( 31 1 ) 



2 - f\ \ 2 

 3 l l n = l*^ + /' N "W ( ö a t m & ) I - .. M- N ^ '•• 



for which we may also write: 



2 



\iNlpg v 4- /iA'Aw ,7 -f- C"; 

 o 



this C", however, does nol agree with Lorentz' C'. 



In this connection I will finally call attention lo an objection to 



the use of* this latter entropy introduced l»v GlBBS. 



Purely thermodynamically the entropy is determined by the diff. 



dQ 

 equation — 7 = di\. So this i\ contains an arbitrary additive constant. 



This is not the case for the kinetically defined one. Boltzmann'h // 



is entirely determined by the equation // = I [flog fdodm and so 



2 r 



also the entropy \iH. In the same way in Gibbs — >/ = — I PlogPdr, 



if the energy is purely kinetic, which we shall assume. 



The same applies to the free energy if?, thermodynamically it con- 

 tains an arbitrary additive constant, kinetically it does not. This 

 uncertainty, however, allows us to choose the constant in thermo- 

 dynamics in a convenient way, which is no more possible in \\iv 

 kinetic theories. This constant is now chosen in such a way that 

 the xp for a certain gas mass (and then also the if) is equal to the 

 sum of the i|**s of the parts (molarly not molecularly separated). 

 This appears clearly in Lorentz '). Here a gramme molecule of a 

 certain gas is considered, and 



ifj= — RTloqv-\- C derived from ——/>:= — 



Or v 



Now C is chosen in such a way, that ip = if v = 1 , so C= Oor 

 ip = — RTlogv. Somewhat further it says: "Haben wir es nicht 

 mit einer, sondern mit m Einheiten zu tun, die zusammen das Volum 

 ?; fiillen, so haben wir nebeneinander /?i-mal die Einheit in dem Volum 



. Wir mussen also in if' = — RTlogv V (lurch ersetzen uml 



V ' r 



dann mit m multiplizieren." So by definition the if' of the whole 

 lias here evidently been put equal to the sum. of the ip's of the 

 parts occurring side by side in the volume v. 



We may also say that this has taken place b\ assigning anothei 

 value to 6' for every quantity. If namely in a volume 2v we had 



i) 1. c. p. 236. 



