REPRESENTATION BY ZETA FUNCTION 303 



stable system M{a) + M{b), i.e., into a mixture of the mixed 

 crystals M(a) and M{h). In this case no continuous series of 

 mixed crystals exists and consequently the two solid components 

 W and X are not miscible with each other in all proportions. 



9. Since vapors (gases) are miscible with one another in all 

 proportions their f-curve always has the form shown in Fig. 4. 



10. If we represent the entropy and volume of a phase by 

 Tj and V respectively, then we have in accordance with Gibbs the 

 following relations: 



d{^)p = -ndt, d(Ot = vdp, (9) 



for de = tdr] — pdv, and differentiation oi ^ = e — t-q -\- pv gives 



d^ = de — tdr] — 7]dt + pdv + vdp, 



whence 



d^ = vdp — -qdt. 



This means that the f of a phase decreases when the temperature 

 (at constant pressure) increases, and increases when the pressure 

 (at constant temperature) increases.* If we apply this to 

 every point of a f-curve in our diagrams we see that every 

 point of a f-curve sinks towards the a:-axis with increase of t. 

 As, however, all phases do not possess the same entropy and 

 consequently all f-points do not sink at the same rate, it 

 follows that with increase of temperature the ^-curve sinks, with 

 decrease of temperature it rises, its form changing at the same time. 

 If we represent the f-points of solid W and solid X by (W) and 

 (X) respectively, then they also will sink with rise of tem- 

 perature and rise with fall of temperature. Since the liquids 

 W and X have greater entropies (at a given temperature) than 

 the corresponding solid substances W and X, the points W and 

 X' sink with rise of temperature and rise with fall of tempera- 

 ture, but in each case at a faster rate than the corresponding 

 points (T^') and (X). 



* When the phases are closed and the components independent, 

 'Lfidm = 0. 



