The Phase Rule | Thermodynamics - Mechanical Engineering PDF Download

The Phase Rule

Originally formulated by the American scientist Josiah Willard Gibbs in the 1870s, the phase rule determines the number of independent variables that must be specified to establish the intensive state of any system at equilibrium. The derivation of the general phase rule is shown in chapter 6, but here we state it without proof:

F = 2 + N −π−r                                          ..(1.10) 

Here, F = degrees of freedom of the thermodynamic system in question; N = Number of components; π = number of co-existing phases, ad r = number of independent reactions that may occur between the system components. For a non-reactive system, the phase rule simplifies to:

F = 2 +N−π                                                 ..(1.11) 

In the most general sense, a thermodynamic system may be multiphase and multicomponent in nature. A phase is a form of matter that is homogeneous in chemical composition and physical state. Typical phases are solids, liquids, and gases. For a multiphase system, interfaces typically demarcate the various phases, properties changing abruptly across such interfaces. Various phases can coexist, but they must be in equilibrium for the phase rule to apply. An example of a three-phase system at equilibrium is water at its triple point (~ 00C, and 0.0061 bar), with ice, water and steam co-existing. A system involving one pure substance is an example of a single-component system. On the other hand, the mixtures of water and acetone have two chemically independent components.  
 

The intensive state of a system at equilibrium is established when its temperature, pressure, and the compositions of all phases are fixed. These are, therefore, regarded as phase-rule variables; but they are not all independent. The degrees of freedom derivable from the phase rule gives the number of variables which must be specified to fix all other remaining phase-rule variables. Thus, F means the number of intensive properties (such as temperature or pressure), which are independent of other intensive variables. For example, for a pure component gaseous system, phase rule yields two degrees of freedom. This implies that if one specifies temperature and pressure, all other intensive properties are then uniquely determined these two variables. Similarly for a biphasic system of a pure component – say water and steam – there is only one degree of freedom, i.e., either temperature or pressure may be specified to fix all other intensive properties of the system. At the triple point the degrees of freedom is zero, i.e., any change from such a state causes at least one of the phases to disappear.