278 



NATURE 



{Feb. 7, 1878 



to discussing the application of electricity for illuminating 

 purposes, to the transmission of motive power, and in 

 metallurgic processes. Recent improvements in the means 

 of obtaining powerful electric currents seem to open up a 

 prospect of such applications as those just mentioned, 

 assuming in the near future greater practical importance 

 than they have hitherto possessed, and it does not seem 

 unlikely that, whether or not they think fit to assume the 

 wider designation, the Society of Telegraph Engineers 

 will have become a Society of Electrical Engineers. 



G. C. F. 



T AIT'S ''THERMODYNAMICS'' ^ 

 II. 

 Sketch of Thermodynatnks. By P. G. Tait, M.A., for- 

 merly Fellow of St. Peter's College, Cambridge, Pro- 

 fessor of Natural Philosophy in the University of 

 Edinburgh. Second Edition, revised and extended. 

 (Edinburgh: David Douglas, 1877.) 



PROF. CLAUSIUS is himself the principal founder of 

 the kinetic theory of gases. The theory of the ex- 

 changes of the energy of collections of molecules was 

 afterwards developed by Boltzmann to a much greater 

 extent than bad been done by Clausius, and it appears 

 from his investigations that whether we suppose the 

 molecules to be acted on by forces towards fixed centres 

 or not, the condition of equilibrium of exchange of energy, 

 or in other words the condition of equality of tempei-ature 

 of two bodies, is that the average kinetic energy of trans- 

 lation of a single molecule is the same in both bodies. 



We may therefore define the temperature of a body as 

 the average kinetic energy of translation of, one of its 

 molecules multiplied into a constant which is the same 

 for all bodies. If we also define the total heat of the 

 body as the sum of the whole kinetic energy of its mole- 

 cules, then the total heat must be equal to the temperature 

 multiplied into the number of molecules, and by the ratio 

 of the whole kinetic energy to the energy of translation, 

 and divided by the above constant. 



The kinetic theory of gases has therefore a great deal 

 to say about what Rankine and Clausius call the actual 

 heat of a body, and if we suppose that molecules never 

 coalesce or split up, but remain constant in number, then 

 we may also assert, all experiments notwithstanding, that 

 the real capacity for heat (as defined by Clausius) is 

 constant for the same substance in all conditions. 



Rankine, indeed, probably biased by the results of 

 experiments, allowed that the real specific heat of a sub- 

 stance might be different in different states of aggrega- 

 tion, but Clausius has clearly shown that this admission 

 is illogical, and that if we admit any such changes, we 

 had better give up real specific heat altogether. 



Statements of this kind have their legitimate place in 

 molecular science, where it is essential to specify the 

 dynamical condition of the system, and to distinguish 

 the kinetic energy of the molecules from the potential 

 energy of their configuration ; but they have no place in 

 thermodynamics proper, in which we deal only with 

 sensible masses and their sensible motions. 



Both Rankine and Clausius have pointed out the im- 

 portance of a certain function, the increase or diminution 



' Continued from p. 259, 



of which indicates whether heat is entering or leaving the 

 body. Rankine calls it the thermodynamic function, and 

 Clausius the entropy. Clausius, however, besides invent- 

 ing the most convenient name for this function, has made 

 the most valuable developments of the idea of entropy? 

 and in particular has established the most important 

 theorem in the whole science, — that when heat passes 

 from one body to another at a lower temperature, there 

 is always an increase of the sum of the entropy of the 

 two bodies, from which it follows that the entropy of the 

 universe must always be increasing. 



He has also shown that if the energy of a body is ex- 

 pressed as a function of the volume and the entropy, then 

 its pressure (with sign reversed) and its temperature are the 

 differential coefficients of the energy with respect to the 

 volume and the entropy respectively, thus indicating the 

 symmetrical relations of the five principal quantities in 

 thermodynamics. 



But Clausius, having begun by breaking up the energy 

 of the body into its thermal and ergonal content, has 

 gone on to break up its entropy into the transformational 

 value of its thermal content and the disgregation. 



Thus both the energy and the entropy, two quantities 

 capable of direct measurement, are broken up into four 

 quantities, all of them quite beyond the reach of experi- 

 ment, and all this is owing to the actual heat which 

 Clausius, after getting rid of the latent heat, suffered to 

 remain in the body. 



Sir William Thomson, the last but not the least of the 

 three great founders, does not even consecrate a symbol 

 to denote the entropy, but he was the first to clearly 

 define the intrinsic energy of a body, and to him alone 

 are due the ideas and the definitions of the available 

 energy and the dissipation of energy. He has always 

 been most careful to point out the exact extent of the 

 assumptions and experimental observations on which 

 each of bis statements is based, and he avoids the intro- 

 duction of quantities which are not capable of experi- 

 mental measurement. It is therefore greatly to be 

 regretted that his memoirs on the dynamical theory of 

 heat have not been collected and reprinted in an acces- 

 sible form, and completed by a formal treatise, in which 

 his method of building up the science should be exhibited 

 in the light of his present knowledge. 



The touchstone of a treatise on thermodynamics is 

 what is called the second law. 



Rankine, as we have seen, founds it on statements 

 which may or may not be true, but which cannot be 

 considered as established in the present state of science. 



The second law is introduced by Clausius and Thomson 

 as an axiom on v/hich to found Carnot's theorem that the 

 efficiency of a reversible engine is at least as great as that 

 of any other engine working between the same limits of 

 temperature. 



If an engine of greater efficiency exists, then, by 

 coupling this engine with Carnot's engine reversed, it is 

 possible to restore to the hot body as much heat as is 

 taken from it, and at the same time to do a certain amount 

 of work. 



If with Carnot v.'e suppose heat to be a substance, then 

 this work would be performed in direct violation of the 

 first law — the principle of the conservation of energy. 

 But if we regard heat as a form of energy, we cannot apply 



