In thermodynamics, the Gibbs–Duhem equation describes the relationship between changes in chemical potential for components in a thermodynamic system:...

The Duhem–Margules equation, named for Pierre Duhem and Max Margules, is a thermodynamic statement of the relationship between the two components of a...

G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i}}.} Gibbs also obtained what later came to be known as the "Gibbs–Duhem equation". In an electrochemical reaction characterized...

scientists, Duhem is best known today for his work on chemical thermodynamics, and in particular for the Gibbs–Duhem and Duhem–Margules equations. His approach...

The Gibbs adsorption isotherm for multicomponent systems is an equation used to relate the changes in concentration of a component in contact with a surface...

named after Willard Gibbs and Pierre Duhem. There are many relationships that follow mathematically from the above basic equations. See Exact differential...

concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions. Effects...

state Gibbs's thermodynamic surface Gibbs vector Gibbs–Appell equation of motion Gibbs–Donnan effect Gibbs–Duhem equation Gibbs–Helmholtz equation Gibbs–Marangoni...

systems, that obey the equations of state and the Gibbs–Duhem equations. To derive Darken's second equation the gradient in Gibb's chemical potential is...

In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol G {\displaystyle G} ) is a thermodynamic potential that can...

on a phase diagram by using the Clapeyron equation, which in turn can be derived from the Gibbs–Duhem equation. They are used to explain colligative properties...

This yields, when applied only to the first term and using the Gibbs–Duhem equation,: { ln ⁡   γ 1 = [ A 12 + 2 ( A 21 − A 12 ) x 1 ] x 2 2 ln ⁡   γ...

solvent. These relationships are related to each other through the Gibbs–Duhem equation. Note that in general activity coefficients are dimensionless. In...

\mu _{\alpha }=\mathrm {d} \mu _{\beta }.} One may therefore use the Gibbs–Duhem relation d μ = M ( − s d T + v d P ) {\displaystyle \mathrm {d} \mu =M(-s\...

chemical potential energy is chemical potential, and sometimes the Gibbs-Duhem equation is used. In most cases of interest in chemical thermodynamics there...

between the molecules are indifferent. It can be shown using the Gibbs–Duhem equation that if Raoult's law holds over the entire concentration range x...

form a system of two equations in two unknowns. Partial derivatives appear in thermodynamic equations like Gibbs-Duhem equation, in quantum mechanics...

Antoine equation Bejan number Bowen ratio Bridgman's equations Clausius–Clapeyron relation Departure functions Duhem–Margules equation Ehrenfest equations Gibbs–Helmholtz...

\mathrm {d} H=+V\mathrm {d} p+T\mathrm {d} S+\mu \mathrm {d} N} The Gibbs–Duhem equation can be derived by using this technique. Notice though that the final...

related to Gibbs phase rule, that is, the number of independent variables depends on the number of substances and phases in the system. An equation used to...

maint: multiple names: authors list (link) Gibbs, Willard (1993). The Scientific Papers of J. Willard Gibbs, Volume One: Thermodynamics. Ox Bow Press....

for the chemical potential μ {\displaystyle \mu } and then use the Gibbs–Duhem equation to express p {\displaystyle p} as a function of ρ {\displaystyle...

difference) coefficients are equal. For many kinetic systems, like the Boltzmann equation or chemical kinetics, the Onsager relations are closely connected to the...

fraction of X in the solution), It is a mathematical consequence of the Gibbs–Duhem equation that at that point, the vapor above the solution will have the same...

during the end of the 19th century by Wilhelm Ostwald, Georg Helm and Pierre Duhem. It was also promoted by physicist Ernst Mach who opposed atomic theory...

also awarded a Gold Medal from the American Society for Metals. Gibbs-Duhem equation#Ternary and multicomponent solutions and mixtures ("Lawrence Stamper...

Boltzmann Bridgman Carathéodory Carnot Clapeyron Clausius de Donder Duhem Gibbs von Helmholtz Joule Kelvin Lewis Massieu Maxwell von Mayer Nernst Onsager...

This is a list of scientific equations named after people (eponymous equations). Contents A B C D E F G H I J K L M N O P R S T V W Y Z See also References...

The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior...

S_{\mathsf {system}}} Via additional steps this expression becomes the equation of Gibbs free energy change Δ G {\textstyle \Delta G} for reactants and products...