Derived thermodynamic properties

The Helmholtz free energy A is the second of the three derived thermodynamic properties. It is defined as... 

The calculation of entropy is required for compression and expansion calculations. Isentropic compression and expansion is often used as a reference for real compression and expansion processes. The calculation of entropy might also be required in order to calculate other derived thermodynamic properties. Like enthalpy, entropy can also be calculated from a departure function ... 

Figure 5.32 Comparison of derived thermodynamic properties (water and Freon-12). (From May-inger, 1981. Copyright 1981 by Hemisphere Publishing Corp., New York. Reprinted with permission.)...

It is also of interest to note that starting from miscibility gap data, attempts have been made to derive thermodynamic properties, i.e., free energies of mixing, and Sundquist (23) summarizes information and discusses a number of binary alloy systems. 

The validity of the assumption that the various thermodynamic properties of the smectite remain invariant, regardless of the state of hydration, has been addressed in detail by Sposito and Prost (1). They point out that one would, for example, expect hydrolysis of the clay to occur at high water contents, and also, it is likely that the exchangeable cations will change their spatial relationship with the clay layers. Thus, the derived thermodynamic properties of the adsorbed water would not represent correct values. 

Finally, it is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be shown independently that equilibrium has been established. One possible exception applies to trace substitution where the assumptions of stoichiometric saturation and unit activity for the predominant component allow close approximation of equilibrium behavior for the trace components (9). The method of Thorstenson and Plummer (10) based on the compositional dependence of the equilibrium constant, as used in this study, is well suited to testing equilibrium for all solid solution compositions. However, because equilibrium has not been found, the thermodynamic properties of the KCl-KBr solid solutions remain provisional until the observed compositional dependence of the equilibrium constant can be verified. One means of verification is the demonstration that recrystallization in the KCl-KBr-H20 system occurs at stoichiometric saturation. 

In application of this method to solubility data (8) in the KCl-KBr- O system at 25°C, it is found that equilibrium is in general not attained, though some mid-range compositions may be near equilibrium. As the highly soluble salts are expected to reach equilibrium most easily, considerable caution should be exercised before reaching the conclusion that equilibrium is established in other low-temperature solid solution-aqueous solution systems. It is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be demonstrated that equilibrium has been attained. 

Messerly, J.F., Finke, H.L., Good, W.D., and Gammon, B.E. Condensed-phase heat capacities and derived thermodynamic properties for 1,4-dimethylbenzene, 1,2-diphenylethane, and 2,3-dimethylnaphthalene, 7 Chem. Thermodyn., 20(4) 485-501, 1988. 

Esperanca, J.M.S.S. et al.. Densities and derived thermodynamic properties of ionic liquids. 3. Phosphonium-based ionic liquids over an extended pressure range, /. Chem. Eng. Data, 51, 237, 2006. 

Figure 17.5 Derived thermodynamic properties at T — 298.15 K and p = 0.1 MPa for (2Cic-CfiHi2 + X2n-CjHi4) (a) excess molar heat capacities obtained from the excess molar enthalpies (b) relative partial molar heat capacities obtained from the excess molar heat capacities (c) change of the excess molar volume with temperature obtained from the excess molar volumes and (d) change of the excess molar enthalpies with pressure obtained from the excess molar volumes.

Heat Capacity and Derived Thermodynamic Properties °f C6oH2n Crystals... 

Chemical Equilibrium with Applications (CEA) is an expert system developed by NASA for determining compositions in chemical equilibria for deriving thermodynamic properties of a chemical system in propulsion jet engines. 

Derived Thermodynamic Properties of Liquid and Vapor Phases 153... 

One reason for the interest in lattice models is that they can be used to try to answer some of the fundamental questions about protein structure. For example, it may be feasible to enumerate all possible conformations for a chain of a given length on the lattice From this set of states statistical mechanics can be used to derive thermodynamic properties and to investigate the relationship between the structure and the sequence. In the HP model [Chan and Dill 1993], a protein is modelled as a sequence of hydrophobic (H) and... 

DERIVED THERMODYNAMIC PROPERTIES At Saturated Vapor Pressure... 

By a combined gravimetric and i.r. technique, spectra of lysozyme protein films have been recorded during sorption isotherms at constant water content h (mg per mg dry protein) in the range 0Computer-aided differential analysis shows the effect of progressive hydration on some significant sites of the protein such as the ionizable acidic side-chains and the backbone amide carbonyls, as well as the spectrum of the absorbed water itself. In order to derive thermodynamic properties of these sites, the... 

Of all the equations of state, only the one derived by S-S explicitly gives the hole fraction, h = l —y, a measure of the free-volume fraction,/. Equation (6.39) provides a corresponding-states description of the PVT surface of any liquid. Once the characteristic parameters (P, V, t, and 3cA) are known, the V, h, and all derivative thermodynamic properties may be computed in the full range of P and T. For the linear molecules, the external degrees of freedom are proportional to the number of segments ic/s = l + 3/s. Thus, for linear polymers, where. y > 3, the external degrees of freedom, 3cA 1, and only knowledge of P, V, and T is required. 

Determining fugacities in fluid mixtures is essentially equivalent to determining an equation of state for the mixture. Deriving thermodynamic properties from... 

This section discusses and tabulates best values for important experimentally derived thermodynamic properties of free atoms and ions, aquo-ions, halides, dioxides, sesquioxides and tripositive hydroxides in an effort to characterize the properties of... 

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