THERMODYNAMIC AL SYSTEM OF GIBBS 177 



difference of volume of quantities of the two phases which 

 contain the same amount (wi') of this component. The terms 

 relating to the entropy can be interpreted in a similar way. 

 Secondly, by (253) or (257) the differential coefficient 

 (dfjLi/dmi)t. p, m, is positive in both phases.* 



40. Konowalow's Laws. In the case in which the first phase 

 is Hquid and the second a gaseous phase, the coefficients of dp 

 in (275) and (276) are evidently positive. Then, when dt = 0, 

 we see that 



(1) From (275), dp has the same sign as (m/' — m/) dm/, and 



from (276), dp has the same sign as (m/' — m/) dmi". 

 Therefore dnii has the same sign as dmi". 



(2) Since dp has the same sign as (mi" — m/) dnii, dp and 



dmi have the same sign if 7ni" > m/, and opposite 

 signs if mi' < mi. 

 Thus we may draw the following conclusions : 



(1) When the composition of the liquid phase is changed, 



that of the vapor phase changes in the same sense. 



(2) If the proportion of Si is greater in the vapor than in 



the hquid phase, when the temperature remains con- 

 stant the pressure is increased by the addition of Si. 

 In the same way, it can easily be shown that when dp = 0, dt 

 and dmi have opposite signs when mi" > mi. Therefore we 

 have 



(3) If the proportion of ^Si is greater in the vapor than in 



the liquid phase, when the pressure remains constant 

 the temperature is decreased by the addition of Si. 



(4) If the proportion of Si is the same in the vapor as in 



the liquid phase, the pressure is a maximum or a 

 minimum at constant temperature, and the tempera- 

 ture a maximum or minimum at constant pressure 

 (See p. 113). 

 These rules, which are illustrated by the examples shown in 

 Figures 2 and 3, were first stated by D. Konowalow.f 



* It may be zero if the phase is at the limit of stability, 

 t Wied. Annalen, 14, 48 (1881). 



