Entropy deficit

A solvent with AAV S°(T, P°)/R>2 is considered structured, or ordered, according to this criterion, whereas solvents with this entropy deficit lower than 2 are considered unstructured. Values of AAyS°(T P°)/R of solvents at 25°C are shown in Table 4.1, and further values, for 60°C, 333.15 K, have also been published (Marcus 1996). 

Table 4.1 The structuredness of solvents, measured by their Trouton s constant, the entropy deficit, the dipole orientation correlation coefficient, and the heat capacity density...

The use of inequalities is very awkward in any subsequent mathematical manipulations. As a remedy it is apposite to introduce a positive entropy deficit function d9 > 0 that converts Eq. (1.12.2b) into an equality ... 

A topic of abiding interest is the issue of characterizing the order in liquids which may be defined as the entropy deficit due to preferential orientations of molecular multipoles relative to random orientations (orientational order) and nonuniformly directed intermolecular forces (positional order). Phenomenologically, two criteria are often claimed to be relevant for deciding whether or not a liquid is to be viewed as ordered the Trouton entropy of vaporization or Trouton quotient and the Kirkwood correlation factor gK. Strictly speaking, however, both are of limited relevance to the issue. 

In solution, the process of spontaneous self-assembly is thought to follow a thermodynamic model where the building blocks form an aggregate in solution that gives rise to initial intermolecular interactions (nucleation) followed by growth. The nucleation step is typically thermodynamically unfavorable and an entropy deficit must be overcome. In a cooperative process, the formation of many small favorable associations during the growth phase work to overcome this initial deficit. Molecular motion is a... 

Ordering. This is the deficit of entropy of the liquid solvent relative to the solvent vapor or the dipole orientation correlation. 

This measure, however, pertains to the normal boiling point rather than to ambient conditions. The deficit of the entropy of the liquid solvent relative to the solvent vapour and to a similar non-structured solvent at any temperature, such as 25 °C, has also been derived (Marcus 1996). An alkane with the same skeleton as the solvent, i.e., with atoms such as halogen, O, N, etc. being exchanged for CH3, CH2, and CH, etc., respectively, can be taken as the non-structured solvent. Since the vapour may also be associated, the temperature dependence of the second virial coefficient, B, of the vapour of both the solvent and the corresponding alkane, must also be taken into account. The entropy of vaporization at the temperature T, wherep P°, is given by ... 

As an extension of earlier definitions, Q may now be viewed as the excess or deficit function needed to have Q - (AE + W - S(i)/iidni) vanish identically for any process under consideration this is equivalent to the requirement imposed by the First Law that E be a function of state. For the case where only mechanical work is involved we may therefore introduce in the usual manner the total entropy function S such that... 

We base our present development on the discussion of Section 1.16 where a distinction was made between the entropy change of a system dS - dQr/T, associated with the reversible transfer of heat across the boundaries, and the entropy change arising from irreversible processes occurring totally within the system. As shown in Section 1.15, the heat transfer is subject to the relation 3Q < TdS whenever the inequality sign applies, one introduces the deficit entropy function 9 so as to render... 

Any information process, e.g., receiving a telegram may be regarded as answering a series of questions which allow alternative or multiple choice answers. It defines an information deficit, referred to as the entropy H, which is a positive quantity ... 

This equation shows that in an infinitesimal irreversible process the entropy change of the system is related but not equal to the heat transfer, that involves the inverse of the temperature of the reservoir. To, which is a well characterized quantity. Eq. (1.12.5) replaces the standard inequality dS > diQ/T and provides a second interpretation of the deficit function dO specifies the difference between the entropy change dS and the experimentally determined value of diQfTo in an infinitesimal step. It is only for a reversible process that these quantities match and that do drops out in the irreversible case the heat transfer is numerically smaller. 

We also generalize the definition of heat Q as the deficit function needed so that dQ — (dE — dW — "J i l i dn ) vanishes identically, in order that E remains a function of state. We then view the entropy change as being given by... 

The deficit of the molar entropy of a liquid with respect to the same substance in the ideal gas phase is a measure of the order existing in the liquid. Trouton s constant, Ayap5 (rb) = AyH T, )/Tb is the negative of this deficit, where is the... 

An entropy effect leading to energy dissipation or exergy loss either within or through the boundary of a system is unavoidable in every irreversible system. Thermodynamic analysis determines the net enthalpy deficits and exergy losses due to irreversibility at each stage of a distillation column by combining the first and second laws of... 

---