Thermodynamic terms Definitions

The thermodynamic dead volume includes those static fractions of the mobile phase that have the same composition as the moving phase, and thus do not contribute to solute retention by differential interaction in a similar manner to those with the stationary phase. It is seen that, in contrast to the kinetic dead volume, which by definition can contain no static mobile phase, and as a consequence is independent of the solute chromatographed, the thermodynamic dead volume will vary from solute to solute depending on the size of the solute molecule (i.e. is dependent on both ( i )and (n). Moreover, the amount of the stationary phase accessible to the solute will also vary with the size of the molecule (i.e. is dependent on (%)). It follows, that for a given stationary phase, it is not possible to compare the retentive properties of one solute with those of another in thermodynamic terms, unless ( ), (n) and (fc) are known accurately for each solute. This is particularly important if the two solutes differ significantly in molecular volume. The experimental determination of ( ), (n) and( ) would be extremely difficult, if not impossible In practice, as it would be necessary to carry out a separate series of exclusion measurements for each solute which, at best, would be lengthy and tedious. 

The rigor and power of equilibrium thermodynamics is purchased at the price of precise operational definitions. In this section, we wish to carefully define four of the most important thermodynamic terms system, property, macroscopic, and state. Although each term has an everyday meaning, it is important to understand the more rigorous and precise aspects of their usage in the thermodynamic context. 

This section reviews some basic definitions and formulas in thermodynamics. These definitions will be used to develop energy balances to describe cooling tower operations. In our discussions we will use the following terms system, property, extensive and intensive properties, and... 

There is no change in (internal) energy of the gas as its volume is increased (i.e. gas is expanded) whilst the temperature is kept constant. This provides a convenient mathematical definition (in thermodynamic terms) of an ideal gas. 

In this form of chromatography retention can readily be expressed in thermodynamic terms. The definition equation for the capacity factor (k) is... 

Thermodynamics uses abstract models to represent real-world systems and processes. These processes may appear in a rich variety of situations, including controlled laboratory conditions, industrial production facilities, living systems, the environment on Earth, and space. A key step in applying the methods of thermodynamics to such diverse processes is to formulate the thermodynamic model for each process. This step requires precise definitions of thermodynamic terms. Students (and professors ) of thermodynamics encounter—and sometimes create—apparent contradictions that arise from careless or inaccurate use of language. Part of the difficulty is that many thermodynamic terms also have everyday meanings different from their thermodynamic usage. This section provides a brief introduction to the language of thermodynamics. 

Polymorphism can be detected by the differences in physical properties due to individual characteristics. Based on the fugacity, which relates to the thermodynamic term, entropy of the solid molecule, polymorphism may be defined as monotropic or enantiotropic. Furthermore, combination of these two systems, monotropic and enantiotropic, may yield a third system. The definition of these categories may best be illustrated by the solubility-temperature plots, based on the van t Hoff equation. In a monotropic category as shown in Figure 9, the solubility of form I (the stable form) and that of form II (the metastable form) will not intersect each other at the transition temperature calculated only from the extrapolation of the two curves. In the enantiotropic category (Fig. 10), the solubility of form I (the stable form) and that of form II (the metastable form) will intersect each other at the transition temperature. In the combined category (Fig. 11), for which there are two transition temperatures, the solubility of form III will not intersect any other curves. 

This introduces the important quantity, S, the entropy which with the definition of G, the free energy, allows discussion of equilibria in thermodynamic terms. 

Equation 3.41 requires that the standard states of the products and reactants be known, that the components can be defined quantitively and in a thermodynamic sense. In soils and much of nature these definitions are rarely possible. The states of ions or molecules in soil systems, and in probably all colloidal systems, are ill-defined thermodynamically. In rigorous thermodynamic terms even ions are undefined. Soil reactions, because of the nonequilibrium in soils and the lack of defined standard states, yield reaction coefficients, rather than reaction constants, and their values vary with soil conditions. 

The brief survey presented here must necessarily begin with a discussion of thermodynamics as a language must of Section 1.2 is concerned with the definition of thermodynamic terms such as chemical potential, fiigacity, and activity. At the end of Section 1.2, (he phase-equilibrium problem is clearly staled in several thermodynamic forms each of these forms is particularly anited for a particular situation, as Indicated in Sections 1.5, 1.6, and 1.7. 

We shall follow Carothers definition of polymerizability 27), described in thermodynamic terms, and relating the polymerizability to the free energy of polymerization (AGp). According to this definition, the more negative AGp the higher the polymerizability. Since AGp = RT In [M]e, the more negative AGp, the lower the equilibrium monomer concentration. 

We are going to specify the meaning of the term ensemble in the field of statistical thermodynamics, whose definition will be a bit more precise in this context than in everyday language. 

It is therefore a great deal of interest to be able to predict which chemical species Y will act as nucleophiles and which will act as bases. Later in this text, we will discuss quantitative measures of basicity. These basicity scales are based on the ability of a substance to remove protons and refer to equilibria or are related to equilibrium measurements. The definition of basicity in aqueous solution is given in thermodynamic terms by the equilibrium constant, which indicates the ability of a substance to remove protons from water ... 

There are alternative ways of defining the various thermodynamic quantities. One may, for example, treat the adsorbed film as a phase having volume, so that P, V terms enter into the definitions. A systematic treatment of this type has been given by Honig [116], who also points out some additional types of heat of adsorption. 

The ultimate definition of thermodynamic temperature is in terms of pV (pressure X volume) in a gas thermometer extrapolated to low pressure. The kelvin (K), the unit of thermodynamic temperature, is defined by specifying the temperature of one fixed point on the scale—the triple point... 

As an example of how the approximate thermodynamic-property equations are handled in the inner loop, consider the calculation of K values. The approximate models for nearly ideal hquid solutions are the following empirical Clausius-Clapeyron form of the K value in terms of a base or reference component, b, and the definition of the relative volatility, Ot. 

Thermodynamic Properties The variation in solvent strength of a supercritical fluid From gaslike to hquidlike values may oe described qualitatively in terms of the density, p, or the solubihty parameter, 6 (square root of the cohesive energy density). It is shown For gaseous, hquid, and SCF CO9 as a function of pressure in Fig. 22-17 according to the rigorous thermodynamic definition ... 

The van der Waals and other non-covalent interactions are universally present in any adhesive bond, and the contribution of these forces is quantified in terms of two material properties, namely, the surface and interfacial energies. The surface and interfacial energies are macroscopic intrinsic material properties. The surface energy of a material, y, is the energy required to create a unit area of the surface of a material in a thermodynamically reversible manner. As per the definition of Dupre [14], the surface and interfacial properties determine the intrinsic or thermodynamic work of adhesion, W, of an interface. For two identical surfaces in contact ... 

The actual state, and absolute amount, of intrinsic energy existing in a body, or system of bodies, are things which lie quite outside the range of pure thermodynamics. This indefiniteness has, however, not the slightest influence on the stringency of the definition, since we can proceed as in the definition of electrostatic potential, and choose any convenient standard state of the body, and use the term intrinsic energy with reference to this standard state. 

A distinction between a solid and liquid is often made in terms of the presence of a crystalline or noncrystalline state. Crystals have definite lines of cleavage and an orderly geometric structure. Thus, diamond is crystalline and solid, while glass is not. The hardness of the substance does not determine the physical state. Soft crystals such as sodium metal, naphthalene, and ice are solid while supercooled glycerine or supercooled quartz are not crystalline and are better considered to be supercooled liquids. Intermediate between the solid and liquid are liquid crystals, which have orderly structures in one or two dimensions,4 but not all three. These demonstrate that science is never as simple as we try to make it through our classification schemes. We will see that thermodynamics handles such exceptions with ease. 

---