458 W. P. White — Melting Point Determination. 



Now the rate of absorption of heat by melting, that is, the 



portion of -=—- required for the melting, is proportional to the 

 d 



amount melted per unit rise in temperature ; that is, propor- 



d A d A. 



tional to -^- z , or, say, equal to m-—~ » where m is merely the 

 d d 



factor of proportion. But ——. — ^-, and since the integral 



d u 



d A K 



of m-^Q » that is, the integral of m—^- , from Q to oo , must 

 d u 6 



equal the latent heat, L, therefore mK is equal to L0 O . 

 Accordingly, if S is put for the true specific heat at any tem- 

 perature, the total virtual, or apparent, specific heat, 2, is 



2 = 8 + ^ (1) 



for temperatures below and not too far from O . Through 

 most of the interval where the equation can be used, S is rela- 

 tively so small as to be usually negligible and the function 

 may then be written simply, 



S=^ (2) 



The form of the resulting melting curve can now be obtained 



d Q 



by writing —z~ for 2 and integrating from Q to 0, giving 

 d u 



[Q] = (S + -£-)(*-*.) (3) 



from which Q can be obtained in terms of 0. If (2) instead 

 of (1) is used, 



Q = L ° whence 



w 



~ L-Q 



from which can be plotted in terms of Q. Here is still 

 measured downward from the true melting point, and Q is 

 really the amount of heat given out as the body freezes. But 

 of course this expression gives the form of the curve as well as 

 any, and is simpler than one with positive temperatures and 

 heat quantities would be. 



Such a curve is the smooth curve of fig. 3. The circles 

 mark a curve actually observed near 900° in a case where 

 all other sources of obliquity were practically eliminated. 



The recognition of the part played by impurity changes 

 radically the ordinary conception of melting point phenomena. 



