( V09 ) 



the last equation for -—, we get finally : 

 d.v 



... (8) 



when for q -\- etc. is written Q, i. e. the total heat of melting. 



This formula, combined with (6), indicates therefore the direction 

 of the melting-point curve throughout its course. 



In the second place we could have derived the same expression 



from the general equation (4). As namely n„ == ii„' -{- RT lorn\, 



du. RT dloq c. I 1 • 1 



we ha\e — = — '- — , assumnig (i, to be mdependent ot .r, and 



dx dx 



hence: 



d log c. 



dT d.v 



dx Q 



d log r 

 Substitution of the above found value of — - — yields immediately 



dx 



(8). But now \vc have still to prove, that really the total heat Q is 

 represented by 



i2-x){x + a{\-x)) 

 .r-\-2a{l — x) 



This takes place in the following way. If a quantity dn of solid 

 substance passes into the liquid phase, the total quantity of heat 

 absorbed is evidently : 



da 



q dn -\- aX dn -j- (1 — x) X—-dn. 

 dn 



For q is the pure latent heat of melting, if only non -dissociated 

 molecules are formed. But of the dn mols. an amount adn is dis- 

 sociated ; the heat required is « dn . X. Finally the existing condition 

 of dissociation n of the 1 — x mols. will be changed by the addition 



da 

 of dn new mols., namely to an amount (1 — x)—dn. For (1 — x)a 



dissociated mols. become (1 — J^') (« + du). 



