State functions and independent variables

The properties whose values at each instant depend only on the state of the system at that instant, and not on the past or future history of the system, are called state functions (or state variables or state parameters). There may be other system properties that we consider to be irrelevant to the state, such as the shape of the system, and these are not state functions. 

Various conditions determine what states of a system are physically possible. If a uniform phase has an equation of state, property values must be consistent with this equation. The system may have certain built-in or externally-imposed conditions or constraints that keep some properties from changing with time. For instance, a closed system has constant mass a system with a rigid boundary has constant volume. We may know about other conditions that affect the properties during the time the system is under observation. 

We can define the state of the system with the values of a certain minimum number of state functions which we treat as the independent variables. Once we have selected a set of independent variables, consistent with the physical nature of the system and any conditions or constraints, we can treat all other state functions as dependent variables whose values depend on the independent variables. 

Whenever we adjust the independent variables to particular values, every other state function is a dependent variable that can have only one definite, reproducible value. For example, in a single-phase system of a pure substance with T, p, and n as the independent variables, the volume is determined by an equation of state in terms of T, p, and n the mass is equal to nM the molar volume is given by Fm = F/n and the density is given by p = nM/V. 

---