Phase rule and phase diagrams in the presence of fields

Abstract

The phase rule in the presence of fields is formulated using two fundamental sets of variables. The first set, which relates to properties and contents of the system, comprises field-independent variables that persist in the absence as well as in the presence of fields. The second set consists of field variables, existing exclusively owing to the sources of the fields. Using the field-dependent differential, it is shown, that the degrees of freedom, in the context of the phase rule, increase by the number of variables of the second set. If each field is represented by a single vector, then the degrees of freedom increase by exactly the number of the fields present. Intensive field-dependent variables, that are defined as partial derivatives of the field-dependent energy with respect to their field-independent extensive conjugates, have the same thermodynamic role as the conventional intensive variables. These field-dependent variables can be used to plot field-dependent phase diagrams that are characterized by the extra degrees of freedom due to the presence of the fields.