Gibbs-Helmholtz equation

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The Gibbs-Helmholtz equation is a thermodynamic relationship useful for calculating changes in the energy or enthalpy (heat content) of a system. It is named after Josiah Willard Gibbs and Hermann von Helmholtz. Two useful general forms of this equation are:

\Delta A - \Delta U = T \left( \frac{\delta\left(\Delta A \right)}{\delta T} \right)_V
\Delta G - \Delta H = T \left( \frac{\delta \left( \Delta G\right)}{\delta T} \right)_P

Where A is the Helmholtz free energy, U is the internal energy of the system, T is the absolute temperature, V is the volume, P is the pressure, G is the Gibbs free energy and H is the heat content(enthalpy) of the system.

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