The rule F = C − P + 2 giving the number of degrees of freedom F at equilibrium from the number of components C and the number of phases P. For condensed systems at constant pressure, F = C − P + 1 is used.
Japanese name: ギブスの相律
Gibbs phase rule appears in 1 practice question across 1 topic, including Phase diagrams and the lever rule.
The number of degrees of freedom F is the number of intensive variables (temperature, pressure and the composition of each phase) that can be changed independently while equilibrium is maintained. With P phases and C components, fixing the composition of each phase takes C − 1 variables, giving P(C − 1) in all, plus the two variables temperature and pressure. In equilibrium, on the other hand, the chemical potential of each component must be equal in every phase, which imposes C(P − 1) conditions. Subtracting the number of conditions from the number of variables gives F = C − P + 2. The amounts of the phases are not counted as degrees of freedom.
For one component (C = 1), F = 3 − P. With only one phase, ice, water or vapor, F = 2, an area of the diagram where temperature and pressure can be varied independently. When two phases coexist, F = 1, a line (the melting curve or vapor-pressure curve) on which fixing the temperature also fixes the pressure. The triple point, where three phases coexist, has F = 0 and is fixed at a single point, 0.01 °C and about 611 Pa for water. The phase rule also shows at once that four phases cannot coexist in equilibrium in a one-component system.
Phase diagrams of metals and ceramics are usually drawn at constant (atmospheric) pressure, and F = C − P + 1, which drops the pressure variable, is used. In a binary system (C = 2), single-phase regions have F = 2 and two-phase regions F = 1; once the temperature is fixed, the compositions of the phases are fixed at the ends of the tie line, and their proportions are found with the lever rule. When three phases coexist, F = 0, and reactions such as eutectic, eutectoid and peritectic reactions appear as horizontal lines at a fixed temperature. In ternary systems, points where four phases coexist at constant pressure are the invariant points.
The phase rule counts phases, not names of microconstituents. Pearlite is a microconstituent made of two phases, ferrite and cementite, not a single phase. The rule also applies to equilibrium states and does not apply to non-equilibrium microstructures such as martensite formed by quenching. The components may be chosen as convenient units, as in the Fe–Fe₃C system. The rule is useful for checking that a phase diagram you have drawn or a cooling curve you have measured does not contradict it, and for identifying how many phases coexist during a temperature arrest.
Answer: A. 0
Gibbs' phase rule is F = C − P + 2, but for condensed systems at constant pressure we use F = C − P + 1. At the eutectic point of a binary system (C = 2), three phases, liquid L, α and β, coexist (P = 3), so F = 2 − 3 + 1 = 0: an invariant point at which the temperature and the composition of every phase are fixed. That is why an alloy of eutectic composition solidifies at a single temperature and its cooling curve shows a thermal arrest. One results from applying F = C − P + 2, which includes pressure as a variable, to a constant-pressure phase diagram. Two is the number of degrees of freedom in a single-phase region (P = 1), where temperature and composition can be varied independently.
They count the intensive variables, such as temperature, pressure and the composition of each phase, that can be changed independently while equilibrium is maintained. The amounts of the phases and the size of the sample are not included. A point with zero degrees of freedom is an invariant point where both temperature and compositions are fixed.
Use +2 when pressure is also treated as a variable, and +1 for condensed systems in which pressure is regarded as constant, such as phase diagrams of metals and oxides. In systems of only solids and liquids, pressure has little effect, so +1 is normally used.
At constant pressure, only at the specific combinations of temperature and composition where the degrees of freedom become zero. Eutectic, eutectoid and peritectic points are examples, and the cooling curve shows a temperature arrest at that temperature until the reaction is complete.
Gibbs' phase rule is F = C − P + 2, but for condensed systems at constant pressure we use F = C − P + 1.
At constant pressure, how many degrees of freedom are there…