State of Single Homogeneous Phases

We distinguish between intensive state and extensive state. The intensive state can be identified solely in terms of intensive properties, and therefore it does not involve amounts of material. In contrast, identification of an extensive state must include a value for at least one extensive property, usually either the total amount of material or the total volume. Often only intensive states are needed to perform process analyses, while extensive states are usually needed to perform process designs. 

To change a thermodynamic state, we stand in the surroundings and apply interactions that cross the boundary. So we would like to know the number of orthogonal interactions that are available for changing the extensive state. 

For a mixture of C components, there are C independent mole numbers, each of which could be manipulated through its own interaction. In addition, most systems of interest have the thermal interaction plus a work interaction that can change the system s volume. Therefore, in most cases the maximum number of orthogonal interactions will be given by 

If other orthogonal work modes are present, such as electrical or surface work, then the number on the rhs of (3.1.2) would increase accordingly. 

The value given by (3.1.2) represents the maximum number of orthogonal interactions. However, the actual number will be less when external constraints are imposed. An external constraint blocks or controls an interaction so that it is not available for manipulating the system. For example, we might insulate the system to block the thermal interaction. Let Sgxt count the number of external constraints imposed on interactions. Then, to manipulate the state, we would have 

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