HETEROGENEOUS EQUILIBRIUM 281 



H2O, the chemical potential of H2O in all three phases is the 

 same. If we simultaneously change the pressure and tem- 

 perature so as to proceed along any one of the three 'p-t curves 

 that intersect at the triple point, one of the phases will dis- 

 appear. By making these changes we have given greater incre- 

 ments to the chemical potential of the phase that disappears 

 than to the chemical potentials of the other two phases; the 

 chemical potential of water remains equal in these two phases 

 since we, by hypothesis, have made such changes of pressure 

 and temperature as to proceed along the -p-t curve of stable 

 coincidence of these phases. 



The fundamental equations of the form of (1) [97] for the three 

 phases that coexist at the triple point are 



Vdj) = Wdt + m\l^\ 

 V'dp = H'rfi + w'^m', 

 V'dp = R'dt + m'dij.% 



in which the indices v, I, s refer to the vapor, liquid, and solid 

 phases. Each of these equations may be divided by the mass m 

 of the phase; in the resulting equations 



v^dp = rj^dt -f- dn", 

 v^dp = rj^dt + djjL^, 

 v'dp = ri'dt + dn', 



the volume and entropy terms refer to the specific volume and 

 entropy of each phase. 



Now if, as stated above, we proceed along the p-t curve of 

 the condensed system, ice-liquid, which is one of the p-t curves 

 that intersect at the triple point, we can obtain a value for dn, 

 the differential of the chemical potential, from the two equations 

 of the type of (1) [97] referring to the liquid and solid phases, 

 by solving the two equations for dt in terms of dp, which will 

 give us 



yl _ y» 



dt = -j , dp, 



and substituting this value of dt in one of the original equations 



