150 BUTLER 



ART. D 



value of niiMi + ^2^2 for any given values of Wi and rrh (for 

 which mi -\- nii = 1) is therefore represented by the point on the 

 line CD corresponding to these values. The expression 



f - Mimi - ilf 2W2 (203) 



is positive for every other phase of the components, other than 

 the one under consideration, when there is no phase for which 

 the value of f , at the same temperature and pressure, lies below 

 the line CD. Thus if the two components form a solid com- 

 pound, of which the composition and value of f are represented 

 by the point P (under CD), the phase E will be unstable 

 (supersaturated) with respect to this phase, for f — MiMi — M^rUi 

 is negative for the phase P. But if the point representing 

 this phase is above CD (say at P'), T ~ Mini], — 71^2^2 will be 

 positive, and the phase E will be stable in respect to the forma- 

 tion of this phase. Similarly if the curve AB is everywhere 

 above the tangent CD, except at the single point of contact, 

 the phase E is stable with respect to the other homogeneous 

 phases, and cannot split into any of the phases represented 

 by the points of this curve. 



28. Condition of Stability Referred to the Pressure of Phases for 

 Which the Temperature and Potentials Are the Same as Those of 

 the Phase in Question. In the expression 



e - Tj] + Pv - Mmi - M2W2 - . . . (204) 



T, P, Ml, M2, etc. are the temperature, pressure and potentials 

 in the fluid mass the stability of which is in question, and e, 17, 

 V, mi, W2, etc. are the energy, entropy, volume, etc. of a given 

 phase with regard to which the stability is being tested. These 

 quantities are related by the equation 



e = tri — pv -\- iiimi H- /X2W2 + . • • , (205) 



where t is the temperature, p the pressure and in, /X2, etc., the 

 potentials in the given phase. If we consider only phases for 



nil + VI2 = 1, d7ni = —dm2, the slope of the tangent is given by 

 d^ — it^i ~ iMi)dm.2. Since ZE = nimi + M2W2, XC = mi'^i + M2W2 

 — (ixi — ni)mi = )ui. Similarly YD = juj. 



