Phase rule

The Gibbs phase rule (after Josiah Willard Gibbs 1876) notes that in thermodynamic equilibrium can not be arbitrarily many phases coexist side by side. Also can be determined with it at a certain point in the phase diagram the maximum possible degrees of freedom. For a physically homogeneous thermodynamic system ranging from two state variables for the determination of the equilibrium state.

The derivation of the Gibbs phase rule via the Gibbs Duhem equation shows that not all intensive variables are independently variable in a thermodynamic system.

Phase-locked to gases and liquids

For fluids, ie gases and liquids, they are:

• - Number of independent types of particles in the system (e.g., H2O, CO2)
• - Number of stages (different states of aggregation, or one or more components coexisting liquid phases (such as water and oil are immiscible, and form two -phase ) )
• - The number of degrees of freedom (here number of state variables that may be changed without changing the number of phases of the system change )

The number of the existing phase of N and P as a function f shown in the following table:

It follows, for example, for a one-component system (), which is present in two different states of aggregation (P) that there is exactly one remaining degree of freedom, ie, a coexistence line in the phase diagram. Exist simultaneously three phases ( for example, water liquid, gaseous and solid), there remains exactly one point in the phase diagram of the triple point, as no degree of freedom left (f = 0).

Furthermore, it follows that there can be at a location up to three coexisting phases in a single-component system, since (see chart, right in the triple point ); in a two-component four phases, etc..

Phase rule for solids

As for solids a (slight ) change in pressure due to the low gas pressure has no or very low impact, is the Gibbs phase rule in this case:

This simplification does not apply at higher pressures, such as those already present in the earth's crust. For the pressure and temperature determination in the geothermobarometry this is for the correct detection of the respective equilibrium paragenesis of great importance.