Vapor pressure of water and ice

Vapor Pressure of Water and Ice and Calculation of Humid Air State Values 71... 

Vapor pressure of water and physical states. Pure water can exist in three different physical states solid ice, liquid, and vapor. The physical state in which it exists depends on the pressure and temperature. 

Sublimation temperatures are in the range of —10 to —40°C and corresponding vapor pressures of water are 2.6-0.13 mbar. Cabinet tray dryers are the most commonly used type. The trays are lifted out of contact with hot surfaces so the heat transfer is entirely by radiation. Loading of 2.5 lb/sqft is usual for foodstuffs. Drying capacity of shelf-type freeze dryers is 0.1-1.0kg/(hr)(m2 exposed surface). Another estimate is 0.5-1.61b/(hr)(sqft). The ice surface has been found to recede at the rate of 1 mm/hr. Freeze drying also is carried out to a limited extent in vacuum pans, vibrating conveyors, and fluidized beds. Condensers operate as low as —70°C. 

Improper selection of coolant for a cold trap may artificially limit the potential vacuum of your system. For instance, the vapor pressure of water (which is often the primary condensable vapor in many vacuum systems) is quite high without any cold trapping, moderate at dry-ice temperatures, and negligible at liquid nitrogen temperatures (see Table 7.11). If your vacuum needs are satisfied within a vacuum of 5 x 10"4 torr, you can safely use dry ice (and save money because dry ice is less expensive than liquid nitrogen). Another temperature option for a coolant is the slush bath (for more information on coolants see Sec. 6.2). 

Preparation of Hydrated Silicates. The hydrated silicate specimens used were all in the paste form—that is, mixtures of one of the calcium silicates with a limited amount of water to form a slurry, which sets and hardens as portland cement itself does. These pastes were prepared by the vacuum mixing procedure described by Powers, Copeland, Hayes, and Mann (23), adapted so that the temperature of the mix upon removal from the mixer was the temperature at which the specimen was to be hydrated. The 5° specimens were made by starting with an ice-water mixture the-50° specimens by starting with preheated water. A manostat was incorporated into the pumping system to prevent the pressure from dropping below the vapor pressure of water at the desired final temperature. This was especially important for the 50° mixes, to prevent excessive cooling. 

The melting and boiling points for a substance are determined by the vapor pressures of the solid and liquid states. Figure 16.51 shows the vapor pressures of solid and liquid water as functions of temperature near 0°C. Note that below 0°C the vapor pressure of ice is less than the vapor pressure of liquid water. Also note that the vapor pressure of ice has a larger temperature dependence than that of the liquid. That is, the vapor pressure of ice increases more rapidly for a given rise in temperature than does the vapor pressure of water. Thus, as the temperature of the solid is increased, a point is eventually reached where the liquid and solid have identical vapor pressures. This is the melting point. 

The nature of the phase rule can be induced from some simple examples. Consider the system represented in Figure 24-3. It is made of water-substance (water in its various forms), in a cylinder with movable piston (to permit the pressure to be changed), placed in a thermostat with changeable temperature. If only one phase is present both the pressure and the temperature can be arbitrarily varied over wide ranges the variance is 2. For example, liquid water can be held at any temperature from its freezing point to its boiling point under any applied pressure. But if two phases are present the pressure is automatically determined by the temperature, and hence the variance is reduced to 1. For example, pure water vapor in equilibrium with water at a given temperature has a definite pressure, the vapor pressure of water at that temperature. And if three phases are present in equilibrium, ice, water, and water vapor, both the temperature and the pressure are exactly fixed the variance is then 0. This condition is called the triple point of ice, water, and water vapor. It occurs at temperature +0.0099 C and pressure 4.58 mm of mercury. 

FIGURE 16.12 (a) The equilibrium vapor pressure of water, ice, and two aqueous... 

Curvature Effects Ice crystals in the atmosphere have a variety of shapes, with hexagonal prismatic being the basic one (Pruppacher and Klett 1997). For illustration purposes, let us ignore this complexity and concentrate on the behavior of a spherical ice particle of diameter Dp. Our analysis for water droplets and the Kelvin effect is directly applicable here and the vapor pressure of water over the ice particle surface p, is... 

In order to account for some of the differences in thermodynamic properties of H2O and D2O, theoretical studies have been applied. Swain and Bader first calculated the differences in heat content, entropy, and free energy by treating the librational motion of each water molecule as a three-dimensional isotopic harmonic oscillator. Van Hook demonstrated that the vapor pressure of H2O and D2O on liquid water and ice could be understood quantitatively within the framework of the theory of isotope effects in condensed systems. Nemethy and Scheraga showed that in a model based on the flickering cluster concept, the mean number of hydrogen bonds formed by each water molecule is about 5% larger in D2O than in H2O at 25 °C. 

See Vapor Pressure of Ice and Vapor Pressure of Water from 0 to 370°C ... 

Combining assumptions, the partial pressure of water in equilibrium with the hydrate at the quadruple point is equal to the vapor pressure of water at that temperature. The effect of temperature is then taken from an estimate of the enthalpy of sublimation. For ice, this is 12.15 kcal mol. From (3) above, the same property of the hydrate is obtained by adding 0.36 kcal mol . This gives 12.5, and the equation for the vapor pressure of chlorine hydrate (in atmospheres) becomes... 

Furthermore, the cell has to heat up to above freezing temperature fast enough to avoid the ice formation from completely shutting down the electrochemical reaction at the cathode catalyst layer. To assist in this, the cathode gas flow rate can be increased (to blow ice away and to carry any excess water) and the inlet gases can be heated (to limit time below freezing temperatures). Because of the low vapor pressures of water at low temperatures, however, and the low heat capacities of the reactant gases, these approaches have limited utility in affecting the startup profiles of full-sized stacks. 

As indicated by the equilibrium-capacity data for the various desiccants, the quantity adsorbed is a function of the vapor pressure of water in the gas stream (and thus of the relative humidity of the feed-gas stream). Capacity values used for design must also be adjusted downward if the gas being dehydrated is less than 100% saturated. Data on two desiccants used to dehydrate natural gas containing a maximum of 7 lb water/million cu ft at 72°F and 570 psig are presented by Harrell (1957). Very complete gas dehydration is required at this plant, since the gas stream is chilled to -105°F, and it is necessary to prevent ice formation in the chillers. Several desiccants were tested, and silica-gel beads and alumina-base pellets were selected as most favorable. Both of these showed capacities of 7% immediately after installation and decreased in capacity as shown in Table 12-15. 

Table 6.2 tells us nothing about the vapor pressure of these hve liquids below 0°C but provides a more detailed view of the vapor pressures in the easily accessible laboratory range between ice water and boiling water. The data for water also give more detail relative to the vapor pressure of water that might be needed for Dalton s law when a gas is collected over water and also give us an appreciation for the relationship between water vapor in the air and a dew point temperature. 

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