Entropy association

The generic case is a subsystem with phase function x(T) that can be exchanged with a reservoir that imposes a thermodynamic force Xr. (The circumflex denoting a function of phase space will usually be dropped, since the argument T distinguishes the function from the macrostate label x.) This case includes the standard equilibrium systems as well as nonequilibrium systems in steady flux. The probability of a state T is the exponential of the associated entropy, which is the total entropy. However, as usual it is assumed (it can be shown) [9] that the... 

Calculate the associated entropy change for the reaction in Equation (4.63), and comment on its sign. 

For a reversible change the associated entropy change dS for the colloidal particles is given by applying the second law ... 

A change in mechanism [at pH pX of (9)] from ElcBi to ElcB is also believed to account for the biphasic Brpnsted plots (/3i 0.7, P2 0) and associated entropy... 

Data derived from pressure experiments on semi-conducting elements by Klement and Jayamaran (1966) and Minomura (1974) have also been useful in obtaining confirmation that the entropies associated with transitions in Si, Ge and Sn form a consistent pattern, supporting the concept that each crystallographic transformation tends to have a characteristic associated entropy change (Miodownik 1972a, 1972b). Similarly, extrapolations from pressure data on alloys can be used to obtain estimates of lattice stabilities at P = 0, which can then be compared with estimates obtained by other routes, such as SFE measurements. 

The melting points, enthalpies, and associated entropies for a series of A -aryl-4//-benzo[ ][l,3]thiazin-2-amines 71 are presented in Table 3 <2004MI6291>. The melting points of the compounds determined by differential scanning calorimetry (DSC) agreed with the results obtained by hot-stage microscope. 

The exergonicity (AG°) is entirely enthalpy-driven, whilst a respectable negative entropy contribution testifies to the formation of a well ordered complex structure. The energetic signature is quite different from ordinary hydrophobic bonding in water which is commonly characterized by positive association entropies thereby reflecting the poor structural definition of the associate. 

PuRh3 was found to become antiferromagnetic below 6.6 K, as derived from the peak in the temperature dependence of x shown in fig. 3.26a. The C(T) curve exhibits a A-anomaly at 6.2 K with an associated entropy of about R In 2 (Brodsky 1978). The magnetic transition is also accompanied by an anomaly in the temperature dependence of resistivity shown in fig. 3.26b (Harvey et al. 1973). 

Another implication of Eq. (5.16) is that if the vibrational frequency of the atoms changes from, say, a frequency a to a, as a result of a phase transformation or the formation of defects, e.g., the associated entropy change is... 

Figure 11 shows the dependence of the transition temperatures on the number of methylene units in the spacer, n, for the CBOnO.lO series [69]. Immediately apparent is that the clearing temperatures show a dramatic alternation which attenuates quite rapidly on increasing n. A dramatic alternation is also exhibited by the nematic-isotropic entropies but which is not attenuated on increasing n (see Fig. 12). As we noted earlier this dependence of the nematic-isotropic transition temperatures and associated entropy changes on varying the length and parity of the flexible spacer is...

Water plays further important roles with respect to enthalpy and entropy. Interactions between hydrophobic partners are favorable in water as the association reduces the net hydrophobic surface in contact with the polar solvent, thus reducing structured and constrained water around the solutes and providing positive association entropy. Hence, this release of ordered water molecules is an entropy-driven... 

Although we shall include the CeSi, compounds with x > 1.9 within the nonmagnetic systems (region IV), the borderline as a function of x is not unequivocal. Specific heat measurements performed under a magnetic field in the x = 1.85 and 1.9 compounds shows the occurrence of a hump at about 3.5 K, with a very low associated entropy, which is mainly gained in the spin-fluctuation temperature region (Dhar et al. 1987). Similar behaviour was observed in CeSnj (Ikeda and Gschneidner... 

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