The family of Gibbs-Helmholtz equations connect phase and chemical equilibrium with enthalpy and volume. This family of equations is one of the most useful yet unappreciated and poorly understood mathematical relations in chemical thermodynamics. This paper rigorously derives several variants of the Gibbs-Helmholtz equation that are applicable to chemical process technology, and evaluates their use for educational and industrial purposes. The focus of the contribution is the manner in which fundamental chemical thermodynamics contributes to the industrial practice of process technology. Some rigorous thermodynamic equations are more useful than others in particular applications of chemical process technology. The paper also studies the early historical development of the Gibbs-Helmholtz equation.