Thermodynamics property relations

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

Thermodynamic properties related to RsSiH can be obtained from negative-ion gas-phase studies. The following thermochemical cycle (cf. Scheme 2.1) ... 

Thompson J. B. Jr., Waldbaum D. R. and Hovis G. L. (1974). Thermodynamic properties related to ordering in end member alkali feldspars. In The Feldspars, W. S. MacKenzie and J. Zussman, eds. Manchester Manchester University Press. 

Fugacity is a thermodynamic property related to the deviation of the p—V—T properties of the gas from those of an ideal gas. At very low pressures, the fugacity of a real gas tends to its partial pressure... 

In order to obtain such expressions it is necessary to apply thermodynamic property relations for multicomponent systems in conjunction with material and energy balances, heat, mass, and momentum transport equations. 

As in most separation processes, thermodynamics play a key role in designing reactive distillation equipment. The process is governed, on the one hand, by the thermodynamic properties related to separation by distillation and on the other hand, by the equilibrium constants related to the reactions. 

An ideal solution is simply defined as a mixture of chemical components with its thermodynamic property related to the linear sum of each pure species thermodynamic property (Equation (1)). A common example is a solution which obeys Raoult s law. This law states that the total pressure of a system is a linear combination of the component s vapors pressure at the system s temperature, provided that the total pressure is less than 5 atm. In order to derive Raoult s law, we start from Equation (5) and assume that the liquid solution is ideal ... 

THERMODYNAMICS TABLE 4 1 Mathematical Structure of Thermodynamic Property Relations... 

A number of properties, including dielectric properties, should be considered in assessing a given polar solvent. Important bulk properties are density, vapor pressure, thermodynamic properties related to vaporization, heat capacity, viscosity, compressibility, and surface tension. Some of these are summarized in table 4.1 and are discussed briefly in this section. 

At sufficiently low frequency and small amplitude the sound velocity W in a fluid can be regarded as a purely thermodynamic property related to the adiabatic compressibility jSs = — 1 [V dVldp)s and the density p = M[V by... 

The sonic velocity w in a fluid is a thermodynamic property related to the adiabatic compressibility by w = l/(pKj), where p is the mass density of the fluid. 

Chemical Equilibrium. For a single-phase fluid and open system a fundamental thermodynamic property relation is given by Smith and van Ness (1987),... 

To prove the applicability of this model to the interpretation of the results obtained with solutions of polystyrenesulphonates we have measured different thermodynamic properties related to different derivatives of the electrostatic free energy. 

The applicability of both models for the interpretation of the experimental results has been illustrated on a variety of thermodynamic properties related to different derivatives of free energy. It is clear that such an agreement cannot be just accidental. In this review, it is true, we have confined ourselves only to the data obtained with polystyrenesulphonates. Unfortunately, there is no complete set of thermodynamic data of other polyelectrolyte systems. It seems, however, that in the polyelectrolyte solutions discussed above the polymeric chain consists of rather long fully extended segments. Between segments belonging to the same or to a neighbouring polyion, there should be a considerable volume where the electric field intensity is close to zero. This justifies the application of a model with cylindrical symmetry. Moreover, the absence of specific interactions permits the application of a pure electrostatic theory. 

Example 8.8 provides justification of the statements above by showing that thermodynamic property relations dictate that vapor and liquid mole fractions are always equal... 

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