4. Thermodynamic Equilibrium in Systems with Other Constraints

The four postulates enable to perform many equilibrium calculations, but they rely on isolated and isentropic (adiabatic) conditions. These conditions are not suitable in many circumstances to do calculations easily. This chapter shows how to derive energy-like potential functions that largely facilitate calculations in systems at constant pressure, constant temperature, or constant pressure and temperature. The respective potentials enthalpy, free energy, and the Gibbs potential are introduced by reformulating the problem of equilibrium within isenthalpic conditions. (The mathematical method of Legendre transformation is explained in the Appendix.) Using these energy-like potential functions, an overview of the equilibrium conditions in terms of extremum principles within different conditions is given, along with the formal relationships concerning the potential functions and their variables. The possibility of calculation of heat and volume work from these functions accompanying changes at different conditions is treated in detail. Based on the machinery of formal relations, the determination of entropy and the energy-like potential functions from measurable quantities such as compressibility, heat capacity, and the coefficient of thermal expansion is demonstrated. It is also shown in detail, how all thermodynamic quantities can be calculated from a particular fundamental equation. At the end of the chapter, a concise treatment of the equations of state of real gases, liquids, and solids is provided, along with a detailed explanation of using fugacity to calculate the chemical potential.