Entropy Gain

Expanding the entropy as a function of temperature and pressure results in 

As the gas normally flows from the subsystem ( ) to the subsystem ( ), dn 0. The total entropy increases, when dp 0, since the molar volume and the temperature are positive quantities. In Eq. (5.32), dp = p - p = p - p. We have expanded here the molar entropy of the subsystem ( ) We could also obtain the result by expanding the molar entropy of the subsystem ( ) which results in 

Now dp = p - p , and therefore the sign turns. On the other hand, we may conclude that in an approximation of first order 

In some other way of consideration, for constant enthalpy H we have 

Note that the entropy is produced essentially in the porous plug. If we had an active device, such as a cooler that absorbs reversibly entropy, then the process would be reversible, and systems of different temperature and pressure would be in equilibrium. 

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The kieveisible phenomena represent entropy gain through irrecoverable heat losses as follows, where X is the thermal conductivity and /is the length ... 

Similarly, the second-order derivative can be shown to be zero (see, Problems, Section 2.20). Evaluating the third term gives an expression for entropy gain along the Hugoniot... 

In order to understand the thermodynamic issues associated with the nanocomposite formation, Vaia et al. have applied the mean-field statistical lattice model and found that conclusions based on the mean field theory agreed nicely with the experimental results [12,13]. The entropy loss associated with confinement of a polymer melt is not prohibited to nanocomposite formation because an entropy gain associated with the layer separation balances the entropy loss of polymer intercalation, resulting in a net entropy change near to zero. Thus, from the theoretical model, the outcome of nanocomposite formation via polymer melt intercalation depends on energetic factors, which may be determined from the surface energies of the polymer and OMLF. 

This explains why the well-defined diffraction peaks up to the (004) plane are observed (see Figure 9.2). The entropic contribution of the intercalants, which leads to the entropy gain associated with the layer expansion after intercalation of the polymer chains, may not be significant because of the interdigitated layer structure. 

In addition to enthalpic contributions, the entropy effects accompanying protein-metal ion interactions are substantial. These effects manifest themselves in the desolvation of the metal ion and its binding site. However, as the metal ion binds to a protein, the entropy gain of solvent release may be offset to some degree by the reduction of the conformational entropy of the polypeptide chain as it becomes more firmly bound... 

If there is only one stereogenic center in the molecule, thermodynamically controlled conditions lead to complete racemization, dictated by an entropy gain of RTl 2. A familiar example is the a-chiral aldehyde 1 which racemizes quickly via the enol (enolate) 2 even under mildly acidic or basic conditions. 

The reaction is exothermic with a small entropy gain from 237 to 238 ... 

Temperature has a minor influence on the phase diagram entropy gain is the main driver of complex coacervation, due to concomitant release of bound counterions into solution by the interacting charged biopolymers, which increases the solution entropy. 

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