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** Ab initio derivation, entropy production **

** Configurational entropy for derivation **

** Derivatives of the Specific Entropy **

** Entropy derivation from partition functions **

** Equation entropy of mixing, derivation **

The uncertainty in the values of the entropy derived from thermochemical data usually does not exceed IJ mol and, hence, cannot practically affect the final results of the determination with the third-law method. If, however (in the absence of reliable data), one uses averaged values of known to within 9 J mol (see Sect.4.5) in the calculation, this factor can no longer be neglected, because the error in determination of the enthalpy becomes as high as 3%. Even in this case, however, this restriction can hardly be a serious obstacle to the use of this method. [Pg.59]

The remaining step is to express the entropy derivative in terms of P, V, T. This is provided by the Maxwell relationship in eg. fa.iQ ). Thus finally we have [Pg.187]

The H-F Eq. 18.6 has two parts the (j)-dependent configurational entropy derived from the lattice model without free volume and the enthalpic part taken from the Hildebrand s theory of regular solutions (Shinoda 1978 Reichart et al. 1997 Maranas et al. 1998). More recent version of Eq. 18.6 was used for the interpretation of SANS data, and it will be discussed in reference to the lattice cluster theory (LCT) (Freed and Dudowicz 2005). [Pg.1590]

Landauer R Inadequacy of entropy and entropy derivatives in characterizing steady-state. Phys RevA 1975, 12(2) 636-638. [Pg.102]

TABLE 1.3 Mean Force Constant, Mean Atomic Displacement, and Vibrational Entropy Derived from the [Pg.38]

It now remains to evaluate the various entropy derivatives, so that the stability restrictions of Eqs. 7.2-7 can be put into a more usable form. Starting from [Pg.279]

It is seen that the general form for b derived above, taking into account both A and the entropy derivative /jlF, is not either identical with the experimental behavior at Hg where b = RT/p F- -K. The general case above is rather of the form R/ F/ T -I- K ) which is not in any way reducible to, or reconcilable with, the experimental Eq. (14) for b for the h.e.r. at Hg. [Pg.134]

The most likely state, which is denoted throughout by an overbar, is the one that maximizes the entropy. In this case the entropy derivative vanishes when the boundary temperatures of the subsystem equal that of the respective reservoirs, [Pg.59]

DSC measurements with a microcalorimeter played a key role in tracing the origin of the step observed in the spin transition curve of [Fe(2-pic)3]-Cl2-EtOH [24]. The mixing entropy derived from the measured heat capacity data showed a significant reduction in the region of the step. This has been [Pg.28]

Show that although the partial molar heat content of the constituent of an ideal solution is independent of the composition ( 34a), this is not the case for the partial molar free energy and entropy. Derive expressions for (d/Lii/dN<)r p and (dSi/dNi)T,p for an ideal solution. [Pg.349]

In Sections IVA, VA, and VI the nonequilibrium probability distribution is given in phase space for steady-state thermodynamic flows, mechanical work, and quantum systems, respectively. (The second entropy derived in Section II gives the probability of fluctuations in macrostates, and as such it represents the nonequilibrium analogue of thermodynamic fluctuation theory.) The present phase space distribution differs from the Yamada-Kawasaki distribution in that [Pg.7]

To evaluate the derivative (dU/dV)T, we start from expression (5.46a) for dU in terms of its natural variables S, V, differentiate with respect to V at constant 7 and use the Maxwell relation (5.49c) to replace the entropy derivative, [Pg.166]

The researchers found that the rate constants for several intramolecular ester formations with a wide variety of E.M. values were directly correlated to the mole fraction of the reactants present as N ACs. The mole fractions were calculated using molecular dynamics simulations. When the ground state resides naturally in an NAC, then an E.M. of around 10 was achieved (the same value that we introduced earlier as the upper limit to proximity effects). To achieve an NAC, the reactant must be placed in a conformation that also has a higher enthalpy, because the reactants are within van der Waals distances. Therefore, the rate enhancement obtained by NAC formation is postulated to be also enthalpy derived, not solely entropy derived. [Pg.499]

Frenkel defects and impurity ions can diffuse through the silver halide lattice by a number of mechanisms. Silver ions can diffuse by a vacancy mechanism or by replacement processes such as collinear or noncollinear interstitialcy jump mechanisms [18]. The collinear interstitial mechanism is one in which an interstitial silver ion moves in a [111] direction, forcing an adjacent lattice silver ion into an interstitial position and replacing it The enthalpies and entropies derived from temperature-dependent ionic conductivity measurements for these processes are included in Table 4. The collinear interstitial mechanism is the most facile process at room temperature, but the other mechanisms are thought to contribute at higher temperatures. [Pg.156]

** Ab initio derivation, entropy production **

** Configurational entropy for derivation **

** Derivatives of the Specific Entropy **

** Entropy derivation from partition functions **

** Equation entropy of mixing, derivation **

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