Single-component systems natural variables

The state of thermodynamic equilibrium of a single component system can be characterized by two independent variables, for example, the entropy and the volume. For natural processes, it can be written ... 

To complete our thermodynamic description of pure component systems, it is therefore necessary that we (1) develop an additional balance equation for a state variable and (2) incorporate into our description the unidirectional character of natural processes. In Sec. 4.1 we show that both these objectives can be accomplished by introducing a single new thermodynamic function, the entropy. The remaining sections of this chapter are concerned with illustrating the properties and utility of this new variable and its balance equation. 

The starting point for the present analysis is the observation in Sec. 8.1 that the equilibrium thennodynamic state of a single-phase C-component system can be fixed by specifying the values of two intensive variables and C — 1 mole fractions. Alternatively. the specification of any C -t- 1 independent state variables could be u.sed to fix the state of this system.- Thus, we can say that a C-component, single-phase system has C -1- 1 degrees of freedom, that is, we are free to adjust C + 1 independent intensive thermodynamic properties of this system however, once this is done, all the other intensive thennodynamic properties are fixed. This is equivalent to saying that if T, P, x 1,. V2,..., xc-1 are taken as the independent variables, there exist equations of state in nature of the form... 

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