[GGQ/TH-09002] Equation of State and Fundamental Relation

 Equations of state are generally much easier to establish than fundamental equations. However, in contrast to a fundamental equation, an equation of state does not contain complete information on the thermodynamic system. This follows from the fact that the intensive variables are (partial) derivatives of the extensive ones. The differentiation results in a loss of information. Nevertheless, the totality (i.e., the complete set) of the equations of state is equivalent to the fundamental equation. To recover the latter it is only necessary to insert all the state equations into the Euler equation from which were derived (cf. §§ 12.3 and 13.8). Since we thus regain the complete information on the system, this is tantamount to an integration. The Euler equation in either representation is therefore a form of the fundamental equation.
 
 \paragraph*{\fbox{REF}:} Nicholas W. Tschoegl, in Fundamentals of Equilibrium and Steady-State Thermodynamics, 2000