Monovariant system indifferent states

The name indifferent state seems to have had its origin in the fact that certain equilibrium states, even though completely defined by the temperature, pressure and composition of each phase, are indifferent to the mass of the phases present. Monovariant and invariant systems, which we have already seen to be indifferent, exhibit in all their equilibrium states this indifference to the masses of the phases For example, in the very simplest case of a monovariant system, a pure liquid in the presence of its vapour, we find just these properties. For at constant temperature, and hence at constant pressure, a closed system containing a pure substance can have an infinite range of equilibrium states which depend simply on the volume in which the system is confined. These equilibrium states differ only in the amounts of the two phases. 

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,... 

Similarity between Indifferent States and Monovariant Systems. 

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. 

For example, by bringing together the conditions of equilibrium and those of indifference, we can show that in a monovariant system with two external intensive variables (P and 7), all the equilibrium states are indifferent states. 

Consider cf>s phases which form an indifferent subsystem. The monovariant curves of all the parent systems containing these s phases in the same state, when projected on the (T, p) plane, have a common tangent at the point corresponding to this state. 

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. 

---