Physical and Chemical Behavior of Solids. 213 



Derivation of the Formula. — The derivation of the formula 

 by means of which the effect of unequal pressure on a sub- 

 stance is computed is based on the thermodynamical fact that 

 pressure acting on any phase increases the "activity" of that 

 phase, or its tendency to pass over into another phase ; in other 

 terms, pressure acting only on the solid phase increases its 

 vapor pressure and hence increases its solubility (in any par- 

 ticular solvent) and lowers its melting point. Into the steps in 

 the derivation of vhis formula it is unnecessary to enter here ;* 

 the final differential equation is : 



dT TV 



dP At£ y ] 



which expresses the lowering of melting point by unequal 

 pressure in terms of the absolute melting point (T), the 

 molecular volume (V s ) of the solid at the temperature and 

 pressure in question, and (AZZ) the molal heat of fusion unde 

 those conditions. The quantities V s and Tare always positive, 

 but All (as here used) is always negative; hence application 

 of excess pressure on the solid phase always lowers the melting 

 point, f 



If we compare the melting point depressions (dT t and dT 2 

 respectively) produced by the same excess pressure (dP) acting 

 on (1) the solid phase alone, (2) both phases ; that is, if w T e com- 

 bine equations III and I, we obtain the result^ 



*It is discussed in another paper: see J. Am. Cbem. Soc, xxxiv, 788- 

 802, 1912; Zs. anorg. Chem., lxvi, 361-79, 1912. 



fThis lowering is, of course, relative to the melting point when that 

 pressure which now acts on the liquid alone (the solid being subject to 

 pressure in excess of this) acts on both solid and liquid. In other terms : 

 if the melting point is denoted by T with subscripts and superscripts to 

 represent the pressure acting on the solid phase and liquid phase respect- 



p p 



ively, then T is always lower than T , the magnitude of this low- 



P+ A P P 



ering being dependent on the excess of pressure AP acting on the solid. 



p 

 Now T may be higher, or lower, than 2V (the ordinary melting point 



at atmospheric pressure), according as the volume change on melting is 



p 

 positive or negative ; consequently, in some cases, T niay be higher 



than T, 1 , but this will be only when AP is small compared to P, a contin- 

 gency which, we believe, does not affect the main considerations advanced 

 in this paper. Similar considerations apply, mutatis mutandis, to the 

 increase in solubility caused by unequal pressure. 



X For a proof of this equation (iu slightly different form) by other methods 

 see J. H. Poynting, Phil. Mag. (5), xii. 32. 1881 ; G. N. Lewis, Proc. Amer. 

 Acad.,xxxvi, 145, 1900; xliii, 268, 1907; or Zs. phys. Chem., xxxv, 346, 

 1900 ; lxi, 139, 1908. The result is stated by LeChatelier (Zs. phys. Chem., 

 ix, 335, 1892), who applies it to several problems of geological interest : cf. 

 the paragraphs which follow. 



