The Influence of Temperature.—As has already been said, a ternary system existing in three phases possesses two degrees of freedom; and the state of the system is therefore dependent not only on the relative concentration of the components, but also on the temperature. As the temperature changes, therefore, the boundary curve of the heterogeneous system will also alter; and in order to represent this alteration we shall make use of the right prism, in which the temperature is measured upwards. In this way the boundary curve passes into a boundary surface (called a dineric surface), as shown in Fig. 86. In this figure the curve akb is the isothermal for the ternary system; the curve aKb shows the change in the binary system AB with the temperature, with
a critical point at K. This curve has the same meaning as those given in Chapter VI. The curve kK is a critical curve joining together the critical points of the different isothermals. In such a case as is shown in Fig. 86, there does not exist any real critical temperature for the ternary system, for as the temperature is raised, the amount of C in the "critical" solution becomes less and less, and at K only two components, A and B, are present. In the case, however, represented in Fig. 87, a real ternary critical point is found. In this figure ak′b is an isothermal, ak″ is the curve for the binary system, and K is the ternary critical point. All points outside the helmet-shaped boundary surface represent homogeneous ternary solutions, while all points within the surface belong to heterogeneous systems. Above the temperature of the point K, the three components are miscible in all proportions. An example of a ternary system yielding such a boundary surface is that consisting of phenol, water, and acetone.[[327]] In this case the critical temperature K is 92°, and the composition at this ternary critical point is—
| Water | 59 per cent. |
| Acetone | 12 ,, |
| Phenol | 29 ,, |
The difference between the two classes of systems just mentioned, is seen very clearly by a glance at the Figs. 88 and 89, which show the projection of the isothermals on the base of the prism. In Fig. 88, the projections yield paraboloid curves, the two branches of which are cut by one side of the triangle; and the critical point is represented by a point on
this side. In the second case (Fig. 89), however, the projections of the isothermals form ellipsoidal curves surrounding the supreme critical point, which now lies inside the triangle. At lower temperatures, these isothermal boundary curves are cut by a side of the triangle; at the critical temperature, k″, of the binary system AB, the boundary curve touches the side AB, while at still higher temperatures the boundary curve comes to lie entirely within the triangle. At any given temperature, therefore, between the critical point of the binary system (k″), and the supreme critical point of the ternary system (K), each pair of the three components are miscible with one another in all proportions; for the region of heterogeneous systems is now bounded by a closed curve lying entirely within the triangle. Outside this curve only homogeneous systems are found. Binary mixtures, therefore, represented by any point on one of the sides of the triangle must be homogeneous, for they all lie outside the boundary curve for heterogeneous states.
2. The three components can form two pairs of partially miscible liquids.
In the case of the three components water, alcohol, and succinic nitrile, water and alcohol are miscible in all proportions, but not so water and succinic nitrile, or alcohol and succinic nitrile.
