Saturated condition

As we have already observed, the vapor-pressure-temperature curve is nonlinear. To reduce this curve to a linear form, a plot of log (p ) versus (1/T) can be made for moderate temperature intervals. The resultant straight line is described by the following expression, which can be derived from the Clausius-Clapeyron equation. 

Equation 2.1 describes the change of a substance s vapor pressure with temperature. The intercept C depends on the specific substance. 

An equation for the change of vapor pressure with total pressure at constant temperature is as follows  

Under normal conditions this effect can be neglected. 

The molecules of water vapor are free to migrate randomly in all directions. If in a closed vessel, the molecules will eventually distribute themselves throughout the entire volume of the container. 

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Many other mixed-feed arrangements are possible which combine the individual advantages of each type of arrangement. Figure 3.13 shows a three-stage evaporator in temperature-enthalpy terms, assuming that inlet and outlet solutions are at saturated conditions... 

Figure 6.25a shows the same grand composite curve with two levels of saturated steam used as a hot utility. The steam system in Fig. 6.25a shows the low-pressure steam being desuperheated by injection of boiler feedwater after pressure reduction to maintain saturated conditions. Figure 6.256 shows again the same grand composite curve but with hot oil used as a hot utility. 

The output from the turbine might be superheated or partially condensed, as is the case in Fig. 6.32. If the exhaust steam is to be used for process heating, ideally it should be close to saturated conditions. If the exhaust steam is significantly superheated, it can be desuperheated by direct injection of boiler feedwater, which vaporizes and cools the steam. However, if saturated steam is fed to a steam main, with significant potential for heat losses from the main, then it is desirable to retain some superheat rather than desuperheat the steam to saturated conditions. If saturated steam is fed to the main, then heat losses will cause excessive condensation in the main, which is not desirable. On the other hand, if the exhaust steam from the turbine is partially condensed, the condensate is separated and the steam used for heating. 

Solution The fraction of liquid vaporized on release is calculated from a heat balance. The sensible heat above saturated conditions at atmospheric pressure provides the heat of vaporization. The sensible heat of the superheat is given by... 

From steam tables, the outlet temperature is 251°C, which is superheated by 67°C. Although steam for process heating is preferred at saturated conditions, it is not desirable in this case to desuperheat by boiler feedwater injection to bring to saturated conditions. If saturated steam is fed to the main, then the heat losses from the main will cause a large amount of condensation in the main, which is undesirable. Hence it is better to feed steam to the main with some superheat to avoid condensation in the main. 

In equation (Cl.4.14) the saturation parameter essentially defines a criterion to compare the time required for stimulated and spontaneous processes. If I then spontaneous coupling of the atom to the vacuum modes of the field is fast compared to the stimulated Rabi coupling and the field is considered weak. If s" 1 then the Rabi oscillation is fast compared to spontaneous emission and the field is said to be strong. Setting s equal to unity defines the saturation condition... 

Quicklime and hydrated lime are reasonably stable compounds but not nearly as stable as their limestone antecedents. Chemically, quicklime is stable at any temperature, but it is extremely vulnerable to moisture. Even moisture in the air produces a destabilizing effect by air-slaking it into a hydrate. As a result, an active high calcium quicklime is a strong desiccant (qv). Probably hydrate is more stable than quicklime. Certainly hydrated lime is less perishable chemically because water does not alter its chemical composition. However, its strong affinity for carbon dioxide causes recarbonation. Dolomitic quicklime is less sensitive to slaking than high calcium quicklime, and dead-burned forms are completely stable under moisture-saturated conditions. 

Syneresis of sodium silicate gels may occur under some conditions, eg, in pure gels or coarse formations. Cement grouting should then precede chemical grouting. Leaching that results from dissolution under water-saturated conditions may be eliminated by use of proper reagent proportions. 

Liquid Heat Capacity The two commonly used liqmd heat capacities are either at constant pressure or at saturated conditions. There is negligible difference between them for most compounds up to a reduced temperature (temperature/critical temperature) of 0.7. Liquid heat capacity increases with increasing temperature, although a minimum occurs near the triple point for many compounds. 

Constant-rate Period In the constant-rate period moisture movement within the sohd is rapid enough to maintain a saturated condition at the surface, and the rate of diying is controlled by the rate of heat transferred to the evaporating surface. Drying proceeds by diffusion of vapor from the saturated surface of the material across a... 

Temperature The waste gas entering a condensation scrubber is generally cooled to saturation conditions, approximately 20 to 26°C (68 to 78°F). 

Condensation scrubbing is a relatively recent development in wet scrubber technology. Most conventional scrubbers rely on the mechanisms of impaction and diffusion to achieve contact between the PM and liquid droplets. In a condensation scrubber, the PM act as condensation nuclei for the formation of droplets. Generally, condensation scrubbing depends on first establishing saturation conditions in the gas stream. Once saturation is achieved, steam is injected into the gas stream. The steam creates a condition of supersaturation and leads to condensation of water on the fine PM in the gas stream. The large condensed droplets are then removed by one of several conventional devices, such as a high efficiency mist eliminator. 

Saturation efficiency A measure of the performance of an air washer. It is the amount of water added to the air leaving the washer expressed as a percentage of the amount of water that would have been added if the air had left the washer in a fully saturated condition. 

Electrolytic method This procedure is also known as the Williams Corfleld test d. It is based on loss of metal from iron electrodes buried in a water-saturated soil through which current from a 6-V battery is passed. It does not reflect field conditions and depends upon soil conductance under saturated conditions. 

The boiling point is limited by the critical temperature at the upper end, beyond which it cannot exist as a liquid, and by the triple point at the lower end, which is at the freezing temperature. Between these two limits, if the liquid is at a pressure higher than its boiling pressure, it will remain a liquid and will be subcooled below the saturation condition, while if the temperature is higher than saturation, it will be a gas and superheated. If both liquid and vapour are at rest in the same enclosure, and no other volatile substance is present, the condition must lie on the saturation line. 

Refrigeration compressors which will probably be used on flooded evaporators (R.717 and the larger machines generally) will be rated with the suction at saturated conditions, since there will be little or no superheat in practice. Compressors for dry expansion systems may be rated at a stated amount of superheat, commonly 8 K. 

The direct measurement of the numeric value of and therefore the calculation of often requires im-practically high concentrations of substrate to achieve saturating conditions. A linear form of the Michaelis-Menten equation circumvents this difficulty and permits and to be extrapolated from initial velocity data obtained at less than saturating concentrations of substrate. Starting with equation (29),... 

Some guidelines have been provided for defining the metastable region. If the seed crystals dissolve when added to the metastable solution, this implies that saturation conditions have not been reached. If the addition of the seed leads to the formation of an oil dispersion, it may be concluded that supersaturation has been realized (Anderson, 2000). 

Electroosmotic soil processing is an in situ separation/removal technique for extracting heavy metals and organic contaminants from soils.17 55 89 The fluid between the soil particles moves because a constant, low DC current is applied through electrodes inserted into the soil mass. The electroosmosis (EO) remedial method provides an advantage over conventional pumping techniques for in situ treatment of contaminated fine-grained soils and is more efficient in saturated conditions. 

The fifth factor is the water content of the soil. Electroosmotic flow is promoted at higher water contents. Therefore, high moisture content, and in particular saturated conditions are favored. However, the technique can be used in partially saturated deposits by supplying a pore fluid at... 

Adsorption-desorption Partly Mechanisms for adsorption on similar materials will be similar. Soil adsorption data generally do not reflect the saturated conditions of the deep-well environment. Organic-matter content is a major factor affecting adsorption in the near-surface its significance in the deep-well environment is less clear. Fate studies involving artificial recharge are probably useful, but differences between fresh waters and deep brines may reduce relevance. 

Care should be exercised in using the coefficients from Table 4.14 to predict two-liquid phase behavior under subcooled conditions. The coefficients in Table 4.14 were determined from vapor-liquid equilibrium data at saturated conditions. 

To solve Equation 9.50, start by assuming a feed condition such that q can be fixed. Saturated liquid feed (i.e. q = 1) is normally assumed in an initial design as it tends to decrease the minimum reflux ratio relative to a vaporized feed. Liquid feeds are also preferred because the pressure at which the column operates can easily be increased if required by pumping the liquid to a higher pressure. Increasing the pressure of a vapor feed is much more expensive as it requires a compressor rather than a pump. Feeding a subcooled liquid or a superheated vapor brings inefficiency to the separation as the feed material must first return to saturated conditions before it can participate in the distillation process. 

The second column in the distillation train of an aromatics plant is required to split toluene and ethylbenzene. The recovery of toluene in the overheads must be 95%, and 90% of the ethylbenzene must be recovered in the bottoms. In addition to toluene and ethylbenzene, the feed also contains benzene and xylene. The feed enters the column under saturated conditions at a temperature of 170°C, with component flowrates given in Table 9.10. Estimate the mass balance around the column using the Fenske Equation. Assume that the K-values can be correlated by Equation 9.68 with constants A , 5 and C, given in Table 9.10. 

Figure 12.34 The two-phase region can be plotted from correlations fitted to VLE or LLE data, and can be plotted at saturated conditions or at a fixed temperature.

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