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Physics. — ''Contributions to the knowledge of van der Waals' 

 ^-surface. VIII. The xp-sur/ace in the neighbourhood of a 

 binary mivture which behaves as a jjur e substance." By Dr. J. E . 

 Verschaffelt. Supplement n". 7 to the Communications from 

 the Physical Laboratory at Leiden by Prof. H. Kamerlingh 

 Onnes. 



(Communioaled in the meeting of October 31, 1903). 



General part. 



Distillation of a mixture without its compositioji being altered, 

 and reversely also condensation of a mixture by decrease of volume, 

 without variation of pressure, quite as a pure substance, can only 

 occur at one special temperature. Experiments of Kuenen^) have 

 shown for the first time that this phenomenon may be observed in 

 the neighbourhood of the plaitpoint of the mixture; this circumstance 

 has been theoretically investigated and explained by van der Waals ^). 



If a mixture behaves as a pure substance just at the plaitpoint 

 temperature the critical point of the homogeneous mixture, the critical 

 point of contact and the plaitpoint coincide at a same point which 

 may therefore properly be called the critical point of the special 

 mixture and of which I shall represent the elements, as for a simple 

 substance, by Tk, pk and v^. 



Then according to van der Waals ^) we have at the plaitpoint 



dp\ 



— ] =z 0. Hence the isothermals of two neighbouring mixtures 



O.vjvic 



at the same temperature must intersect in pairs, so that the system 

 of isothermals of the mixtures at the critical temperature of the 

 special mixture must agree with fig. 16 of my paper in these Proc. 

 Oct. 25 1902 p. 345. In the annexed figure a similar system of 

 isothermals is drawn according to observations of Quint '*) with 

 mixtures of hydrochloric acid and ethane. 



Although the special mixture behaves as a simple substance at the 

 critical point, yet it does not follow from this that its border curve 

 on the j9, V, t diagram may be found in the same way as for a 

 simple substance, i, e. by making use of the theorem of Maxwell- 

 Clausius. For just below the critical temperature the pressure no 

 longei' remains unchanged during the condensation and the expe- 

 rimental isothermal is no longer perfectly parallel with the r-axis, 



1) Phil. Mag., 40, 173—194, 1895. Co7nm. phys. lab. Leiden, n". 16. 



2) Arch. Neerl., 30, 266, 1896. 

 •■') Gontin. II p. 116. 



*) Thesis for the doctorate, Amsterdam 1900. 



