SURFACES OF DISCONTINUITY 591 



Now tdrj/dt is the ordinary heat capacity of the mass of the 

 fluid, and if the left hand side of the equation is not zero, the 

 specific heat will depend on s. 



The fact that extension of the surface of a liquid (all the other 

 variables remaining constant) involves cooling in most cases (as 

 is obvious since, in general, heat must be supplied to maintain 

 the temperature constant) can be seen very easily from mechan- 

 ical considerations. We can imagine the system of liquid and 

 vapor to be contained in a flexible but non-expanding enclosure 

 which will permit a change of extent of surface without altera- 

 tion in volume, etc. of the two individual phases. In enlarging 

 the surface some molecules must pass from the interior to the 

 surface; i.e., must travel through the molecular cushion against 

 the inward attracting field of force there. This involves an in- 

 crease of potential energy, and with no supply of energy from 

 without there must be a diminution of molecular kinetic energy, 

 which means a fall of temperature. 



The equation [593] or the form which we have given it above 

 can be written in another form involving the total surface 

 energy. Thus 



a(t, p,r) - t = <x{t, p,r) +t — 



Also, by the third equation of (22), we see that 



dxjt, V, s, r) dyjt, p, s, r) 



^s ^=^ ^s + ^(''P'^>' 



where on the left-hand side we suppose that Gibbs' "heat 

 function," x, is expressed in terms of the variables t, p, s, r. 

 Hence 



,, X . da(t, p, r) dxjt, P, s, r) 

 c{t,p,r)-t—^^—= ■' 



This will be found on careful examination to be equation 22 

 of Chapter XXI of Lewis and Randall's Thermodynamics. 

 The equation [594] of Gibbs can be obtained by similar 



