( 639 ) 



Physics. "On tin' shape <>/ the three-phase-line solid-liquid-vapoür 

 for a binary mixture." By Dr. Ph. Kohnstamm. (Communicated 

 by Prof. J. D. van der Waals.) 



Already for a considerable time I have been engaged in arranging 

 Prof. Van dkr Waals' thermodynamic lectures, and having arrived 

 at the discussion of the three phase line solid-liquid-vapour, and the 

 metastable and unstable equilibria solid-lluid which are in connection 

 with it, I have formed on some points a different opinion from that laid 

 down in the literature known to me on this subject.' It does nol 

 seem unprofitable to me to shortly discuss the points of deviation in 

 this and the following communication. 



The first concerns the shape of the three phase line solid-liquid- 

 vapour when the solid substance is one of the components, viz. the 

 least volatile one. We find given for this that this line must always 

 possess a pressure maximum x ), and that it must also possess a 

 temperature maximum 2 ) when the solid substance, — as is usual, 

 — melts with expansion of volume. The latter remark is the 

 generalisation of a supposition, advanced by Van der Waals') with 

 respect to the line for ether and anthraquinone. These consider- 

 ations, however, hold only for definite assumptions on the extent 

 of the difference of volatility of the two components. This appears 

 immediately from the differential equation of the three phase line 

 given by van der Waals 4 ) : 



x . 



d P_ __ ■£/ 



dT x v 



v„ — v s (vi— v s ) 



(1) 



in which i], x and v denote resp. entropy, concentration and volume 

 of the coexisting' phases, the index v, I and s denoting that resp. 

 the vapour, liquid and solid phase is meant. cc s does not occur, 

 because we assume, that the solid phase is the first component itself 

 so x s = 0. The pressure maximum will now occur in the line when 

 the numerator, the temperature maximum when the denominator can 

 become zero. Now ij„— i ]s > r tl — i if and r„— /•, > r t — r s - the two 

 cases are therefore only possible when x„ >,/•/, i.e. when the vapour 

 is richer in the component which does not form the solid phase, 



!) Bakhuis Roozeboom. Die heterogenen Gleichgewichte II. p. 331. 

 3 ) Smits. These Proc. VIII, p. 196; Zeitsch. phys. Cli. L1V, p. 498. 

 3 ) These Proc. VI, p. 243. 

 *) Verslag Kon. Akademie V, p. 490. 



