( 787 ) 



If llio mutual attraction of llic molecules of the two components rt lt 

 is small compared with the attraction of the molecules of one ofthe 

 components inter se, '/,,, the appearance of complete miscibility will 



be determined solely by the molecular motion, and then the tempe- 

 rature will have to be raised to an amount which, if some propor- 

 tions of the 6's can occur then, may greatly exceed the critical 

 temperature of the least volatile component, 7/,, ' , and with it the 

 critical temperatures of all mixtures of' these components. Thus from 

 the equation (a) of \ \\ deb W.wi.s, Oontin. II p. 43, follows 

 Tt M = 1 .6875 7'/., for the critical temperature of complete miscibility 

 wan dhr Waals I.e.) 7/,„„ it* a„ = a ls = and 6 n = b„ may be 

 put. At a lower temperature the two substances considered are only 

 partially niiscible, whereas for such a temperature above 7*, there 

 may be coexistence of two phases which, as will he further explained 

 in § 3 and 4, are to be considered as gas phases. 



Now it seems to follow from the nature of most of the substances 

 known to us, most likely from the structure of their atoms, that 

 6„ is also small, when rr 22 becomes very small ; hence for a gas 

 without cohesion 6 aa may not be put equal to 6 n of a gas with 

 cohesion, and as according to the equation cited of van der Waals 

 a small value of h. l% furthers the mixing greatly, the critical tem- 

 perature of complete miscibility cannot rise as high as was derived 

 iust now. But though most likely the case mentioned just now as 

 example does not occur in nature, yet it is certainly conducive to 

 a better insight of what is to be expected for gases of exceedingly 

 slight cohesion. 



§ 2. The shape of the spinodal curves >ni</ the form of the plait 

 on the ^-surface for binary mixtures of which one component is a 

 gas with molecules with extension mid tritium t co/iesion. In tig. 1 

 PI. I the spinodal curves are represented for such a case. The tigure 

 refers to the ip-surface for the unity of weight of the mixtures, as 

 we hope to give a further discussion of such a ip-surface icomp. § 1), 

 also with a view to the treatment of the barotropic phenomena which 

 may occur for these mixtures 2 ) in case of a suitable proportion of 

 the molecular volumes of the components, for which treatment the 

 use of the ip-surface for the unity of weight readily suggests itself. 

 As was also mentioned in Comm. N". 96" A, the conditions for 



') van der Waals, in the paper cited p. 786 footnote | I |, brought this in connec- 

 tion with the great, amount of heat absorbed at the mixing of such substances. 

 [Added in the English translation]. 



8j Gf. Comm. N°. 96a (Nov. *06), 96 6 (Dec '06j and 96c (Dec. '06, Febr. '07). 



