Gibbs formula

It is beyond our control how the cross-links are spaced along the polymer chains during the vulcanization process. This extraordinary important fact demands a generalization of the Gibbs formula in statistical mechanics for amorphous materials that have fixed constraints of which the exact topology is unknown. Details of a modified Gibbs formula of polymer networks can be found in the pioneering paper of Deam and Edwards [13]. 

As known, the free energy of an uncross-linked polymer melt can be calculated by the usual Gibbs formula,... 

THL.4. R. Defay et 1. Prigogine, Sur 1 extension de la fonnule de Gibbs a la tension superficielle des surfaces non en equilibre (On the extension of Gibbs formula to the surface tension of nonequilibrium surfaces), Bull. Cl. Sci. Acad. Roy. Belg. 32, 36-51 (1946). 

In Section 1.3.2 we saw that the Gibbs formula for entropy applies equally well to an isolated system as to a closed isothermal system. To determine whether or not this formula applies to NPT systems as well, we can substitute the NPT probability law of Equation (1.18) into Equation (1.15) ... 

The key to calculating the activation energy associated with nucle-ation from supersaturated (metastable) solutions is Gibbs formula (G3) for the work of forming a new phase within a homogeneous fluid ... 

AG Gibbs free energy. The change in Gibbs formula AG = AH - TAS. A process occurs... 

To calculate the thermodynamics of this model we can start by writing down the entropy of each site. If the probability that the ith site is occupied is pi then we can write down the entropy using the Gibbs formula as... 

The main point of our elaboration is, that the Gibbs measure (4) of the potential lattice under interest ctin be considered as a nontrivial prior in the Bayes formula for the conditional probability, applied to the problem of image restoration ... 

Cmpd. no. Name Formula CAS no. Mol wt Ideal gas enthalpy of formation, J/kmol X lE-07 Ideal gas Gibbs energy of formation, J/kmol X lE-07 Ideal gas entropy, J/(kmol-K) X lE-05 Standard net enthalpy of combustion, J/kmol X lE-09... 

As found in commerce, the cinchona alkaloids are not necessarily pure quinidine, for example, may contain up to 30 per cent, of dihydroquinidine. Working with carefully pmdfied specimens of the four chief cinchona alkaloids and their dihydro-derivatives, Buttle, Henry and Trevan found the results recorded in the table (p. 471) in tests with malaria in canaries. The figures in brackets represent the dose of quinine necessary to produce the same degree of protection as unit dose of the alkaloid named. To the results are also added the data found later by the same authors, with Solomon and Gibbs, for some of the transformation products (p. 449) of quinine and quinidine. The Roman numeral at the head of each column refers to the type formula on p. 470. 

The method of deduction also applies when B is a liquid, or a solid, and (6) therefore holds for these cases. The equation (6) is called Gibbs s Adsorption Formula it was deduced independently by J. J. Thomson W (1888). The present deduction is due to Milner <12> (1907). 

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... 

FIGURE 7.27 The standard Gibbs free energy of formation of a compound is defined as the standard reaction Gibbs free energy per mole of formula units of the compound when the compound is formed from its elements. It represents a "thermodynamic altitude" with respect to the elements at "sea level." The numerical values are in kilojoules per mole. 

Here we sketch a heuristic derivation of the quasichemical formula (9.34). Consider a solution of species a and w. The Gibbs free energy is... 

The Kh values derived from kinetic data are close to those obtained by IR and NMR spectroscopies. An empirical formula for the evaluation of the hydrogen bond enthalpy and Gibbs potential was derived [47] ... 

If the Gibbs energy of adsorption AG-M is considered as independent of the coverage the resulting formula is known as the Langmuir isotherm this assumption is reasonable when the interaction between the adsorbed particles is small. 

A quantitative test of the Gibbs-Thomson formula will accordingly involve the following measurements we first determine the surface tension of a solution for a number of different concentrations, plot the [Pg.41]

In view of the fundamental importance of the Gibbs-Thomson formula, and the magnitude of the discrepancies between the figures calculated from it and the experimental results, it is of obvious interest to inquire to What causes the deviations may be due. The first point to be noticed is that the complex substances which exhibit them most markedly form, at least at higher concentrations, colloidal and not true solutions. It is, therefore, very probable that they may form gelatinous or semi-solid skins on the adsorbent surface, in which the concentration may be very great. There is a considerable amount of evidence to support this view. Thus Lewis finds that, if the thickness of the surface layer be taken as equal to the radius of molecular attraction, say 2 X io 7 cms., and the concentration calculated from the observed adsorption, it is found, for instance, for methyl orange, to be about 39%, whereas the solubility of the substance is only about 078%. The surface layer, therefore, cannot possibly consist of a more concentrated solution of the dye, which is the only case that can be dealt with theoretically, but must be formed of a semi-solid deposit. 

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