Gibbs s theorem

Gibbsitic [14762-49-3] Gibbs-Kelvin equation Gibbs phase rule Gibbs s phase rule Gibbs s theorem Gibbs-Thomson equation... 

There is a lid, of area A, which can be slid along the surface so as to cover the surface of either I or II completely, or both partially. This lid is made of material such that the interfacial tensions of the two solutions against it are equal, and the composition of each solution remains constant right up to contact with it i.e. there is no adsorption of any of the components of the solutions, a condition which really follows from the first, by Gibbs s theorem. 

An ideal gas is a model gas comprised of imaginary molecules of zero volu that do not interact. Each chemical species in an ideal-gas mixture therefore its own private properties, uninfluenced by the presence of other species. This the basis of Gibbs s theorem ... 

An ideal gas (Sec. i. is a irrodel gas comprised of iirragiirary irrolecules of zero volume that do irot iirteract. Thus, propertiesfor each chemical species are iirdepeirdeirt of the preseirce of other species, and each species has its own set of private properties. This is the basis for the following statement of Gibbs s theorem. ... 

Gas, cells, 464, 477, 511 characteristic equation, 131, 239 constant, 133, 134 density, 133 entropy, 149 equilibrium, 324, 353, 355, 497 free energy, 151 ideal, 135, 139, 145 inert, 326 kinetic theory 515 mixtures, 263, 325 molecular weight, 157 potential, 151 temperature, 140 velocity of sound in, 146 Generalised co-ordinates, 107 Gibbs s adsorption formula, 436 criteria of equilibrium and stability, 93, 101 dissociation formula, 340, 499 Helmholtz equation, 456, 460, 476 Kono-walow rule, 384, 416 model, 240 paradox, 274 phase rule, 169, 388 theorem, 220. Graetz vapour-pressure equation, 191... 

Clausius great paper of 1850 can be recognized as a landmark in the development of thermodynamics. As remarked by Thomson in 1851, the merit of first establishing [Carnot s theorem] upon correct principles is entirely due to Clausius. In his 1889 eulogy of Clausius, Gibbs praised the 1850 paper in the following terms ... 

The last member of Equation (2) shows that n, is the partial molar quantity associated with the Gibbs free energy, G. Euler s theorem gives then... 

As the Gibbs energy is a first-order homogenous function of the extensive variables A7 and n. the application of Euler s theorem yields... 

Gibbs s adsorption theorem (Chap. HI, eq. (7)) shows that the solubility of the substance in a surface film, in equilibrium with the interior, should increase according to the equation... 

Spear F. S. (1988) The Gibbs method and Duhem s theorem the quantitative relationships among P, T, chemical potential, phase composition and reaction progress in igneous and metamorphic systems. Contrib. Mineral. Petrol 99, 249-256. 

Since Zi is homogeneous in the zeroth degree in ni, n2,..., etc., Euler s theorem (Chapter 2) gives the Gibbs-Duhem equation ... 

Euler s theorem for the intensive Gibbs free energy of mixing of an r-component mixture is expressed in terms of activities and activity coefficients as follows ... 

Duhem s theorem is applied to closed systems at equilibrium, when both intensive and extensive parameters are known, i.e., for systems of totally defined state. Both extensive and intensive parameters may be independent. However, their interrelation is defined by Gibbs phase rule. At C = 0 both parameters must be extensive, and at C = 1 at least one of them must be extensive. 

We start in 9.1 by giving prescriptions for determining the number of properties needed to identify the thermodynamic state in multicomponent mixtures. Those prescriptions include Duhem s theorem and the Gibbs phase rule as special cases. The required number of properties determines the dimensionality of the state diagram needed to represent phase behavior. Then in 9.2 we summarize some features of pure-component diagrams that have not been discussed in earlier chapters. 

Consider a closed system. Gibbs theorem enables us to determine the Gibbs variance Vq pertaining solely to the intensive physico-chemical variables (external and compositional). Duhem s theorem gives a variance Vd=P pertaining to both the intensive and extensive values of a closed... 

In addition to the phase rule discovered by Gibbs, there is another general observation which Pierre Duhem made in his treatise Traite elementaire de Mecanique Chimique, which is referred to as Duhem s theorem. It states ... 

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