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# Gibbs phase rule

Gibbs' phase rule (formulated by the American physical chemist Josiah Willard Gibbs) specifies the number of degrees of freedom for a given system at equilibrium. In thermodynamics the number of degrees of freedom is the smallest number of intensive variables (i.e. pressure, temperature, and concentrations of components in each phase) that must be specified to completely describe the state of the system.

Gibbs' phase rule can be expressed as:

F = c - p + 2

where, F is the number of degrees of freedom, c is the number of components in the system, and p is the number of phases in the system.

Gibbs' phase rule implies that the number of degrees of freedom increases as the number of components in the system increases and decreases as the number of phases increases. For example the phase rule indicates that a single component system with only one phase, such as liquid water, has 2 degrees of freedom. For this case the degrees of freedom correspond to temperature and pressure, indicating that the system can exist in equilibrium for any arbitrary combination of temperature and pressure. However, if we allow the formation of a gas phase, there is only 1 degree of freedom. This means that at a given temperature, water in the gas phase will evaporate or condense until the corresponding equilibrium water vapor pressure is reached. It is no longer possible to arbitrarily fix both the temperature and the pressure, since the system will tend to move toward the equilibrium vapor pressure. For a single component with three phases (gas, liquid, and solid) there are no degrees of freedom. Such a system is only possible at the temperature and pressure corresponding to the Triple point. At other conditions one of phases will evaporate, condense, melt or freeze.

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