590 RICE ART. L 



This is equation [593] ; the left-hand side is the rate of change of 

 entropy with increase of surface, while t, p and the composition 

 of the masses are unchanged (this is the condition stated in 

 the paragraph preceding [593] in Gibbs), and so is equal to 

 Q/t. In the right hand side the variables p, n, r^, ... are kept 

 unchanged in the differentiation; in Gibbs' case no ratios occur 

 in the variables on which a depends, since he is dealing with two 

 components only and there would only be one ratio r, and even 

 this does not appear since we have just stated in the footnote 

 that in general <r depends on only n — 2 of the n — 1 ratios 

 ri, r2, ... as well as t and p. Indeed c depends only on n 

 variables; for we know it can be expressed as a function of 

 /, m, y.i, ... nn in general, but the assumption of the equality of 

 pressures in the two phases reduces the number of variables to n. 

 The addition of Q to cr gives the total energy acquired by the 

 surface when extended one unit of area if the temperature, 

 pressure and composition of the phases remain unchanged. 

 This quantity 



<r(f, p, r) - « -^ . 



is sometimes called the total surface energy, a being called the 

 free surface energy. With the exception of a few molten metals, 

 liquids exhibit a decreasing surface tension with rising tem- 

 perature, and so as a rule total surface energy is greater than free 

 surface energy. In many liquids the relation between a and t 

 is linear, so that the total surface energy does not vary with 

 temperature. Actually, if the variation is not zero, we can easily 

 see that the ordinary specific heat of a liquid will vary with the 

 extent of surface offered by a definite mass of it which will 

 change with a change of form in the mass. For 



^ d^vjt, p, s, r) ^ d dr}{t, p, s, r) 

 dt ds ds dt 



* For brevity let r stand for the series n, u, ... r»_i. 



