem's 

 " total thermodynamic potential " and Helmholtz's " free 

 energy" find their explanations. The book concludes 

 with an application of the free energy principle to the 

 galvanic cell, and a discussion on the triple point, which 

 latter leads naturally up to the more general theorem 

 embodied in Gibbs's phase rule. The discussion of this 

 theorem is somewhat condensed, the author referring to 

 the original papers for a more detailed investigation ; 

 but for the readers of a book such as the present the 



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