190 Dr. J. P. Kuenen on the Condensation and Critical 



In the following account of some of the theoretical results 

 I will only consider the case of the coexistence of vapour and 

 liquid, i. e. a separation of the liquid into two will be excluded 

 from the consideration. 



I shall sometimes follow a method different from van der 

 Waals's, chiefly for the sake of shortness and simplicity. 



27. Let us suppose a set of isothermal curves ( p-v diagram) 

 to be drawn for the mixture as determined by observations of p, 

 v, and t in homogeneous states, and completed by partly un- 

 stable interpolation-curves joining the curves in the homo- 

 geneous gaseous and liquid condition. 



Suppose we forget for a moment that the substance is a 

 mixture, and apply the Maxwell-Clausius criterion for finding 

 the coexisting phases in the usual manner. We should then 

 get the border or saturation-curve separating the homoge- 

 neous states from those where these are unstable or less stable 

 than the separated states. The diagram thus obtained gives 

 us the condensation-pressures, the vapour- and liquid-densities, 

 and the critical point for the mixture, if supposed to behave 

 like a pure substance, i. e. not dividing into phases which 

 have a different composition. The real border-curve can only 

 be found by a more complicated application of thermody- 

 namics : still we may easily see one thing, that the real 

 border-curve would lie entirely outside the hypothetical one 

 just obtained. Instead of the horizontal line cutting off 

 equal areas from the isothermal, we get a sloping line : this 

 line has again to cut off equal areas. Obviously this is only 

 possible by making it start lower and finish higher than the 

 straight line. This is true at all temperatures, and the con- 

 clusion is, as stated, that the border-curve will be entirely 

 outride the hypothetical one. From this it follows, e.g., that 

 the real critical temperature is higher than the critical tem- 

 perature for the undivided mixture ; also that the critical 

 isothermal does not touch the border-curve at the top M but 



dp 

 at a point to the right C, where -~< instead of =0 as for a 



single substance. The volume in the critical point is obviously 

 larger and the pressure smaller than the same quantities at 

 the top of the border-curve. 



28. The last fact about the critical pressure (point 0) not 

 being the maximum pressure (point M) for the mixture on 

 the border-curve was pointed out above with reference to the 

 p-t diagram. In fact the loops for the mixtures are nothing 

 but the real border-curves represented in a different manner. 

 The third point P which we considered in that case (plait- 

 point), the point of contact of the loop and the enveloping 



