The Algebra of State Functions
Juan H. Vera, Grażyna Wilczek-Vera, Claudio G. Olivera-Fuentes, Costas G. Panayiotou · 2024
Two important additional state functions are added to the internal energy U and enthalpy H already discussed. These are the Helmholtz A and the Gibbs G functions, defined as the difference of U and H with the product of the absolute temperature times the entropy, respectively. For an open system, the total differential of these state functions is expressed as the sum of the partial derivative with respect to their independent variables, times the differential of the independent variable. The all-important chemical potential of compound i in a mixture is defined as the partial derivative of the state function with respect to the number of moles of compound i , at constant values of the other independent variables. The fact that for state functions the order of differentiation with respect to two variables is immaterial is used to obtain Maxwell’s relations which are the stepping stone to relate thermodynamic functions with measurable properties. The presentation of other useful mathematical relations for partial derivatives completes the chapter.