Gibbs-Duhem equation

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The Gibbs-Duhem equation (according to Josiah Willard Gibbs and Pierre Duhem ) describes the relationship between the changes in the chemical potentials of the components in a thermodynamic system .


Here referred to

The Gibbs-Duhem equation is often used with isothermal and isobaric process management at the same time . Then follows:

In such a process, the sum of the products from the amount of substance of the individual components and the change in their chemical potential disappears


The Gibbs-Duhem equation is of great interest for thermodynamics because it shows that in a thermodynamic system not all intensive variables (variables such as temperature, pressure, chemical potential, which do not depend on the amount of a substance) are mutually variable .

If you take z. If, for example, the temperature and the pressure are variable, only the components can have independent chemical potentials. From this follows Gibbs' phase rule , which specifies the number of possible degrees of freedom for this system.


The Gibbs energy is a positively homogeneous function of the degree in the quantities of matter ; that is for each and : true . Therefore, Euler's homogeneity relation applies to the Gibbs energy:

Thus applies to the total differential

On the other hand, because of the definition of

By comparing the two expressions, the Gibbs-Duhem equation follows:

See also