Reminder of Gibbs phase rule

Gibb s phase mle states that the variance of a system with p external intensive physical variables, containing c independent components and  

The number of independent components is the difference between the number of components in the system and the number of independent transformations - i.e. the dimension of the vector space of the balance equations. This number must be decreased by 1 in the case of the presence of ions, due to the electrical neutrality condition, and decreased by 1 in the case of the species belonging to a solid phase if the condition of conservation of the crystallographic sites is imposed. 

Remember that the variance is the number of free variables in the system, among the p external intensive physical variables and the molar fractions. This number gives us the maximum number of degrees of freedom of the system that maximum number of degrees of freedoms may be reduced by the imposition of specific constraints. Gibbs phase mle applies equally to open systems and closed systems, and pertains solely to the intensive variables. 

Duhem s phase rule enables us to define a Duhem variance, which applies only to closed systems and pertains to the external intensive variables, the composition variables and the quantities of matter. The goal is always to determine the number of free variables. 

As before, we suppose that the system contains Ncomponents in phases and is home to R independent transformations. The variation, over an arbitrary length of time, of the quantity of one of the components kina. phase in the system will be given as a function of the reactional extents of the different transformations by  

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