Entropy neglect

In actual calculation for equilibrium between ice and clathrate hydrate, the free energy of a whole clathrate hydrate, which is either empty or may contain spherical guest molecules, is calculated as the sum of the interaction energy at OK, the harmonic vibrational free energy, and the residual entropy neglecting the anharmonic term [47] as... 

Consider an isotropic fluid in which viscous phenomena are neglected. Concentrations and temperature are non-unifonn in this system. The rate of entropy production may be written... 

What enthalpy difference would lead to a 25-75% mixture of syn and skew rotamers of 1-butene Neglect any entropy change. 

In writing Eq. (8.41), we have clearly treated Aw as a contribution to enthalpy. This means we neglect volume changes (AHp jj. versus AUp jj.) and entropy changes beyond the configurational changes discussed in the last section (AGp jj. versus AH jj.). In a subsequent development it is... 

In this section we study a system with purely repulsive interactions which demonstrates the importance of entropy effects on the stability of phases when the effect of the corrugation potential due to the structured surface is completely neglected. The phase diagrams are determined by finite size scaling methods, in particular the methods of Sec. IV A. 

Although AGrxn depends on both enthalpy and entropy, there are many reactions for which the entropy contribution is small, and can be neglected. Thus, if AHjxn = AErxn, wc cuu estimate equilibrium constants for such reactions by the following equation ... 

Reaction rate constants, k,x , are also related to free energies. As before, if entropy contributions can be neglected, the rate constant can be obtained directly from the activation energy, AE, by ... 

There is also a small contribution from thermal entropy, but this can be neglected. 

As Gibbs and Helmholtz pointed out, however, this so-called Thomson Rule (which had also been proposed by Helmholtz in 1847) cannot be true in general, because the change of entropy cannot always be neglected. 

The temperature coefficient of the potential of zero charge has often been suggested to indicate the orientation of solvent molecules at the met-al/solution interface. However, this view is based only on the response of a simple two-state model for the interfacial solvent, and on neglecting any contribution from the electronic entropy.76,77 This is in fact not the case. The temperature coefficient of 0in many instances is negative and of the... 

It can be expected that the electronic structure changes would be reflected by the heats of adsorption of suitable chosen molecules. Indeed, Shek et al (17) report that one maximum in the thermal desorption profile of CO shifts to lower temperatures when the Cu content of alloys increases. If the variations in the entropy changes upon adsorption can be neglected (probably - they can) this would indicate a lower heat of adsorption of CO on alloys than on Pt from abt. 33 Kcal/mol on pure Pt,to 26 Kcal/mol for an alloy with abt. 20% Cu. 

A certain ambiguity arises in the proper choice of the thermodynamic parameter p, since entropy changes due to solvent orientation are neglected. The available experimental data (cf. Sect. 4) indicate, however, that the free energy of reaction for systems showing a spin change is close to zero. The numerical analysis has been therefore performed for the specific case p = 0, for which value the rate constant in Fig. 15 has been computed as a function of S and h lkgT. 

As in the linear case, it should be stressed that the asymmetric part of the transport matrix (equivalently fj) cannot be neglected just because it does not contribute to the steady rate of first entropy production. The present results show that the function makes an important and generally nonnegligible contribution to the dynamics of the steady state. 

The end effects have been neglected here, including in the expression for change in reservoir entropy, Eq. (178). This result says in essence that the probability of a positive increase in entropy is exponentially greater than the probability of a decrease in entropy during heat flow. In essence this is the thermodynamic gradient version of the fluctuation theorem that was first derived by Bochkov and Kuzovlev [60] and subsequently by Evans et al. [56, 57]. It should be stressed that these versions relied on an adiabatic trajectory, macrovariables, and mechanical work. The present derivation explicitly accounts for interactions with the reservoir during the thermodynamic (here) or mechanical (later) work,... 

The first term on the right-hand side is independent of the subsystem and may be neglected. With this, the entropy of the total system constrained to be in the macrostate Es is the sum of that of the isolated subsystem in that macrostate and that of the reservoirs,... 

The Debye temperatures of stages two and one were determined by inelastic neutron scattering measurements [33], The total entropy variation using equation 8 is in the order of about 2 J/(mol.K). Although smaller in value, such variation accounts for 10-15% of the total entropy and should not be neglected. We are currently carrying on calculations of the vibrational entropy from the phonon density of states in LixC6 phases. 

---