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XV. On Clausius' Theorem for Irreversible Cycles, and on 

 the Increase of Entropy*. q f \\ 



To the Editors of the Philosophical Magazine. (J 



GENTLEMEN, Berlin, Nov. -2, 1904. 



I BEG leave to make a few observations on Prof. \Y. McF. 

 Orr's paper f of the above title, in which he criticises 

 among other things my treatment of Thermodynamics J, for 

 otherwise I fear that it may perhaps give rise to one or two 

 misconceptions. 



1. I will not quarrel with Prof. Orr as to whether he is 

 right in saying (p. 509) that I use the words " reversible " 

 and " irreversible " in an unusual sense, since these words 

 are seldom expressly defined. Yet, I really must show by an 

 example that the form of the definition I use is practical. 



Clausius, as is well known, founded his proof of the Second 

 Law of Thermodynamics on the simple proposition that heat 

 cannot of itself pass from a colder to a hotter body. Here it is 

 not only stated, as Clausius repeatedly and expressly pointed 

 out, that heat does not pass directly from a colder to a hotter 

 body, but that heat can in no way whatsoever be conveyed 

 from a colder to a hotter body without leaving behind some 

 lasting change (t. e. without compensation). 



If 1 now say, the process of heat conduction is irreversible, 

 this proposition, according to my definition of irreversibility, 

 means exactly the same as Clausius' fundamental proposition. 

 Whether this proposition is in reality true cannot be directly 

 settled and requires a special investigation ; but if once we 

 assnme its truth, then the whole import of the Second Law of 

 Thermodynamics can be deduced from it. If, on the other 

 hand, we understand by the irreversibility of a process, only that 

 it cannot be directly reversed, then the proposition that the 

 passage of heat from a higher to a lower temperature is irre- 

 versible is, to be sure, self-evident, but it is of no value for the 

 derivation of the Second Law of Thermodynamics, for we are 

 not in a position to draw therefrom any conclusions regarding 

 other processes 



'I. Prof. Orr >ays (p. ."ill) " Planck gives one Definition 

 of Reversibility, but uses another." As I searched for a 

 proof of this assertion, the only thing I could find was the 

 following statement : — " Under ordinary circumstances, how- 

 ever, no body can expand without producing a change of 



Translated and communicated by A. Ogg, Ph.D. 

 •i- Phil. Mag. Oct. 1904, p. 509. 



100:5. 



