Water vapor pressure curves for

Table 13-8 Points on the Vapor Pressure Curve for Water...

Equations (3.72) to (3.74) are solved simultaneously by trial with the vapor-pressure curve for water, which relates and and the latent-heat data. It is easiest to > .. t- which is checked when q, from Eqs. (3.72) and (3.73) agree. 

As mentioned previously, the water content in the catalyst layer will be determined by the extent of drying of the fuel cell before freezing, so the various literature studies may have widely different starting water contents in the catalyst layer. Furthermore, because the saturated vapor pressure curve for water is a strong function of temperature, even cells that operate at undersaturated conditions can exhibit condensation and freezing as the temperature drops after shutdown. It is expected that liquid-water and ice contents will be highest at the periphery of the cell, as the cell should cool first at the outer perimeter, and water will be transported to the coldest regions, condense, and subsequently freeze. 

A glance at the vapor pressure curve for butane will, however, reveal that in winter there is a possibility of butane vapor liquefying after the vaporizer if the temperature is allowed to fall in the pipeline, even at moderate pressure. For this reason, such pipework is usually heated, either by electrical tapes or, if available, by steam or hot-water lines. 

The horizontal line at 101.3 kPa intersects the vapor pressure curve for the solid at -78.5°C. Therefore, solid carbon dioxide sublimes at this temperature. This sublimation point is equivalent to the normal boiling point of a liquid such as water. Because dry ice is at equilibrium with carbon dioxide gas at -78.5°C, it is frequently used to provide this low temperature in the laboratory. 

As explained in Appendix M, you can estimate the values of the coefficients in Eq. (3.32) by the method of least squares. We look at another way, a graphical method. Over very wide temperature intervals experimental data will not prove to be exactly linear as indicated by Eq. (3.31), but have a slight tendency to curve. This curvature can be straightened out by using a special plot known as a Cox chart. The In or logic of the vapor pressure of a compound is plotted against a special nonlinear temperature scale constructed from the vapor-pressure data for water (called a reference substance). 

Figure 3.8 Critical mixture curves for water-normal hydrocarbon mixtures near the critical point of water (Yiling, Michelberger, and Franck, 1991). The solid line is the vapor pressure curve for pure water.

Extensions beyond the data base of (2) are largely untested and include additions to PITZER.DATA for (1) the calculation of the thermodynamic properties of aqueous solutions containing Fe(II), Mn(II), Sr +, Ba2+, Li+, and Br (2) the estimation of the temperature dependence of many of the single-salt parameters from selected literature data and (3) the calculation of the thermodynamic properties of NaCl solutions to approximately 300 °C along the vapor pressure curve of water beyond 100 C (18)-Except for the NaCl-H20 system, the PHRQPITZ aqueous model should not be used outside the temperature range 0 to 60 C. Several recent evaluations of the temperature dependence of Pitzer interaction parameters to relatively high temperatures (19-21) have not yet been incorporated in the PHRQPITZ data base. 

Carbon dioxide gas is relatively nonreactive and nontoxic. It will not burn, and it will not support combustion or life. When dissolved in water, carbonic acid (H2CO3) is formed. The pH of carbonic acid varies from 3.7 at 1 atmosphere to 3.2 at 23.4 atm. Carbon dioxide may exist simultaneously at its triple point as a solid, liquid, and gas at a temperature of -69.9°F (-56.6°C) and a pressure of 60.4 psig (416 kPa). Figure 1 is the vapor pressure curve for carbon dioxide. Figure 2 shows the triple point and full equilibrium curve for carbon dioxide. 

Suppose a solid is warmed at a pressure below the pressure at the triple point. In a phase diagram, this corresponds to moving along a horizontal line below the triple point. You can see from Figure 11.11 that such a line will intersect curve AD, the vapor-pressure curve for the solid. Thus, the solid will pass directly into the gas that is, the solid will sublime. Freeze-drying of a food (or brewed coffee) is accomplished by placing the frozen food in a vacuum (below 0.00603 atm) so that the ice in it sublimes. Because the food can be dried at a lower temperature than if heat-dried, it retains more flavor and can often be reconstituted by simply adding water. 

On a phase diagram, the preceding experiment corresponds to following the vapor-pressure curve where the liquid and vapor are in equilibrium. Note that this curve in Figure 11.12 top ends at a point at which the temperature and pressure have their critical values. This is the critical point. If you look at the phase diagram for water, you will see that the vapor-pressure curve for the liquid similarly ends, at point C, which is the critical point for water. In this case, the critical temperature is 374°C and the critical pressure is 218 atm. 

Figure4.4 shows the possibly simplest of all phase diagrams in the t-v- and in the 1-p-plane. The solid line in the upper diagram is the same as the dashed line, i.e. the phase coexistence curve, in Fig. 4.1. The dotted line is the spinodal. The lower graph shows the phase boundary between gas and liquid in the pressure-temperature plane. Notice that here no coexistence region appears because the pressure is constant throughout this region (at constant t). The crosses are vapor pressure data for water taken from HCP.

Assume that a boiler feed water is being pumped at 180 °F. Read the chart in Figure 3-46 and the water vapor pressure curve, and follow over to read NPSH reduction = 0.45 feet. A pump selected for the sertice requires 6 feet cold water service NPSHr ... 

The only parts of Fig. 5 which can meaningfully be described as solubility in a compressed gas are WX and XV. However, a very different situation arises if the saturated vapor pressure curve cuts the critical curve (M—N of Fig. 3). Figure 4 shows that this does not happen for the three sodium halides. The complete course of the critical curve is not known, but enough is known in the case of the sodium chloride system51 75 for it to be clear that it rises well above the maximum of the saturated vapor pressure curve. However, it is cut by the vapor pressure curves of less soluble salts such as sodium carbonate and sodium sulphate.40 87 The (p, T) projection of a system of the type water + sodium chloride is... 

Typically, sorption isotherms are constructed for a single food ingredient or food system. An alternative approach is to plot the moisture content versus water activity (or relative vapor pressure) values for a variety of as is food ingredients and food systems. The result is a composite food isotherm (Figure 17). The composite isotherm fits the typical shape observed for a sorption isotherm for an individual food system, with a few products falling above or below the isotherm curve (chewing gum, honey, raisins, bread, and colby and cheddar cheeses). Slade and Levine (1991) were the first to construct such a plot using moisture content and aw values from van den... 

Table 13.1). In the solid P(CH4) > P(CD4) but the curves cross below the melting point and the vapor pressure IE for the liquids is inverse (Pd > Ph). For water and methane Tc > Tc, but for water Pc > Pc and for methane Pc < Pc- As always, the primes designate the lighter isotopomer. At LV coexistence pliq(D20) < Pliq(H20) at all temperatures (remember the p s are molar, not mass, densities). For methane pliq(CD4) < pLiq(CH4) only at high temperature. At lower temperatures Pliq(CH4) < pliq(CD4). The critical density of H20 is greater than D20, but for methane pc(CH4) < pc(CD4). Isotope effects are large in the hydrogen and helium systems and pLIQ/ < pLiQ and P > P across the liquid range. Pc < Pc and pc < pc for both pairs. Vapor pressure and molar volume IE s are discussed in the context of the statistical theory of isotope effects in condensed phases in Chapters 5 and 12, respectively. The CS treatment in this chapter offers an alternative description.

The pressure-temperature-composition diagram presented by Morey is shown in Fig. 8. The vapor pressure of pure water (on the P-T projection) terminates at the critical point (647 K, 220 bar). The continuous curve represents saturated solutions of NaCl in water, i.e., there is a three-phase equilibrium of gas-solution-solid NaCl. The gas-phase pressure maximizes over 400 bar at around 950 K. Olander and Liander s data for a 25 wt. % NaCl solution are shown, and T-X and P X projections given. At the pressure maximum, the solution phase contains almost 80% NaCl. 

Figure 2.2 Temperature, pressure, and density relations for water substance. The heavy curve corresponds to the saturated vapor pressure of liquid water. Note the extreme sensitivity of density to pressure near the critical temperature.

Figure A2.1.2 Effect of temperature on vapor pressure measurement. The upper curve is the vapor pressure of pure water, pw°. The lower curve is a system whose partial water vapor pressure, pw, is always a constant fraction of the vapor pressure of pure water. See text for details.

Liquid and vapor are at equilibrium along the vapor pressure curves shown for pure water (solid line) and an aqueous solution (dashed line). The vapor pressure is lower for the solution, in accord with Raoult s law, and thus the boiling point is increased (liquids boil at 1 atm)... 

VL(L) E measurements for binaries involving water with alcohol and acid have been done, as described elsewhere [2]. Figure 8.6 presents experimental vapor pressure data for 2-ethylhexyl laurate. The normal boiling point (nbp) is 607.6 K, close to the prediction by Gani s method. On the other hand, the prediction of the whole saturation curve by Riedel s method (noted estimation in Figure 8.6) is in large error at lower pressures. This fact can affect the accuracy of chemical equilibrium calculation, but fortunately the errors compensate each other [2]. 

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