Question

Define free energy and derive gibbs hamilton's equation

Answer 1

The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs energy of a system as a function of temperature. It is named after Josiah Willard Gibbs and Hermann von Helmholtz.

Equation

The equation is:[1]

{\displaystyle \left({\frac {\partial ({\frac {G}{T}})}{\partial T}}\right)_{p}=-{\frac {H}{T^{2}}},} {\displaystyle \left({\frac {\partial ({\frac {G}{T}})}{\partial T}}\right)_{p}=-{\frac {H}{T^{2}}},}

where H is the enthalpy, T the absolute temperature and G the Gibbs free energy of the system, all at constant pressure p. The equation states that the change in the G/T ratio at constant pressure as a result of an infinitesimally small change in temperature is a factor H/T2.

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