Intensive variables surface quantities

We shall consider two kinds of boundary conditions which are compatible with stationarity. One of these is to prescribe each of the intensive variables such as temperature, a chemical potential everywhere at the boundary surface. These boundary values should be independent of time. However, it is not necessary to give these intensive quantities ever5where, when some part of the boundary is made of an adiabatic and impenetrable wall. As intermediate of the above two conditions, it is also possible to use the semipermeable membrane and to give, at the same time, some of variables at this portion of boundary. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

The other group of properties are the intensive properties these are characteristic of the substance (or substances) present, and are independent of its (or their) amount. Temperature and pressure are intensive properties, and so also are refractive index, viscosity, density, surface tension, etc. It is because pressure and temperature are intensive properties, independent of the quantity of matter in the system, that they are frequently used as variables to describe the thermodynamic state of the system. It is of interest to note that an extensive property may become an intensive property by specifying unit amount of the substance concerned. Thus, mass and volume are extensive, but density and specific volume, that is, the mass per unit volume and volume per unit mass, respectively, are intensive properties of the substance or system. Similarly, heat capacity is an extensive property, but specific heat is intensive. 

Therefore, we assume that energy and entropy are additive—each of them sums corresponding quantities of both phases taken as pure uniform bodies (i.e., we neglect surface energy or entropy on the phase contact). Memory is excluded because independent and dependent variables are taken in the same present instant. On the other hand, the pressure (2.109) and also temperature T (intensive quantities) are assumed to be the same in both phases (cf. discussion at the end of this Sect. 2.5). Using the deflnitions of free energies F for the whole system (2.12) and for both phases... 

Integral and differential thermodynamic relationships between the different excess quantities defined by Eq, (2) and the set of experimental variables (P, r,y,) or (T,nf) can be derived analogously to those for conventional bulk-phase thermodynamic properties [9], However, an additional intensive property called the surface potential (cf>, ca /g) is necessary to completely define the Gibbsian adsorbed phase. The surface potential can be calculated by using the relationship [9] ... 

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