508 RICE 



ART. L 



phase from or to its environment by reason of a simple volume 

 change in the phase. Now it is to be observed that equation 

 [500] opens up the possibility of giving a mechanical significance 

 to a, despite the purely formal introduction of it in [493] or 

 [497]. It is well known that if a non-rigid membrane or a liquid 

 film, such as a soap bubble, separates two regions in which 

 there exist two different pressures p' and p" then there exists a 

 surface tension T uniform in all directions in the membrane or 

 film, and moreover 



V' - v" = T{c, + C2) , 



where ci and c^ are the principal curvatures at any point of the 

 membrane or film. The exact agreement of the form of this 

 equation with [500] suggests a plausible mechanical interpreta- 

 tion for (7 as a "superficial" or "surface" or "interfacial" tension. 

 Actually in a converse fashion T, which is introduced as a tension 

 in the membrane, can easily be given an interpretation in terms 

 of energy. If the membrane, for instance, encloses a gas at 

 pressure p' which receives (reversibly) an elementary amount of 

 heat and expands by an amount bv, the increase of energy of the 

 system, gas and membrane, is 



t b-q — p"bv , 



where p" is the external pressure, since p"bv is the amount of 

 energy transferred by mechanical work from the internal gas- 

 membrane system to the external gas system. Now, since 



p" = p' - T{c, + C2) , 



it can be proved (the proof is a familiar one and will be found 

 in the standard texts, being just a reversal of the steps in Gibbs' 

 treatment between [499] and [500]) that 



p"bv = p'8v - Tbs, 



where s is the area of the whole membrane; and thus the increase 

 of energy of the system, gas and membrane, is 



tbri - p'bv + Tbs. 



