The planar interface of macroscopic phases
Using the relation F = U – TS and the definitions given above, we obtain
The absolute temperature T is assumed constant in all parts of the system.
Determination of surface tension. Let the area of the boundary A (Fig. 21.1 a) increase by a value dA by means of a reversible isothermal displacement of the side walls of the vessel. If the system is in hydrostatic equilibrium at a pressure P, the work done by it in the described process can be divided into two parts: the work PdV spent on increasing the volume dV, and the excess work associated with the increase in the area of the boundary by dA, which we denote –σdA. Then the total work done by the system in this process is PdVσdA. Now let’s shift the upper and lower covers of the vessel so that we return the system to its original volume. The work done by the system in this process is –PdV. At the end of these two processes, the system will have the same pressure, composition and temperature as it originally had.