Vaporization curve

Thermodynamic and mechanical equilibrium on a curved vapor-liquid interface requires a certain degree of superheat in order to maintain a given curvature. Characteristics of homogeneous and heterogeneous nucleation can be estimated in the frame of classical theory of kinetics of nucleation (Volmer and Weber 1926 Earkas 1927 Becker and Doring 1935 Zel dovich 1943). The vapor temperature in the bubble Ts.b can be computed from equations (Bankoff and Flaute 1957 Cole 1974 Blander and Katz 1975 Li and Cheng 2004) for homogeneous nucleation in superheated liquids... 

Within the PV region delimited by the two saturation boundary curves, liquid and vapor phases coexist stably at equilibrium. To the right of the vapor saturation curve, only vapor is present to the left of the liquid saturation curve, vapor is absent. Let us imagine inducing isothermal compression in a system composed of pure H2O at T = 350 °C, starting from an initial pressure of 140 bar. The H2O will initially be in the gaseous state up to P < 166 bar. At P = 166 bar, we reach the vapor saturation curve and the liquid phase begins to form. Any further... 

For continuous systems, molar flow rates Q can be used instead of n. The thermodynamic activity (ax) can be calculated according to Equation 2, but requires knowledge of the saturation pressure of the pure compound (Ppsatx). This data can be obtained from the saturation curves (vapor-liquid equilibrium curves) and is taken at the working temperature of the gas stream. The thermodynamic activity is then calculated using the following equation ... 

In order to determine the endpoint of the process, many procedures have been suggested, including pressure rise measurement, the Karl Fischer method, weight curves, vapor tension, moisture equilibration, nuclear magnetic resonance, and dielectric measurement. 

Fig. 4 Comparative study of transverse magnetoresistance at low temperature (as indicated in parentheses) for highly oriented pyrolytic graphite (the dot-dash curve), typical MPCFs heat treated at different temperatures (the solid curves), VGCFs (the dashed curve), and MWNTs (the dotted curve). Vapor-grown carbon fibers exhibit a similar magnetoresistance behavior to that of MWNTs.

Energy and Phase Changes Heating Curves Vapor Pressure Phase Diagrams The Solid State... 

For a single-component, two-phase system such as a liquid and vapor of the same substance, the relationship between the vapor pressure p, and temperature is usually of the form shown in Fig. 9.1. The region to the right of the curve represents unsaturated vapor, whereas the region to the left represents liquid underpressure. Along the curve, vapor and liquid coexi.st in equilibrium. Similar considerations apply to solid-vapor equilibria. 

Boiling Pressure Curve (Vapor Pressure Curve)... 

Another important projection of the PvT-diagram is the PT-graph (see Figure 2.5). In this projection, the dew-point line coincides with the boiling point in the vapor pressure curve. Similarly, solidus and liquidus curve coincide in the melting curve. The phase transition between the solid state and the gaseous state is described by the sublimation curve. Vapor pressure curve, melting curve, and sublimation curve meet at the triple point, where the three phases vapor, liquid, and solid coexist in equilibrium. The triple point of water is very well known and can be reproduced in a so-called triple point cell. It is used as a fix point of the International Temperature Scale ITS-90 [4] (Tt, = 273.16 K or = 0.01"C, Ptr = 611.657 0.01 Pa). The vapor pressure curve ends at the critical point no liquid exists above the critical temperature T. ... 

Values of Cp, Cy, internal energy E, enthalpy H, and entropy S of the real gas are also available from calculations using reference values for the ideal gas and a modified Benedict-Webb-Rubin equation of state, the melting curve, vapor and liquid density curves, and the vapor pressure curve mentioned above. They are parameterized in the same way (along coexistence lines and isochores) as the pgT data, see p. 202 [2]. In a similar manner, H and S were calculated earlier from a Martin-Hou equation of state, see p. 202 [3]. 

Figure 10.6 Hydrothermal processes mapped into a pressure-temperature diagram (solid curve vapor pressure curve of water).

FIGURE 10.7 A series of constant-pressure slices through the equivalent of Figure 10.6, for the ethane- -heptane system. Each pair of curves (e.g., the 400-psia curves) divides the space into liquid (below both curves), vapor-liquid mix (between the curves), and vapor (above the upper curve). (Reprinted with permission from Kay, W. B. Liquid-vapor phase equilibrium relations in the ethane- -heptane system. Ind. Eng. Chem. 30 459-465. Copyright (1938), American Chemical Society.)... 

A graph of vapor pressure as a function of temperature is known as a vapor pressure curve. Vapor pressure curves always have the appearance of those in Figure 12-18 Vapor pressure increases with temperature. Vapor pressures of water at different temperatures are presented in Table 12.5. 

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

The composite curves for this flowsheet are shown in Fig. 14.86. The composite curves are dominated by the reboilers and condensers of the two distillation columns and the feed vaporizer for the acetone feed. It is immediately apparent that the two distillation columns are both inappropriately placed across the pinch. Linnhoflf and Parker ... 

The pressure in distillation column 1 has been increased to allow feed vaporization by heat recovery (from the distillation column condenser). Inspection of the new curves in Fig. 14.9a raises further possibilities. With the proposed modification, the overheads from the... 

At a given temperature and pressure, a pure compound can exist in one, two or three states. The compound exists at three different states at the triple point and at two different states along the curves of vaporization, freezing and sublimation. Refer to Figure 4.6. 

The liquid -vapor equilibria, along the vaporization curve is expressed as ... 

In practice, however, it is recommended to adjust the coefficient m, in order to obtain either the experimental vapor pressure curve or the normal boiling point. The function f T ) proposed by Soave can be improved if accurate experimental values for vapor pressure are available or if it is desired that the Soave equation produce values estimated by another correlation. 

At low temperatures, using the original function/(T ) could lead to greater error. In Tables 4.11 and 4.12, the results obtained by the Soave method are compared with fitted curves published by the DIPPR for hexane and hexadecane. Note that the differences are less than 5% between the normal boiling point and the critical point but that they are greater at low temperature. The original form of the Soave equation should be used with caution when the vapor pressure of the components is less than 0.1 bar. In these conditions, it leads to underestimating the values for equilibrium coefficients for these components. 

The flash curve of a petroleum cut is defined as the curve that represents the temperature as a function of the volume fraction of vaporised liquid, the residual liquid being in equilibrium with the total vapor, at constant pressure. 

The density and the volatility, expressed by the distillation curve and the vapor pressure, constitute the most important physical characteristics of motor fuels for obtaining satisfactory operation of a vehicle in all circumstances. 

The volatility of the fuel is expressed then by the temperature levels for which the V/L ratio is equal to certain particular values for example V/L = 12, V/L = 20, V/L = 36. There are correlations between the temperatures corresponding to these vaporization ratios and the conventional volatility parameters such as the RVP and the distillation curve. 

For optimum combustion, the fuel should vaporize rapidly and mix intimately with the air. Even though the design of the injection system and combustion chamber play a very important role, properties such as volatility, surface tension, and fuel viscosity also affect the quality of atomization and penetration of the fuel. These considerations justify setting specifications for the density (between 0.775 and 0.840 kg/1), the distillation curve (greater than 10% distilled at 204°C, end point less than 288°C) and the kinematic viscosity (less than 8 mm /s at -20°C). 

Composition is normally expressed by a distillation curve, and can be supplemented by compositional analyses such as those for aromatics content. Some physical properties such as density or vapor pressure are often added. The degree of purity is indicated by color or other appropriate test (copper strip corrosion, for example). 

At first we tried to explain the phenomenon on the base of the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary [12]. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. We worked out the mathematical description of both gas-vapor diffusion and evaporation-condensation processes in cone s channel. Solving the system of differential equations for evaporation-condensation processes, we ve derived the formula for the dependence of top s (or inner) liquid column growth on time. But the calculated curves for the kinetics of inner column s length are 1-2 orders of magnitude smaller than the experimental ones [12]. 

The Kelvin equation (Eq. HI-18), which gives the increase in vapor pressure for a curved surface and hence of small liquid drops, should also apply to crystals. Thus... 

Fig. XII-12. Top friction traces for two calcium alkylbenzenesulfonate monolayers on mica where the monolayers are in a liquidlike state. A—in inert air atmosphere B—in saturated decane vapor. Bottom contact radius-load curves showing adhesion energy measured under the same conditions as the friction traces. (From Ref. 53.)...

Thus D(r) is given by the slope of the V versus P plot. The same distribution function can be calculated from an analysis of vapor adsorption data showing hysteresis due to capillary condensation (see Section XVII-16). Joyner and co-woikers [38] found that the two methods gave very similar results in the case of charcoal, as illustrated in Fig. XVI-2. See Refs. 36 and 39 for more recent such comparisons. There can be some question as to what the local contact angle is [31,40] an error here would shift the distribution curve. 

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