Line, equilibrium indifferent

If we express the state of a system in terms of intensive variables, then the representative points of a system in equilibrium form a continuum in w dimensions. The equilibrium indifferent states, or static indifferent states, will also be represented in this continuum but they must satisfy in addition, the further ( - 1) conditions of indifference (29.19). These ( - 1) relations among the w variables leave only one independent variable the static indifferent states of the system hence fall on a line, called the indifferent line. 

In the same way, for an indifferent state of a closed poly variant system, the temperature is sufficient to determine p and the composition of the phases, but not the masses of the individual phases. Furthermore, as we have seen, the law governing the variations hp and hT along an indifferent line, are of just the same form as the law which relates Sp and ST along the equilibrium states of a monovariant system. However, a profound difference is apparent between monovariant systems, and indifferent states of a pol3rvariant system when we consider the possibility of a closed system moving along the line of indifference. A closed mono variant system can clearly traverse its indifferent line, for this is simply its equilibrium line on the other hand, for a polyvariant closed system the ability to move along the indifferent line is exceptional as we shall now proceed to show. 

Comparison of (29.77) with (29.63) shows immediately the close similarity between the indifferent line of a polyvariant system, and the equilibrium line of a monovariant system. This similarity is perhaps less surprising when we remember that all equilibrium states of a monovariant system are indifferent states. Thus (29.63) can be regarded as a particular case of (29.77), for in this case, since w = l,... 

If the sub-system also is monovariant, then it is indifferent in all its states and the indifferent line of the sub-system is also its equilibrium line. It then follows from the theorem of 17 that the projection of the mono variant line of the parent system on the T,p) plane is coincident with the projection of the monovariant line of the sub-system. 

One kind of indifference occurs when we have specified too few property values to solve a problem for example, we give an (F-spedfication when we actually need an F"-specification (recall, T < T ). An example occurs when we specify T and P for a one-component vapor-liquid equilibrium system, but we need to determine the fraction of material in the vapor phase. This is an indifferent situation because, at the specified T and P, om system can be at any of an infinite number of points along the tie line between liquid and vapor. 

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