Clausius' Theorem for Irreversible Cycles. 72i» 



Prof. Planck objected that a proof which I suggested of the 

 Principle of the Increase of Entropy starts with the assumption 

 expressed in Lord Kelvin's version of the Second Law. 

 I understand that he withdraws this objection on learning 

 that by Lord Kelvin's version of the Second Law T mean the 

 principle that it is impossible for a substance to go through a 

 cycle in which it does work and exchanges heat with bodies at 

 one definite temperature only. This principle constitutes his 

 own starting-point. 1 regret that in this matter also I 

 unintentionally misrepresented him in my paper : I stated 

 that he assumes as a result of experience that the expansion 

 of a gas without doing external work is " irreversible " 

 (" irreversibel '*) ; but on reperusal I find that this is deduced 

 from Lord Kelvin's axiom *. 



2. With most of Prof. Buckingham's remarks f I find myself 

 in substantial agreement, as was indeed to be anticipated from 

 the fact that he also had, in his 'Theory of Thermodynamics/ 

 expressed the view that Clausius' inequality cannot be 

 deduced from the Two Laws. 



If, however. lam to say with him that any logical physicist 

 finds the so-called proofs of this theorem worthless, I fear I 

 must add an expression of regret that so few logical physicists 

 have ever given publicity to their views on the subject. 



Whether the " new substance" on which this theorem is to 

 be based should take the form of an emendation of the Second 

 Law as I suggested, or should form, so to say, a Third Law, 

 as he prefers, is a question chiefly of individual taste. It 

 may indeed be considered presumptuous to suggest any modi- 

 fication of the famous and time-honoured Second Law, though 

 here it may be urged that the words of Lord Kelvin and of 

 Clausius do not, without comment, convey clearly what is 

 generally considered to be their authors' meanings. 



That the choice also among the various methods of Carnot's 

 cycles. Entropy. Available Energy, and Thermodynamic 

 Potential should be largely governed by considerations of 

 expediency and individual liking I of course admit, provided 

 all these methods are logically sound. My plea for the use 

 of cycles i^. however, based partly on the view that the con- 

 ception- of Entropy, of Thermodynamic Potential, and, as a 

 measurable quantity, that of Available Energy also, are intel- 

 ligible only for such states as can be reached in a reversible 

 way : there seems therefore a difficulty in justifying the 

 statement, for example, that when a system is in stable 



* Lee. cit Art. 1 18. 



' Phil. Mag. Feb. I90o ; p. 208. 



