Gibbs’ law

The second law of thermodynamics says that in a Carnot cycle Q/T = constant. This law allows for the definition of a temperature scale if we arbitrarily assign the value of a reference temperature. If we give the value T3 = 273.16K to the triple point (see Gibbs law, Section 8.2) of water, the temperature in kelvin units [K] can be expressed as ... 

The equilibrium distribution function of the particle magnetic moment or (if we neglect interactions) of an assembly of magnetic moments is determined by the Gibbs law... 

Adsorbed amounts of electrolyte can be Inferred from the change of the surface tension with Increasing concentration. According to Gibbs law 13.4.1) for one electrolyte 1... 

Volume 11 mainly dealt with interfaces of solids. For such systems, the adsorption of molecules and ions is the primary phenomenon. Interfaclal tensions cannot generally be measured, although interfacial pressures are obtainable from adsorption isotherms using Gibbs law. 

As a logical sequel, in this third Volume of FICS, liquid-fluid (LG or LL) interfaces will be treated. For such systems the interfaclal tension y is the primary, and measurable, variable. Often the areas involved are so small that the analytical determination of adsorbed amounts (F s) is difficult. In those cases Gibbs law can be used to relate interfacial tension to the adsorption, provided adsorbate and... 

By contrast, Gibbs monolayers are continually at equilibrium with the subphase which, in this case, may be called a solution. Surface tension and concentration are related through Gibbs law, so that the surface pressure can be related to the solution concentration. By analogy with [II. 1.1.6 and 7J we have for a single adsorbed component in an ideal solution... 

Subjecting y[x) curves to analysis in terms of Gibbs law immediately confronts us with the basic issue of where to locate the dividing plane. Let us start from Gibbs law at constant pressure... 

The other difference is that in our approach we do not have to introduce single chemical potenbals in the surface layer ( s) because these are automabcally equated to those in the bulk via Gibbs law. So, making some assumpbon regarding the shape of the relabon between and n is not necessary. This does not mean... 

Long ago McBain and co-workers ) tried to verify Gibbs law by actually determ-... 

We are now interested in the structure and physical properties of surfactant monolayers at LL and LG Interfaces. The primary physical characteristic is y. Let us first consider equilibrium states. Then, y can be related to the composition of the solution via Gibbs law. 

Most measurements reported here have been carried out under well-defined conditions, especially with respect to temperature and purity. The latter is not always verifiable, since inadvertent impurities may always be present the trend is the higher the better , because of Gibbs law. 

The ideal surface, discussed in Section II, is the surface of an ideal lattice. A real lattice contains a considerable number of defects. Lattice vacancies or interstitial atoms (ions) occur and are inherent to the lattice at a given temperature or may result from a temperature treatment and a freezing in before equilibrium is reached. We may, undoubtedly, expect to find similar defects at the surface. But here also we may not extrapolate the bulk situation to the surface. According to the Gibbs law, the equilibrium between the bulk phase and the surface will be determined by whether the distortions contribute to an increase or a decrease of the surface energy. 

It is known that the surface energy depends not only on the composition of the surface layer, but also on that of the bulk phases [130]. To formulate the Gibbs law for the non-equilibrium chemical potential, additional so-called cross-chemical potentials (the partial derivatives of the surface free energy with respect to the component concentrations in the bulk phases) have been introduced. Rusanov and Prokhorov [131] derived the Gibbs equation and the expression for the free energy of the surface layer in terms of the ordinary chemical potentials by dividing the transition layer adjacent to the surface into n thin layers. For each layer an equilibrium state was assumed. The expression for surface energy was derived by the summation of the equilibrium equations over all these layers. Further, the expression for the additional contribution to the surface tension due to the non-equilibrium diffusion layer was derived in [48, 132]... 

Exerowa 1981 Ekici et al. 2005). Foaming can be induced by air or inert gas bubbling through the enzyme solution and proteins will accumulate at the gas-liquid interface as predicted by Gibbs law (Thomas and Winkler 1977) ... 

Polymer molecules in the region between two very closely-spaced particles cannot adopt all the conformations normally available to them, when they are further apart (cf. Fig. 3.14b)-. This volume restriction effect causes a reduction in the degrees of freedom, or loss of entropy, which is equivalent to an increase in the free energy of the system, according to Gibbs law. Such a situation being thermodynamically unfavourable, the system tries to evolve in the opposite way, in order to reduce this effect, and the particles tend to move apart. 

According to Gibbs law (Equation 3.88), adsorption leads to a lowering of the interfacial tension. Reduction of y and at constant y (no surfactant adsorp-... 

The Gibbs Law of Therniodynamics simulation (eChapt-er 19.5) allows you to explore the relationship between spontaneity and temperature, (a) Of the five reactions available in the simulation, which are spontaneous at all temperatures (b) Which are nonspontaneous at aU temperatures (c) Is it possible for a reaction with a positive enthalpy change and a negative entropy change to be spontaneous Explain. 

The meaning of Gibbs law (Equation 2.2) can be formally stated as follows the snrface tension of a liquid phase (or in the general case the interfacial free energy), o(c), decreases with the increase in surfactant concentration c of the adsorbing component, and the rate of this (relative) decrease at constant temperature is described by the value of adsorption, E... 

A general mathematical description of physisorption equilibria is given by Gibbs law, which relates the adsorbed amoimt r to the decrease in surface tension o if the concentration c of an adsorbable substance in solution increases. In its complete form Eq. (2.45), Gibbs law displays ct as a function of the chemical... 

Before offering a model interpretation, the two regimes can be thermodynamically characterized through surfactant adsorption that is accompanied by expulsion and uptake of NaCl, respectively. This follows immediately from Gibbs law, written as... 

Let us look again at Gibbs phase rule for these systems. In both cases, the number of independent components is 2 (salt and water), and the number of external parameters taken into account is also 2 (pressure and temperature). In both systems, there is a gaseous phase, and if we let (p denote the number of solid phases, then Gibbs law is written as follows ... 

Also, the Gibbs law can be written thus, following the barycentric motion defined hyd/dt ... 

---