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XLIX. On Clausius’ Theorem for Irreversible Cycles, and on 
the Inerease of Entropy. By Prof. W. McF. Orr, WW. A.* 
Introduction. 
lh BELIEVE that many persons interested in the exposi- 
tion of Thermodynamics are dissatisfied with the 
discussions which are accorded to the theorem generally known 
as Clausius’ theorem for irreversible cycles and to equivalent 
theorems relating to increase of entropy by most writers 
on the subject. I venture to put forward some criticisms on 
such discussions, and to suggest a slight modification of the 
statement of the Second Law of Thermodynamics, which I 
believe is necessary if any such theorem is to be logically 
deduced therefrom. 
Planch’?s Discussion. His peculiar Definition of 
“ Trreversibility.” 
2. Planck’s treatment of the subject takes the form of a 
series of propositions relating to entropy, and is of peculiar 
interest on account of the unusual sense in which he uses the 
words “reversible” and ‘irreversible.’ An _ irreversible 
process is defined + not merely as one such that it cannot be 
directly reversed, but one such that it is impossible, starting 
with the final state of the system (which we may denote by B) 
and using appliances of any kind whatsoever, mechanical, 
thermal, chemical, &c., to obtain the initial state (which may be 
denoted by A) and leave all the materials and machines used 
in the same condition exactly (at A) as before their applica- 
tion (at B). A process which is “reversible” in this sense 
only is described as “reversibel;”? one which can be 
directly reversed as “ umkehrbar.”’ 
He begins by considering perfect gases. The properties 
postulated for such bodies are not stated as clearly as is 
desirabie {; and the entropy ¢ of a mass M of a perfect gas 
of molecular weight m is defined by means of the equation :— 
o=M(c, log. 6+ R/m.log.v). He demonstrates the theorem 
that if a system of perfect gases has its total entropy the 
same in two different states, it may be transformed from one 
* Qommunicated by the Author. 
+ Vorlesungen wiber Thermodynamk ; or Oge’s translation, Arts. 109, 
112. 
t The reviewer of Oge's translation in ‘Nature,’ Dec. 31, 1903, remarks 
with justice that a student may be thus led into the fallacy of reasoning 
in a cycle, and also that he is likely to be confused by being given two 
different definitions of entropy, firstly one which is applicable to perfect 
gases only, and afterwards another to be applied to all bodies. 
