## Unary Diagrams

Invariant Equilibrium. According to the phase rule, three phases can exist in stable equilibrium only at a single point on a unary diagram (/ = 1 -3 + 2 = 0). This limitation is illustrated as point O in the hypothetical unary pressure-temperature (PT) diagram shown in Fig. 2. In this diagram, the three states (or phases)—solid, liquid, and gas— are represented by the three correspondingly la-

Fig. 2 Schematic pressure-temperature phase diagram

beled fields. Stable equilibrium between any two phases occurs along their mutual boundary, and invariant equilibrium among all three phases occurs at the so-called triple point, O, where the three boundaries intersect. This point also is called an invariant point because, at that location on the diagram, all externally controllable factors are fixed (no degrees of freedom). At this point, all three states (phases) are in equilibrium, but any changes in pressure and/or temperature wil I cause one or two of the states (phases) to disappear.

Univariant Equilibrium. The phase rule says that stable equilibrium between two phases in a unary system allows one degree of freedom (f= 1-2 + 2). This condition, called univariant equilibrium or monovariant equilibrium, is illustrated as lines 1, 2, and 3 separating the single-phase fields in Fig. 2. Either pressure or temperature may be freely selected, but not both. Once a pressure is selected, there is only one temperature that will satisfy equilibrium conditions, and conversely. The three curves that issue from the triple point are called triple curves: line 1, representing the reaction between the solid and the gas phases, is the sublimation curve-, line 2 is the melting curve; and line 3 is the vaporization curve. The vaporization curve ends at point 4, called a critical point, where the physical distinction between the liquid and gas phases disappears.

Bivariant Equilibrium. If both the pressure and temperature in a unary system are freely and arbitrarily selected, the situation corresponds to having two degrees of freedom, and the phase rule says that only one phase can exit in stable equilibrium (p = 1-2 + 2). This situation is called bivariant equilibrium.

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### Responses

• MERRY
What are the two lines in the unary phase diagram?
8 years ago