Surface phenomena related to the system

We consider a two-phase, multicomponent system in which there is one planar surface. The state of the system is defined by assigning values to the entropy and volume of the system, the area of the surface, and the mole numbers of the components. The differential of the energy of the system is 

The quantity y is usually called the surface tension for liquid-gas interfaces and the interfacial tension for liquid-liquid interfaces. We see from Equation (13.2) that y da is the differential quantity of work that must be done reversibly on the system to increase the area of the system by the differential amount da at constant entropy, volume, and mole numbers. 

Many relations between the surface tension or the area and other variables can be obtained by the application of the mathematical properties of 

Equations (13.3)—(13.6). Six of the more important relations are obtained by application of the conditions of exactness to Equations (13.5) and (13.6). These six are 

If we multiply Equations (13.8) and (13.11) by the temperature, we find that T(dy/dT)y a and T(8y/8T)P a give the differential quantity of heat absorbed by the system for a reversible differential increase in the area for the specified conditions of constant T, V, and n or constant T, P, and n, respectively. 

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