Gibbs–Helmholtz equation

The Gibbs–Helmholtz equation relates the temperature dependence of Gibbs free energy to enthalpy. At constant pressure, it is commonly written as ∂(G/T)/∂T = −H/T².

Gibbs free energy: A thermodynamic potential that determines the maximum non-expansion work available at constant temperature and pressure. The equation tracks how this potential changes with temperature.
Chemical equilibrium: A state in which forward and reverse reactions proceed at equal rates, leaving concentrations macroscopically constant. The equation helps relate equilibrium thermodynamics to temperature.
First law of thermodynamics: The principle that energy is conserved and can be transferred or transformed but not created or destroyed. It underlies the energy accounting that defines enthalpy.
Clausius–Clapeyron relation: A relation connecting the slope of a phase boundary to the enthalpy and volume changes of a transition. It links temperature and enthalpy too, but describes phase-boundary pressure.
Enthalpy: A thermodynamic state function equal to internal energy plus pressure–volume work. At constant pressure, it supplies the energy term in the equation.
Van ’t Hoff equation: A relation describing how an equilibrium constant varies with temperature through the reaction enthalpy. It is a closely related temperature-dependence relation for chemical equilibria.
Gibbs–Duhem equation: A thermodynamic relation constraining changes in chemical potentials, temperature, and pressure in a mixture. It illustrates how thermodynamic state variables are linked by differential identities.
Kirchhoff’s law of thermochemistry: A relation describing how a reaction’s enthalpy changes with temperature through heat-capacity differences. It concerns the temperature variation of enthalpy, not Gibbs energy.
Entropy: A thermodynamic state function that quantifies energy dispersal and the number of accessible microscopic arrangements. Its contribution to Gibbs energy makes the temperature derivative yield enthalpy.
Reaction enthalpy: The enthalpy change associated with a chemical reaction at specified conditions. Reaction enthalpy determines the temperature dependence of reaction Gibbs energy.

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Josiah Willard GibbsBroader topic: It connects Gibbs’s energy functions to measurable temperature variation.