Thermodynamically consistent widely-used

Two simulation methods—Monte Carlo and molecular dynamics—allow calculation of the density profile and pressure difference of Eq. III-44 across the vapor-liquid interface [64, 65]. In the former method, the initial system consists of N molecules in assumed positions. An intermolecule potential function is chosen, such as the Lennard-Jones potential, and the positions are randomly varied until the energy of the system is at a minimum. The resulting configuration is taken to be the equilibrium one. In the molecular dynamics approach, the N molecules are given initial positions and velocities and the equations of motion are solved to follow the ensuing collisions until the set shows constant time-average thermodynamic properties. Both methods are computer intensive yet widely used. 

The solubility parameter approach is a thermodynamically consistent theory and it has some links with other theories such as the van der Waals internal pressure concept, the Lennard-Jones pair potentials between molecules, and entropy of mixing concepts of the lattice theories. The solubility parameter concept has found wide use in industry for nonpolar solvents (i.e. solvent selection for polymer solutions and extraction processes) as well as in academic endeavor (thermodynamics of solutions), but it is unsuccessful for solutions where polar and especially hydrogen-bonding interactions are operating. 

The most widely used geochemical modeling programs consist of a computer code plus a related file of data called a database. The database contains thermodynamic and kinetic parameters. The code uses the thermodynamic and kinetic parameters in the database and concentrations or other constraints as input, and produces results that describe a geochemical model for a particular chemical system. 

In the following example we illustrate the first type of use of the second thermodynamic principle discussed in Section 6, namely, by verifying a constitutive model of EPS geofoam a posteriori for thermodynamic consistency. This model was developed by the authors (Wong and Leo, 2006) based on experimental results from a series of standard "drained" tiiaxial tests. It initially adopted the Mohr-Coulomb yield function used widely in soil mechanics but upon further testing with a true triaxial apparatus (Leo et al., 2008), a Drucker-Prager type yield function was subsequently preferred. This is written as ... 

Kemball, Ridcal, and Guggenheim and independently Broughton have shown that thermodynamic consistency requires = q 2- physical adsorption of molecules of widely different size such an assumption is unrealistic. If the extended Langmuir equation is regarded as an analytical description rather than a physical model, the use of different values of q for each component becomes permis.sible although the equations cannot then be expected to apply over the entire concentration range and extrapolation on such... 

Although not thermodynamically consistent, these expressions have been shown to provide a reasonably good empirical correlation of binary equilibrium data for a number of simple gases on molecular sieve adsorbents and are widely used for design purposes. However, because of the lack of a proper theoretical foundation this approach should be treated with caution. 

Segmented polyurethanes (SPUs) are widely used as biomedical materials because of their excellent mechanical properties, stability in the biological environment, and their ease of process [7-11]. The SPU consists of alternating hard and soft segments. The segments are thermodynamically incompatible and generally, the phases are separated into distinct domains, with a typical domain size in the order of 3-10 nm. 

In this book, we prefer the mass system of variables (mass, specific enthalpy, mass fractions). Nevertheless, also the molar system is worth mentioning. The molar system is widely used in chemistry and classical chemical thermodynamics. Based on the elementary idea that matter is composed of molecules, a conventional number of molecules is taken as a unit traditionally (and later precised for scientific purposes), it is the number of molecules in 32 grammes of oxygen O2, which equals 0.602x10 (Avogadro s number). This quantity of matter is called mole, or g-mole more precisely. Then 10 g-moles (1 kg-mole) is denoted as 1 kmol in the system of units consistent with 1 kg as unit of mass. 

Figures 11-14 and 11-15, which are based on the work of Polderman (1957) and Parrish et al. (1986), present data on the water dew points of gases in equilibrium with diethylene and triethylene glycol solutions at various temperatures. The TEG curves are based on the Parrish et al. data rather than the widely used Worley (1967) data because the Parrish et al. data cover a wider range of dew-point depressions and TEG concentrations are thermodynamically consistent and generally result in more conservative designs.

This discontinuous process is widely used, even in industrial reactors it consists of mixing the reactants at a time =0, and homogenizing constantly the reaction mixture. It is possible to operate at a constant pressure or volume, isothermally, etc. The system is thermodynamically closed, the concentrations of the different reactants and products vary continually with time hence a transient operation. 

This forms the basis for a widely used method of testing experimental VLE data for thermodynamic consistency. Using the data in Table 8.1 and following the procedure in Example 8.2, compute the value of In iyjyb) for 3ch data point in that table, and plot the values vs. x. If the consistency test is met, then the areas above and below the ln(yjyb) = 0 fine should be equal. Test visually or mathematically to see if they are. 

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