Gibbs–Duhem equation

The Gibbs -Duhem equation (after Josiah Willard Gibbs and Pierre Duhem ) describes the relationship between the changes of the chemical potentials of the components of a thermodynamic system:

Referred to this

• The amount of substance of a system component i
• The total differential of the chemical potential of the system component
• S is the entropy
• T is the absolute temperature
• V is the volume
• P the pressure.

The equation follows by comparing the total differential of the thermodynamic potential ( Gibbs free energy ),

With the total differential of

The Gibbs -Duhem equation is of great interest to the thermodynamics, as it demonstrates that in a thermodynamic system not all intensive variables ( variables that do not depend on the amount of a substance, such as temperature, pressure, density, etc. ) are variable independently. Assuming the temperature and pressure as variable, so only the components may have independent chemical potentials. It follows the Gibbs phase rule that specifies the number of possible degrees of freedom for this system.

Often, the Gibbs -Duhem equation for isothermal (), isobaric () litigation will be used. Then follows:

In such a process that is always disappears the sum of the products of the molar amount of each component and the change in its chemical potential.