Fundamental Equations of Homogeneous Open Systems

In this section we shall generalize the equations obtained in Sec. 6-1 to include positive or negative changes in the mass of the system due to a transfer of mass between the system and its surroundings. A criterion for equilibrium for a homogeneous open system in which there are no chemical reactions is immediately obtainable from Eq. (6-6) in the form 

In the field of equilibrium states, the internal energy can be expressed as a function of the volume V, entropy S, and the number of moles of component i, ,( = 1,. . . , r), in the system, that is, 

The first two partial derivatives in Eq. (6-39) can be determined from the equations for closed systems, since the composition is held constant. For an infinitesimal reversible process in which no mass is transferred, we obtain from Eq. (6-18) 

In a similar manner, using the Helmholtz work function A and the Gibbs free energy F, two additional equations, analogous to Eqs. (6-42) and (6-46), are obtained. The four equations 

The symbol Pi was first used by Gibbs and called by him the chemical potential of component i. It can be seen from Eq. (6-52) and the definition of partial molal quantities [Eq. (2-5)] that Pi is the partial molal free energy /( and is an intensive property. 

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