Feb. 7, 1878] 



NATURE 



279 



this method of rednctio ad absurdnvi, for the work may 

 be derived from the heat taken from the colder body. 



Clausius supposes all the work gained by the first 

 engine to be expended in driving the second. There is 

 then no loss or gain of heat on the whole, but heat is 

 taken from the cold body, and an equal quantity com- 

 municated to the hot body, and this process might be 

 carried on to an indefinite extent. 



In order to assert the impossibility of such a process in 

 a. form of words having sufficient verisimilitude to be 

 received as an axiom, Clausius, in his first memoir, simply 

 says that this process " contradicts the general deportment 

 of heat, which everywhere exhibits the tendency to 

 equalise differences of temperature, and therefore to pass 

 from the warmer to the colder body." ^ 



In its obvious and strict sense no axiom can be more 

 irrefragable. Even in the hypothetical process, the im- 

 possibility of which it was intended to assert, every com- 

 munication of heat is from a warmer to a colder body. 

 When the heat is taken from the cold body it flows into 

 the working substance which is at that time still colder. 

 The working substance afterwards becomes hot, not by 

 communication of heat to it, but by change of volume, 

 and when it communicates heat to the hot body it is itself 

 still hotter. 



It is therefore hardly correct to assert that heat has been 

 transmitted or transferred from the colder to the hotter 

 body. There is undoubtedly a transfer of energy, but in 

 what form this energy existed during its middle passage 

 is a question for molecular science, not for pure thermo- 

 dynamics. 



In a note added in 1864 Clausius states the principle 

 in a modified form, " that heat cannot of itself pass from 

 a colder to a warmer body '' ^ and finally, in the new edi- 

 tion of his " Theory of Heat" (1876) he substitutes for the 

 words "of itself" the expression "without compensa- 

 tion." ^ 



With respect to the first of these emendations we must 

 remember that the words "of itself" are not intended to 

 exclude the intervention of any kind of self-acting ma- 

 chinery, and it is easy, by means of an engine which takes 

 in heat from a body at 200° C, and gives it out at 100° to 

 drive a freezing machine so as to take heat from water at 

 0°, and so freeze it, and also a friction break so as to 

 generate heat in a body at 500°. It would therefore be 

 necessary to exclude all bodies except the hot body, the 

 cold body, and the working substance, in order to exclude 

 exceptions to the principle. 



By the introduction of the second expression, " without 

 compensation," combined with a full interpretation of this 

 phrase, the statement of the principle becomes complete 

 and exact ; but in order to understand it we must have a 

 previous knowledge of the theory of transformation- 

 equivalents, or in other words of entropy, and it is to be 

 feared that we shall have to be taught thermodynamics 

 for several generations before we can expect beginners to 

 receive as axiomatic the theory of entropy. 



Thomson, in his "Third Paper on the Dynamical 



' Und das widerspricht dem sonstigen Verhalten der Warme, indem sie 

 fiberall das Bestreben zeigt, vorkommende Temperaturdifferenzen aus- 

 zugleichen und also aus den wjirmeren Korpern in die kiilteren uberzu- 

 gehen. 



" Dass die Warme nicht von selbst aus einem kalteren in einem warmeren 

 Korper ubergehen kann. 



3 Ein Warmeiibergang aus einem kalteren in einem warmeren Korper 

 kann nicht ohne Compensation stattfinden, 



Theory of Heat" {Trans. R.S. Edin., xx., p. 265 (read 

 March 17, 1851) has stated the axiom as follows : — 



" It is impossible, by means of inanimate material 

 agency, to derive mechanical effect from any portion of 

 matter by cooling it below the temperature of the coldest 

 of surrounding objects." 



Without some further restriction this axiom cannot be 

 considered as true, for by allowing air to expand we may 

 derive mechanical effect from it by cooling it below the 

 temperature of the coldest of surrounding objects. 



If we make it a condition that the material agency is to 

 be left in the same state at the end of the process as it 

 was at first, and also that the mechanical effect is not to 

 be derived from the pressure of the hot or of the cold 

 body, the axiom will be rendered strictly true, but this 

 brings us back to a simple re-assertion of Carnot's prin- 

 ciple, except that it is extended from heat engines to all 

 other kinds of inanimate material agency. 



It is probably impossible to reduce the second law of 

 thermodynamics to a form as axiomatic as that of the first 

 law, for we have reason to believe that though true, its 

 truth is not of the same order as that of the first law. 



The first law is an extension to the theory of heat of 

 the principle of conservation of energy, which can be 

 proved mathematically true if real bodies consist of 

 matter "as per definition," acted on by forces having 

 potentials. 



The second law relates to that kind of communication 

 of energy which we call the transfer of heat as distin- 

 guished from another kind of communication of energy 

 which we call work. According to the molecular theory 

 the only difference between these two kinds of com- 

 munication of energy is that the motions and displace- 

 ments which are concerned in the communication of heat 

 are those of molecules, and are so numerous, so small 

 individually, and so irregular in their distribution, that 

 they quite escape all our methods of observation ; whereas 

 when the motions and displacements are those of visible 

 bodies consisting of great numbers of molecules moving all 

 together, the communication of energy is called work. 



Hence we have only to suppose our senses sharpened 

 to such a degree that we could trace the motions of mole- 

 cules as easily as we now trace those of large bodies, and 

 the distinction between work and heat would vanish, for 

 the communication of heat would be seen to be a com- 

 munication of energy of the same kind as that which we 

 call work. 



The second law must either be founded on our actual 

 experience in dealing with real bodies of sensible magni- 

 tude, or else deduced from the molecular theory of these 

 bodies, on the hypothesis that the behaviour of bodies 

 consisting of millions of molecules may be deduced from 

 the theory of the encounters of pairs of molecules, by 

 supposing the relative frequency of different kinds of 

 encounters to be distributed according to the laws of 

 probability. 



The truth of the second law is therefore a statistical, 

 not a mathematical, truth, for it depends on the fact that 

 the bodies we deal with consist of millions of molecules, 

 and that we never can get hold of single molecules. 



Sir William Thomson ' has shown how to calculate the 



I " On the Kinetic Theory of the Dissipation ot Energy," Proc. R.S. 

 Edin., February i6, 1874, vol. viii, p. 323, also in Nature, vol. ix. p. 441. 



