A thermodynamic framework

Recently, there have been a number of significant developments in the modeling of electrolyte systems. Bromley (1), Meissner and Tester (2), Meissner and Kusik (2), Pitzer and co-workers (4, ,j5), and" Cruz and Renon (7j, presented models for calculating the mean ionic activity coefficients of many types of aqueous electrolytes. In addition, Edwards, et al. (8) proposed a thermodynamic framework to calculate equilibrium vapor-liquid compositions for aqueous solutions of one or more volatile weak electrolytes which involved activity coefficients of ionic species. Most recently, Beutier and Renon (9) and Edwards, et al.(10) used simplified forms of the Pitzer equation to represent ionic activity coefficients. 

In this study, a thermodynamic framework has been presented for the calculation of vapor-liquid equilibria for binary solvents containing nonvolatile salts. From an appropriate definition of a pseudobinary system, infinite dilution activity coefficients for the salt-containing system may be estimated from a knowledge of vapor pressure lowering, salt-free infinite dilution activity coefficients, and a single system-dependent constant. Parameters for the Wilson equation may be determined from the infinite dilution activity coefficients. 

The constitutive equations use a thermodynamic framework, that in fact embodies not only purely mechanical aspects, but also transfers of masses between the phases and diffusion of matter through the extrafibrillar phase. Since focus is on the chemo-mechanical couplings, we use experimental data that display different salinities. The structure of the constitutive functions and the state variables on which they depend are briefly motivated. Calibration of material parameters is defined and simulations of confined compression tests and of tree swelling tests with a varying chemistry are described and compared with available data in [3], The evolution of internal entities entering the model, e.g. the masses and molar fractions of water and ions, during some of these tests is also documented to highlight the main microstructural features of the model. 

Abstract In a thermodynamic framework which exploits the entropy inequality to obtain constitutive equations, it is common practice to assume charge neutrality and enforce this restriction using Lagrange multipliers. In this paper we show that the Lagrange multiplier used to enforce charge neutrality does not correspond to any known physical parameter, raising the question of whether charge neutrality can really be enforced. 

Fang, X., Pan, T., and Sosnick, T. R. (1999). A thermodynamic framework and coopera-tivity in the tertiary folding of a Mg2+-dependent ribozyme. Biochemistry 38,... 

It is the aim of this paper to present a comparison of thermal and chemical recuperation options 1n a thermodynamic framework. The paper will begin by identifying the major irreversibilities in a simple gas-turbine cycle with liquid methanol fuel continue with a comparison of thermodynamic losses and overall efficiencies among various options utilizing thermal and/or... 

To transform the above equations into a predictive tool is not an easy task, for reasons already outlined. They constitute, however, a thermodynamic framework on the basis of which further development could follow. 

The shape of the solid-state proton NMR free induction decay (FID) of a molten polyethylene (PE) sample has been examined as a function of time during isothermal crystallization in situ The crystallization rate as a function of crystallization temperature is derived and the results discussed within a thermodynamic framework. 

According to the above considerations, a thermodynamic framework has long existed for interpreting swelling equilibria of ionic as well as nonionic gels in terms of their osmotic pressures. Although our greatest concern for the present should be how to describe theoretically the osmotic pressure (II) of a gel, let us start with Flory s formula [2] in which II is written as a sum of three contributions ... 

The historical development of chemical equilibrium has been described in several reviews (e.g., Berger, 1997 Laidler, 1985 Lindauer, 1962 Lund, 1965, 1968). The concept of chemical equilibrium was introduced in the 1860s in the context of empirical studies of incomplete and reversible chemical conversions. Explanations for these phenomena were formulated on the basis of two essentially different theoretical perspectives, a kinetic framework and a thermodynamic framework. 

Within a thermodynamic framework, a qualitative explanation for equilibrium phenomena was first put forward by Horstmann (1873). He used the Second Law of Thermodynamics as a starting point to reason that, in a state of chemical equilibrium, the entropy of a system was at a maximum. In his view, molecular processes merely influenced the time it takes to reach a state of equilibrium. Horstmann discussed his explanation with Pfaundler (1867), the two accepting the validity of each other s theories, but differing in their view of the importance of these theories to provide a causal explanation for chemical equilibrium (Snelders, 1977). In later years quantitative formulations for chemical equilibrium were derived on the basis... 

Bakshi B.R. 2000. A thermodynamic framework for ecologically conscious process systems engineering, Comput. Chem. Eng., 24, 1767-1773. 

Mdlek, J., Rajagopal, K.R. A thermodynamic framework for a mixture of two liquids. Nonlinear Anal. Real World Appl. 9, 1649-1660 (2008)... 

Kannan, K., Rajagopal, K.R. A thermodynamical framework forchemicaUy reacting systems. Z. Angew. Math. Phys. 62(2), 331-363 (2011)... 

In order to calculate the equOibrium composition of a system consisting of one or more phases in equilibrium with an aqueous solution of electrolytes, a review of the basic thermodynamic functions and the conditions of equilibrium is important, This is particularly true inasmuch as the study of aqueous solutions requires consideration of chemical and/or ionic reactions in the aqueous phase as well as a thermodynamic framework which is, for the most part, quite different from those definitions associated with nonelectrolytes. Therefore, in this section we will review the definition of the basic thermodynamic functions, the partial molar quantities, chemical potentials, conditions of equilibrium, activities, activity coefficients, standard states, and composition scales encountered in describing aqueous solutions. 

The Young, Wenzel, and Cassie equations wete deduced on the basis of simple semi-empirical considerations. Later investigations put these equations into a thermodynamic framework, however, they also showed that thete is no one single... 

---