588 JV. L. Bowen — Melting Phenomena of the 



Allen for the melting point of anorthite (1532°) and the extra- 

 polated value, 1220°, for albite, and with reasonable simplify- 

 ing assumptions concerning the latent heats was able to show* 

 that there should be large melting intervals. 



For the case of complete solid solution of the type exhibited 

 by the feldspars, we may derive equations expressing the rela- 

 tions between the composition of the liquid and solid in equi- 

 librium at any temperature in the following manner. If both 

 the liquid solutions and the solid solutions are perfect physical 

 solutions, i. e., if there is no heat effect or volume change on 

 mixing, then Raoult's law of vapor pressure lowering, and the 

 Clausius equation for the change of vapor pressure with tem- 

 perature, should apply to both components in both phases. 



Raoult's law may be written in the following manner : 



P = l\ i 1 - ») 

 where^? = vapor pressure of the pure solvent at any tempera- 

 ture, and p = partial vapor pressure of the solvent at the same 

 temperature, from a solution in which the mol fraction of sol- 

 vent is (1 — x). 



The Clausius equation in its most general form is written 



dp _ I 



dT~ (v ± -vjT 



where dp is the change of vapor pressure of liquid (or solid) 

 corresponding with a change of temperature clT at absolute 

 temperature T, I = latent heat of vaporization of one gram 

 of the liquid (or solid) at T, v t = the volume of one gram of 

 the gas at T, and v 2 = the volume of one gram of liquid (or 

 solid) at T. 



By assuming that the gas laws apply to the vapor and that 

 the volume of the liquid (or solid) is negligible compared with 

 that of the gas, then the equation may be written in a form 

 easily integrated. 



d log p _ L 

 dT ~^BT T 

 where L is the latent heat of vaporization of one mol. of the 

 liquid (or solid) and R the gas constant. By assuming that L 

 remains constant over the temperature range under considera- 

 tion, we may integrate between the temperature limits T l and 

 T^ when the equation becomes 



In 



p Tl L I 1 



-jr). 



Pt ,-x\t 2 tj 



This, written in the exponential form, is the equation used 

 in the present instance. Its complete derivation is given in 

 order that the fundamental assumptions involved may be clear. 



* Zs. phys. Chemie, lv, 4, p. 435. 



