Thermodynamic Properties of a Gas-Solid Mixture

The analysis of a multiphase flow system is complex, in part because of the difficulties in assessing the dynamic responses of each phase and the interactions between the phases. In some special cases, the gas-solid mixture can be treated as a single pseudo-homogeneous phase in which general thermodynamic properties of a gas-solid mixture can be defined. This treatment provides an estimate for the bulk behavior of the gas-solid flow. The following treatment is based on the work of Rudinger (1980). 

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This chapter addresses the various phenomena indicated. In addition, the thermodynamic laws governing physical properties of the gas-solid mixture such as density, pressure, internal energy, and specific heat are introduced. The thermodynamic analysis of gas-solid systems requires revisions or modifications of the thermodynamic laws for a pure gas system. In this chapter, the equation of state of the gas-solid mixture is derived and an isentropic change of state is discussed. 

In many processes, we are concerned with mixtures, i.e., gas, liquid or solid solutions, and hence we are concerned with the thermodynamic properties of a component in a solution - partial molar quantities ... 

In 1952 James and Martin [12] replaced the liquid mobile phase with a gas phase two new chromatographic techniques were developed gas-liquid and gas-solid chromatography. This led to an unprecedented development in the analytical and preparative separation of mixtures and then, from 1969 [13,14], it allowed the determination of structure and morphology of stationary phases especially polymers and, from 1971 [15], the determination of the thermodynamic properties of polymer solutions. 

Table 16.7 lists selected physical properties of SO3. In the gas phase, it is an equilibrium mixture of monomer (planar molecules, 16.45, S-0= 142 pm) and trimer. Resonance structures 16.46 are consistent with three equivalent S—O bonds, and with the S atom possessing an octet of electrons. Solid SO3 is polymorphic, with all forms containing SO4-tetrahedra sharing two oxygen atoms. Condensation of the vapom at low temperatures yields y-SO which contains trimers (Fig. 16.17a) crystals of y-S03 have an ice-like appearance. In the presence of traces of water, white crystals of P-SO3 form P-SO3 consists of polymeric chains (Fig. 16.17b), as does a-S03 in which the chains are arranged into layers in the solid state. Differences in the thermodynamic properties of the different polymorphs are very small, although they do react with water at different... 

If surface equilibrium prevails, then it is relatively straightforward to generalize the interface condition to chemical processes that are more complex than equations (1) and (8). This of interest, since propellant materials often experience processes of this type for example, NH4CIO4 undergoes dissociative sublimation into NH3 and HCIO4 [33]. For a general process in which the condensed material is transformed to 1 the surface equilibrium condition (for an ideal gas mixture and a solid whose thermodynamic properties are independent of pressure) is... 

Whether the adsorption isotherm has been determined experimentally or theoretically from molecular simulation, the data points must be fitted with analytical equations for interpolation, extrapolation, and for the calculation of thermodynamic properties by numerical integration or differentiation. The adsorption isotherm for a pure gas is the relation between the specific amount adsorbed n (moles of gas per kilogram of solid) and P, the external pressure in the gas phase. For now, the discussion is restricted to adsorption of a pure gas mixtures will be discussed later. A typical set of adsorption isotherms is shown in Figure 1. Most supercritical isotherms, including these, may be fit accurately by a modified virial equation. ... 

In Chapter 4, we dealt with the thermodynamic, physical and chemical properties of pure liquids. However, in most instances solutions of liquids are used in chemistry and biology instead of pure liquids. In Chapter 5, we will examine the surfaces of mainly nonelectrolyte (ion-free) liquid solutions where a solid, liquid or gas solute is dissolved in a liquid solvent. A solution is a one-phase homogeneous mixture with more than one component. For a two-component solution, which is the subject of many practical applications, the major component of the solution is called the solvent and the dissolved minor component is called the solute. Liquid solutions are important in the chemical industry because every chemical reaction involves at least one reactant and one product, mostly forming a single phase, a solution. In addition, the understanding of liquid solutions is useful in separation and purification of substances. 

Of these featores, the pressure-dependence of SCF properties dominates or influences virtually every process conducted on polymers. Pressure governs such properties as density, solubility parameter, and dielectric constant changes of more than an order of magnitude are common when pressure is sufficiently increased to transform a gas into a supercritical fluid. This chapter primarily compiles experimental data on the pressure dependence of physical properties of fluid phase polymer-SCF mixtures. Phase equilibria are addressed, including the solubility of polymers in SCFs, the solubility of SCFs in liquid polymers, and the three-phase solid-fluid-fluid equilibria of crystalline polymers saturated with SCFs. Additional thermodynamic properties include glass transition temperature depressions of polymers, and interfacial tension between SCF-swollen polymers and the SCF. The viscosity of fluid phase polymer-SCF mixtures is also treated. 

The principles of IGC, as a gas-phase technique used to characterize the surface and bulk properties of solid materials, are very simple as the process is the reverse of conventional gas chromatography. Typically, an empty cylindrical column is uniformly packed with the solid material of interest, normally a powder, fiber, or film. A pulse or constant concentration of gas is then injected down the column at a fixed carrier gas flow rate, and the retention behavior of the pulse or concentration front is measured with a detector (Figure 10.1). The retention of a solvent or probe molecule on the material is recorded and the measurement is made effectively at an inflnite dilution of the probe. A range of thermodynamic parameters can then be calculated. A major advantage of IGC is that it is readily applicable to mixtures of two or more polymers. 

Precise control and monitoring of the oxygen pressure in the experimental chamber is required for the determination of thermodynamic and transport properties in MIECs. Electrochemical devices have been developed since more than thirty years, allowing the control of the oxygen pressure in the 1 - 10-27 p,aj. range in various gas mixtures or under partial vacuum. Solid electrolyte micropjrobes have also been proposed for the local determination of the oxygen activity on the surface of a non-stoichiometric oxide. 

Thermodynamics has the remarkable ability to connect seemingly unrelated properties. For example, the temperature coefficient of adsorption is directly proportional to the heat of immersion of the solid adsorbent in the gas. The most important application of thermodynamics to adsorption is the calculation of phase equilibrium between a gaseous mixture and a solid adsorbent. 

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