The Equilibrium State

This chapter deals with homogeneity, Legendre transforms—leading to the Helmholtz and Gibbs energies and the concept of enthalpy—followed by Maxwell relations and minimum principles and establishing the framework that is needed for the theoretical analysis of thermodynamic systems in equilibrium. A thermodynamic system in equilibrium is homogeneous, meaning that its intensive properties do not vary from point to point inside the system. This property leads to an Euler’s relationship between its extensive variables and the Gibbs-Duhem equation. This equation found, simultaneously, by Josiah Willard Gibbs and Pierre Maurice Marie Duhem enables a Lagrangian description of thermodynamic systems, of crucial importance in the analysis of open systems in non-equilibrium states. Minimum principles state that when a restriction that prevents a system from reaching equilibrium is removed, this system will attain an equilibrium state given by the minimization of one of its energies—internal, Helmholtz, Gibbs, or enthalpy—in accordance with the thermodynamic variables that are maintained constant during the equilibration process.