Vapor pressure, curves defined

The phase envelope of a mixture is analogous to the vapor pressure curve of a pure component. The vapor pressure curve defines temperature and pressure conditions at which a pure component can exist as vapor and liquid at equilibrium. In this two-phase regime only one parameter, the temperature or the pressure, may be varied independently. 

To extend the PCS correlation to fluids other than the simple fluids, it is observed that deviation from the PCS correlation of the simple fluids occurs in a systematic way, depending on the shape, size, and chemical nature of the molecule. A prominent example is the reduced vapor pressure p as a function of the reduced temperature T. Although it is almost exactly the same function for the three simple fluids, the reduced-vapor-pressure lines of other substances are lower with more elongated or more polar molecules. Pitzer and Brewer [1] adopt the lowering of the reduced-vapor-pressure curve of a substance from that of the simple fluids as the basis for defining a parameter to extend the PCS correlation to substances other than simple fluids. At the reduced temperature of... 

A very effective third constant is the acentric factor introduced by Pitzer et al. It is widely used in thermodynamic correlations based on the theorem of corresponding states. The acentric factor accounts for differences in molecular shape and is defined by the vapor pressure curve as... 

The saturated vapor-air mixtures curve in Figure 20 is the vapor pressure curve expressed in terms of the combustible concentration rather than the partial pressure. The lower limit and upper limit curves refer to the combustible concentrations that define the flammable mixtures zone. Lower-limit mixtures contain less, and upper-limit mixtures more, than the concentration of combustible required... 

An increase in the boiling point or a decrease in the freezing point of a solution containing a nonvolatile component is compared to pure solvent caused by a reduction in the vapor pressure. The reduction of the freezing point AT of a solution is T — T, as shown in Fig. 1-42 where T is the freezing point (or melting point) of the pure solvent. At Tg the vapor pressure is the same for the liquid and solid phases of the solvent. Tg is defined by the intersection A of the vapor pressure curve VC and the sublimation pressure curve SC of the solvent. If only pure solvent freezes, the freezing point T of the solution occurs at the intersection B of the vapor pressure curve of the solution VCS and the sublimation pressure curve of the solvent SC. 

The introduction of the acentric factor co as defined above adds the information on the reduced vapor pressure at the reduced temperature Tr = 0.7 to the equation of state. The acentric factor can be illustrated in a log — 1/Tr diagram as shown in Figure 2.16. The diagram shows the vapor pressure curve of the simple fluids (Ar, Kr, Xe) and the vapor pressure curve of ethanol, both in their reduced form. 1 he... 

As discussed in Section 2.5.4, the simple two-parameter corresponding states principle indicates that a generalized equation of state for all substances can be created using only two specific parameters, for example, T, and P. The success of this approach is restricted to simple, spherical molecules like Ar, Kr, Xe, or CH4, where vapor pressure and compressibility factor can be reasonably described. For other molecules, the simple two-parameter corresponding states principle leads to significant errors. A large improvement has been achieved with the introduction of a third parameter which describes the vapor pressure curve (extended three-parameter principle of corresponding states). The most common parameter of this kind is the so-called acentric factor, which is defined as... 

Although estimation methods for the acentric factor are available (e.g., group contribution method of Constantinou and Gani [11]), this concept is not recommended, as an estimation of co would only be a redundancy of the normal boiling point estimation. To avoid inconsistencies, it is recommended that co is always calculated by its defining equation 2.157. If the vapor pressure curve is unknown, the normal boiling point and the critical point can be estimated, and the Hoffmann-Florin equation or the Rarey/Moller method (Section 3.2.1) can be used to calculate the vapor pressure curve. 

Relative saluration. Relatiiie saturation, also called r ladmJitmudiiyi expressed as a percentage is defined as lOOp // , where is the vapor pressure at the dry-bulb temperature of the mixture. For any vapor, the graphical representation of conditions of constant relative saturation can easily be constructed on a vapor-pressure-temperature chart, as in Fig. lAa, by dividing the ordinates of the vapor-pressure curve into appropriate intervals. Thus the curve for 50 percent relative saturation shows a vapor partial pressure equal to one-half the equilibrium vapor pressure at any temperature. A reference-substance plot, such as Fig, 7.2, could also be used for this. 

Since the contents of a storage tank for liquid hydrogen will always be a saturated liquid from the constant heat leak into the tank, the fluid at the inlet of the pump may be expected to be substantially at the vapor pressure curve shown in Figure 1 as point 1. This results in little, or perhaps no Net Positive Suction Head, NPSH, at the pump inlet. (The latter is defined as the total head above the vapor pressure in feet of liquid.)... 

A comparison of the liquid temperatures and pressures with the equilibrium values indicated that, immediately after venting, the liquids were superheated the temperatures were higher than indicated by equilibrium conditions. As the pressure increased, the bulk-liquid temperature also increased, but at a rate considerably lower than indicated by equilibrium (saturated) conditions. Stratification of the liquid temperatures provided a surface condition which within a short time followed the equilibrium vapor-pressure curve, while the bulk of the liquid became subcooled. The liquid-surface locations were not well defined but the level measurements (capacitance) indicated that the surface was around the 20-in. height at the beginning. The vapor temperature increased from about 43 to 46.5 R during the pressure rise without any major fluctuations. 

The solubility is defined with respect to a second precipitated phase. The solubility of an impurity is the maximum concentration, which can be incorporated in the liquid or solid phase without precipitating a second phase. For most impurities in solid silicon at high-temperatures, equilibrium is achieved with the liquid phase governed by the liquidus in the phase diagram. Solid solubility is temperature-dependent as represented by the solidus or solvent curves in the phase diagram. At lower temperatures, the reference phase is usually a compound or an impurity-rich alloy. When the impurity is volatile, the saturated crystal is in equilibrium with the vapor, and the impurity solubility also depends on its vapor pressure. 

Figure 12.11 shows that lowering the vapor pressure of the solution shifts the solid-liquid curve to the left. Consequently, this line intersects the horizontal line at a temperature lower than the freezing point of water. The freezing point depression (ATf) is defined as the freezing point of the pure solvent (TJ) minus the freezing point of the solution (Tf) ... 

Consequently, it would be expected that the predictive capability of the two models will also be equivalent, and any limitations in terms of prediction of one model will reflect analogous limitations of the other model. Indeed, if the vapor pressure model fails to describe the tailing of the concentration versus time curve - which is an indication of sink effects - the mass transfer model is also unable to describe the same part of the experimental data (Tichenor et al., 1993). It should be noted, however, that the parameters of the mass transfer model have well-defined physical meanings [e.g., vapor pressure (C ), molecular diffusivity (Dy), boundary layer thickness ( )], and the parameter estimation does not rely heavily on curve fitting. The parameter estimation is the first step in the model performance and validation process, as we will see later in this Chapter. 

In a closed vessel, the volume becomes fixed. An input of heat (i.e., an increase in temperature) into a system consisting of liquid and vapor in equilibrium must result in an increase in the vapor pressure. It must happen that with the increase of pressure, the density of the vapor increases, while with the corresponding increase in temperature, the density of the liquid decreases. At some temperature value, the densities of the liquid and vapor will become identical, and at that point the heterogeneous system becomes homogeneous. At this critical point (defined by a critical temperature and a critical pressure), the entire system passes into one homogeneous phase. The vaporization curve must terminate at the critical point, unless there are accessible metasta-... 

A solid substance in equilibrium with its vapor phase will exhibit a well-defined vapor pressure for a given temperature, which will be independent of the relative amounts of solid and vapor present. The curve representing the solid/vapor equilibrium conditions is termed a sublimation curve, which generally takes a form similar to that of a vaporization curve. Although the sublimation pressure of a solid is often exceedingly small, for many substances it can be considerable. 

The point at which the sublimatiOTi, boiling, and melting pressure curves all converge is called the triple point because at the conditions of temperature and pressure there, the substance is simultaneously in a solid, liquid, and gaseous state. At the triple point both pressure and temperature are characteristic properties of a pure substance. The triple point of water, for example, is at 273.16 K and 611 Pa. Only at this exact temperature and this exact pressure are ice, liquid water, and water vapor in equilibrium with each other. This triple point is used to define the unit called Kelvin (compare Sect. 3.8). If the pressure at the triple point lies noticeably above 100 kPa, the liquid state cannot exist no matter what the temperature, and only sublimation can be observed. An example of this is carbon dioxide (217 K, 518 kPa), which, when exposed to air, changes directly from solid to gas (so it is called dry ice ). 

Supercritical fluids are defined as a fluid at a pressure above the critical pressure and a temperature above the critical temperature. Below the critical point, the vapor-the pressure curve separates the Hquid and gaseous phase. The vapor pressure ends up at the critical point. Beyond the critical point, the density of the fluids can be varied continuously from liquid-hke to gas-like values without phase transition. This variability of density corresponds to diversity of properties. Supercritical fluids are tunable solvents [26] for which the properties can be adjusted as a function of temperature and pressure. This chapter focuses on the utilization of supercritical CO2 and water. The properties of these two supercritical fluids will now be introduced. 

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