Vaporization thermodynamic basis

The method proposed in this monograph has a firm thermodynamic basis. For vapo/-liquid equilibria, the method may be used at low or moderate pressures commonly encountered in separation operations since vapor-phase nonidealities are taken into account. For liquid-liquid equilibria the effect of pressure is usually not important unless the pressure is very large or unless conditions are near the vapor-liquid critical region. 

Discusses the thermodynamic basis for computer calculations for vapor-liquid equilibria computer programs are given. Now out of date. 

The fugacity of a pure liquid or solid can be defined by applying Eq. si.4 to the vapor in equilibrium with the substance in either condensed phase. Usually, the volume of the vapor will follow the ideal gas equation of state very closely, and the fugacity of the vapor may be set equal to the equilibrium vapor pressure. The thermodynamic basis of associating the fugacity of a condensed... 

Interaction characteristics in polymer-related areas frequently make use of solubility parameters (16). While the usefulness of solubility parameters is undeniable, there exists the limitation that they need to be estimated either by calculation or from indirect experimental measurements. The thermodynamic basis of IGC serves a most useful purpose in this respect by making possible a direct experimental determination of the solubility parameter and its dependence on temperature and composition variables. Price (17) uses IGC for the measurement of accurate % values for macromolecule/vapor pairs, which are then used for the evaluation of solubility parameters for a series of non-volatile hydrocarbons, alkyl phthalates, and pyrrolidones. It may be argued that IGC is the only unequivocal, experimental route to polymer solubility parameters, and that its application in this regard may further enhance the practical value of that parameter. Guillet (9) also notes the value of IGC in this regard. 

Several other vapor pressure-temperature relationships of a more complicated character have been proposed from time to time, but as these have no obvious thermodynamic basis or significance they will not be considered here. It may be mentioned, however, that if the experimental vapor pressure data can be expressed with some accuracy as an empirical function of the temperature, for example of the form... 

Chapters 2-5 deal with chemical engineering problems that are expressed as algebraic equations - usually sets of nonlinear equations, perhaps thousands of them to be solved together. In Chapter 2 you can study equations of state that are more complicated than the perfect gas law. This is especially important because the equation of state provides the thermodynamic basis for not only volume, but also fugacity (phase equilibrium) and enthalpy (departure from ideal gas enthalpy). Chapter 3 covers vapor-liquid equilibrium, and Chapter 4 covers chemical reaction equilibrium. All these topics are combined in simple process simulation in Chapter 5. This means that you must solve many equations together. These four chapters make extensive use of programming languages in Excel and MATE AB. 

Despite widespread use of the ideal K-value concept in industrial calculations, particularly during years prior to digital computers, a sound thermodynamic basis does not exist for calculation of the fugacity coefficients for pure species as required by (4-85). Mehra, Brown, and Thodos discuss the fact that, for vapor-liquid equilibrium at given system temperature and pressure, at least one component of the mixture cannot exist as a pure vapor and at least one other component cannot exist as a pure liquid. For example, in Fig. 4.3, at a reduced pressure of 0.5 and a reduced temperature of 0.9, methane can exist only as a vapor and toluene can exist only as a liquid. It is possible to compute vl or f v for each species but not both, unless vl = vy, which corresponds to saturation conditions. An even more serious problem is posed by species whose critical temperatures are below the system temperature. Attempts to overcome these difficulties via development of pure species fugacity correlations for hypothetical states by extrapolation procedures are discussed by Prausnitz. ... 

Thus, like ebulliometry or cryoscopy, the method would have a strong thermodynamic basis if heat transfer other than that due to vapor condensation could be prevented. Vapor and drop are, however, in contact with one another, and the temperature thus tends to equilibrate in time by convection, radiation, and conduction. This again causes renewed condensation of solvent vapor, which proceeds until a final steady state with a temperature difference A r is reached. Equation (9-25) becomes, with AT = A Ttn ... 

Equation (5.2-3) iHovides a rigonous thermodynamic basis for the prediction of the vapor-liquid equilibrium ratio. Sometimes k can be simpliiied, as the following special cases denMnstiate ... 

The introductory Section 3.1.2.5 in Chapter 3 identifies the negative chemical potential gradient as the driver of targeted separation, and the relevant species flux expression is developed in Section 3.1.3.2 (see Example 3.1.9 also). Section 3.1.4 introduces molecular diffusion and convection and basic mass-transfer coefficient based flux expressions essential to studies of distillation and other phase equilibrium based separation processes. Section 3.1-5.1 introduces the Maxwell-Stefan equations forming the basis of the rate based approach of analyzing distillation column operation. After these fundamental transport considerations (which are also valid for other phase equilibrium based separation processes), we encounter Section 3.3.1, where the equality of chemical potential of a species in all phases at equilibrium is illustrated as the thermodynamic basis for phase equilibrium (Le. = /z ). Direct treatment of distillation then begins in Section 3.3.7.1, where Raouit s law is introduced. It is followed by Section 3.4.1.1, where individual phase based mass-transfer coefficients are reiated to an overall mass-transfer coefficient based on either the vapor or liquid phase. 

Almost all of the directly measured thermochemical data for the sulfoxides, sulfones, sulfites and sulfates are due to the work of Busfield and Mackle and their coworkers at the University of Leeds and The Queens University, Belfast1-14. This work involved measurement of enthalpies of combustion, fusion and vaporization. It is the basis of the subsequent compilations of Benson and coworkers15, Cox and Pilcher16 and Pedley, Naylor and Kirby11. The data given by the latter are used as the basic data set in the present work. Corrections and omissions are noted in the next section. Data on additional compounds were sought by searching the IUPAC Bulletin of Thermochemistry and Thermodynamics for the years 1980 198318, and by searches of Chemical Abstracts. 

This paper reviews data on certain thermodynamic aspects of the nonstoichiometric Pu-0 system, which may serve as a basis for use In reactor safety analysis. Emphasis Is placed on phase relationships, vaporization behavior, oxygen-potential measurements, and evaluation of pertinent thermodynamic quantities. Limited high temperature oxygen potential data obtained above the fluorite, diphasic, and sesquioxide phases In the Pu-0 system are presented. 

A homogeneous flow basis must be used when thermodynamic equilibrium is assumed. For furtl er simplification it is assumed there will be no reaction occurring in the pipeline. The vapor and liquid contents of the reactor are assumed to be a homogeneous mass as they enter the vent line. The model assumes adiabatic conditions in the vent line and maintains constant stagnation enthalpy for the energy balance. 

Equation 4.26 defines the relationship between the vapor and liquid mole fractions and provides the basis for vapor-liquid equilibrium calculations on the basis of equations of state. Thermodynamic models are required for (/) and [ from an equation of state. Alternatively, Equations 4.21, 4.22 and 4.25 can be combined to give... 

In developing the thermodynamic framework for ECES, we attempted to synthesize computer software that would correctly predict the vapor-liquid-solid equilibria over a wide range of conditions for multicomponent systems. To do this we needed a good basis which would make evident to the user the chemical and ionic equilibria present in aqueous systems. We chose as our cornerstone the law of mass action which simply stated says "The product of the activities of the reaction products, each raised to the power indicated by its numerical coefficient, divided by the product of the activities of the reactants, each raised to a corresponding power, is a constant at a given temperature. ... 

The experimental basis of sorption studies includes structural data (SANS, SAXS, USAXS), isopiestic vapor sorption isotherms,i and capillary isotherms, measured by the method of standard porosimetry. i 2-i44 Thermodynamic models for water uptake by vapor-equilibrated PEMs have been suggested by various groupThe models account for interfacial energies, elastic energies, and entropic contributions. They usually treat rate constants of interfacial water exchange and of bulk transport of water by diffusion and hydraulic permeation as empirical functions of temperature. 

The Soave modification of the Redlich-Kwong equation is the basis for the fourth thermodynamic properties method. This equation of state is applied to both liquid and vapor phases. Binary interaction coefficients for these applications are from Reid-Prausnitz-Sherwood (13) and the mathematical derivations used here are from Christiansen-Michelson-Fredenslund (14). Temperature and composition derivatives of the thermodynamic functions are included in the later work. These have applications in multistage calculations. 

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