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These relationships are related to each other through the Gibbs-Duhem equation.
In a similar way, he also obtained what later came to be known as the "Gibbs-Duhem equation".
The Gibbs-Duhem equation can be derived by using this technique.
The Gibbs-Duhem equation is useful because it relates individual chemical potentials.
This yields, when applied only to the first term and using the Gibbs-Duhem equation,:
Deriving the Gibbs-Duhem equation from basic thermodynamic state equations is straightforward.
This equation is only applicable for binary systems that follow the equations of state and the Gibbs-Duhem equation.
In thermodynamics, the Gibbs-Duhem equation describes the relationship between changes in chemical potential for components in a thermodynamical system:
In chemical thermodynamics the term used for the chemical potential energy is chemical potential, and for chemical transformation an equation most often used is the Gibbs-Duhem equation.
Chemical potentials can be used to explain the slopes of lines on a phase diagram by using the Clapeyron equation, which in turn can be derived from the Gibbs-Duhem equation.
By normalizing the above equation by the extent of a system, such as the total number of moles, the Gibbs-Duhem equation provides a relationship between the intensive variables of the system.
Combining expressions for the Gibbs-Duhem equation in each phase and assuming systematic equilibrium (i.e. that the temperature and pressure is constant throughout the system), we recover the Gibbs' phase rule.