( 190 ) 



the line v = b to another point of this line, tlie value of x may be 



dx dx dx 



maximum or minimum. Then — -, — and — = 0, and the three re- 



dT dv dp 



maining differential quotients must be determined — and lastly also 



dv dv dv 



v might be maximum or minimum ; then —. — and — would be 



dl dp dx 



dT dp dp 



equal to zero, and — , — and — would have to be determined. 

 dx dx dT 



Three phase pressure and final point of the three phase pressure 

 on the plaitpcint line. 



If at a certain temperature three phase pressure exists, there must 

 be a hidden plaitpoint on the ip-surface, as appears from the foregoing 

 remarks. If the spinodal curve is closed on the side of the small volumes 

 there is moreover a realisable plaitpoint, and there can even be another 

 realisable plaitpoint if the temperature is above the Tk of one of the 

 components. Let us call x x and v x , x, and w„ x t and v t the com- 

 positions and volumes of the three phases, assuming the first two to 

 be liquid phases and the third to be a gas-phase, and let us put 

 x 7 ^> a\. Now three cases may occur, viz. : x t > #, > a:, ; .r, ^> #, > x t 

 and x„ ^> x, ^> x x . The first case occurs when the gas phase contains 

 more of the second component than each of the liquid phases, and 



so when [ — ] is always positive ; the second case when the gas 

 \dxJ,T 



fdp\ 

 phase contains less of the second component, and so when I — 1 



\dx JvT 

 fdp\ 

 is negative, and the third case requires that the line — = runs 



\dxJ vT 



between the two liquid phases. Of the first case an example may 

 be found in the mixture water in SO s , mixtures of ethane and some 

 alcohols (above methylalcohol) constitute an example of the second 

 case, and of the third case the mixture water and phenol is an example. 

 As we have an equilibrium which is independent of the size of 

 the volume, when for a mixture of 2 substances there exists equili- 

 brium of 3 phases, the formula of Clapeyron may serve for the 



dp 

 computation of the value of — , and we may put: 



dl 



dp W 



T~ = — 



dT u 



if W represents the heat which is released with decrease of volume 

 when part of the middle phase is converted into the state of the 



