A Comprehensive View of the State Functions Including Maxwell Relations

Abstract

The fundamental state functions have certain general, mathematically expressed characteristics, e.g. the Schwarz theorem, i.e. that the order of derivation for second derivatives of the state functions is unimportant. The Maxwell relations are based on the Schwarz theorem. The 12 Maxwell relations is an important toolbox which can be used to solve thermodynamic problems. The full differentials of the state function can all be derived from the fundamental expression for internal energy based on the first and second laws of thermodynamics and the definitions of the state function (enthalpy, Gibbs free energy and Helmholtz free energy).