Closed system several phases

In many problems of thermodynamics we are concerned with both open and closed systems simultaneously. As an example we may consider a heterogenous system composed of several phases. The whole system is closed. However, we can consider each phase as a system, and these phases are open because material can be transferred from one phase to another. 

This equation, combining the first and second laws, is derived for the special case of a reversible process. However, it contains only properties of the system. Properties depend on state alone, and not on the kind of process that produces the state. Therefore, Eq. (6.1) is not restricted in application to reversible processes. However, the restrictions placed on the nature of the system cannot be relaxed. Thus Eq. (6.1) applies to any process in a system of constant mass that results in a differential change from one equilibrium state to another. The system may consist of a single phase (a homogeneous system), or it may be made up of several phases (a heterogeneous system) it may be chemically inert, or it may undergo chemical reaction. The only requirements are that the system be closed and that the change occur between equilibrium states. 

When monomer vapor is introduced into the reaction system, some monomers will be adsorbed or sorbed by a porous substrate. The partition between vapor phase and sorbed phase is dependent on the adsorbing capability of a porous substrate. For instance, when a porous glass tube is used as a substrate, nearly 100% of the monomer fed into a closed system is adsorbed, and it is difficult to establish a steady-state flow of monomer vapor until the substrate is saturated with the monomer, which takes several hours at the flow rates generally used in plasma polymerization. 

It must be emphasized that the results derived above, like those obtained in 20b, et seq, are applicable only to closed systems, as stated in 20g. Such systems may be homogeneous or heterogeneous, and may consist of solid, liquid or gas, but the total mass must remain unchanged. It will be seen later that in some cases a system consists of several phases, and although the mass of the whole system is constant, changes may take place among the phases. In these circumstances the equations apply to the system as a whole but not to the individual phases. Since it has been postulated that the work done in a change in state is only work of expansion, equal to PdV, the second condition stated in 20g, that the system is always in equilibrium with the external pressure, must also be operative. 

At this point you might ask how S can achieve a maximum value if U and V are fixed, since the specification of any two intensive variables completely fi.xes the values of all others. The answer to this question was given in Chapter 4, where it was pointed out that the specification of two intensive variables fixes the values of all other state variables in the uniform equilibrium state of a single-component, single-phase system. Thus, the equilibrium criterion of Eq. 7.1-5 can be used for identifying the final equilibrium state in a closed, isolated system that is initially nonuniform, or in which several phases or components are present. 

We next consider a closed heterogeneous system of v phases and r components in which one chemical reaction is in progress. In a heterogeneous system, the reaction may have progressed to a different degree in the several phases so that there may be a different progress variable for each phase. For a closed system the change in mass of component i is due to the chemical reaction, and we may write... 

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