Isothermal evaporation vapor pressure

The thermos phon circulation rate can be as high as 10 to 15 times the coolant evaporation rate. This, in turn, eliminates any significant temperature difference, and the jacket is maintained under isothermal conditions. In this case, the constant wall temperature assumption is satisfied. During starting of the thermosiphon, the bottom can be 20-30°C hotter, and the start of circulation can be established by observing that the difference between the top and bottom jacket temperature is diminishing. Figure 2.2.5 (Berty 1983) shows the vapor pressure-temperature relationship for three coolants water, tetralin, and Dowtherm A. 

Water evaporation occurs when the vapor pressure of the water at the surface, which is temperature dependent, is greater than the water pressure in the subsurface, which is dependent on relative humidity and temperature. The isothermal evaporation process is described by Stumm and Morgan (1996) via a reaction progress model, in which the effects of the initial reaction path are based on the concept of partial equilibrium. Stumm and Morgan (1996) describe partial equilibrium as a state in which a system is in equilibrium with respect to one reaction but out of equilibrium with respect to others. As an example, Stumm and Morgan (1996) indicate (Fig. 7.1) that water with a negative residual alkalinity (i.e.. 

Now consider the isothermal evaporation of water from a surface and the subsequent diffusion through a stagnant air layer, as shown in Fig. 11-4. The free surface of the water is exposed to air in the tank, as shown. We assume that the system is isothermal and that the total pressure remains constant. We further assume that the system is in steady state. This requires that there be a slight air movement over the top of the tank to remove the water vapor which... 

Determine the minimum number of cubic feet of dry air required to evaporate 20 lb of ethanol if the total pressure is maintained at 740 mm Hg. The evaporation process is isothermal at 70°F and the vapor pressure of the alcohol is 0.9psia at this temperature. 

Now, conversely, if we consider a spherical liquid drop in air, having a radius of r, the vapor pressure of a drop, Pcv > P that is Pv is higher than that of the same liquid with a flat surface, Pv (the superscript c indicates a curved surface). If d mol of liquid evaporates from the drop and condenses onto the bulk flat liquid under isothermal and reversible conditions, the free-energy change of this process can be written by differentiating Equation (155) as... 

Because the free energy of formation of a surface is always positive, a particle that consists only of surfaces (that is, platelets or droplets of atomic dimensions) would be thermodynamically unstable. This is also apparent from the Kelvin equation [Eq. 3.70], which states that a particle that falls below a certain size will have an increased vapor pressure and will therefore evaporate. There must be a stabilizing influence, however, that allows small particles of atomic dimensions to form and grow a common occurrence in nature. This influence is given by the free energy of formation of the bulk condensed phase. In this process, n moles of vapor are transferred to the liquid phase under isothermal conditions. This work of isothermal compression is given by... 

Chang et al. (1991) have studied the dehydration process in relation to IM meats. They stated that if the unbound moisture in meats is defined as that which exerts water vapor pressure like that of pure water, all unbound moisture must evaporate before equilibrium can be achieved with air that is less than saturated. In other words, the water will evaporate until the water vapor pressure of the meat is equal to the partial water vapor pressure in the air. Data on the equilibrium moisture content-relative humidity (i.e., isotherms) of meat or meat mixtures are needed over a wide range of temperatures for dehydration applications. For example, isotherms for meat/meat mixtures below ambient temperature are needed for salami and raw ham, and isotherms above steam temperatures are needed for high-temperature finished dried IM meats (Chang et al, 1991). 

Vapor-phase sorption onto the same dry Woodbum soil is illustrated in Figure 3.16 where soil uptake is expressed as a function of the relative pressure-equilibrium partial pressure/saturated vapor pressure. The data indicate a BET adsorption process. Increasing relative humidity decreases the adsorption (Fig. 3.17) of dichlorobenzene ultimately resulting in a linear isotherm. It is concluded that at low humidities adsorption on the mineral surfaces is involved. Increasing availability of water reduces the availability of these sites until sorption is due to partitioning into the SOM. It will be demonstrated that the converse of this relation is important in assessing the potential for evaporative loss from soils. 

Figure 15.1 shows the mass flux ratios computed by Loyalka et al. for zy = 0.10 and zy = 13.95. The latter mass ratio corresponds to the evaporation of a dioctyl phthalate (DOP) in air. Also shown in the figure are the evaporation data of Ray et al. [18] for DOP/air at relatively large Knudsen numbers. The Knudsen numbers shown in the figure are given by (15.22). The fact that the mass flux ratio is a weak function of zy justifies to some extent the use of the Fuchs-Sutugin equation, which should apply only to systems with Zy < 1. Because DOP has a very low vapor pressure at room temperature, the droplet evaporation process is very nearly isothermal, that is, the interfacial temperature is approximated closely by the bulk gas temperature. 

Sublimation and evaporation are zero-order processes. Under isothermal conditions the rate of mass loss is expected to be constant if the free surface area does not change. Langmuir equation for free evaporation relates the rate of mass loss to the vapor pressure ... 

For a convex surface, that is, R> 0, as is the case for liquid droplets in vapor, it follows that the saturated vapor pressure is higher than that for a flat surface, causing transport of molecules through the vapor phase from the curved toward the flat surface. As a result, the droplets evaporate and condensation occurs at the flat surface. This process accelerates as the droplets become smaller. If the dispersion is heterodisperse, containing a variety of droplet sizes, the larger droplets grow at the expense of the smaller ones. This phenomenon is called isothermal distillation. 

In the calculations of partial pressures (Hastie et al., 1968), ionization of dimeric molecules accompanied by loss of more than one atom (especially in reaction steps that can interfere with ionization of monomers) was assumed to be improbable. This assumption was experimentally confirmed in studies of the congruent evaporation of SmCl3 (Chervoimyi et al., 1974). Isothermal evaporation of a sample of known weight was carried out at several temperatures, and the saturated vapor pressure was determined by the Hertz-Knudsen equation. In each experiment, the state of an imsaturated vapor caused by the presence of an nonvolatile species ( 1.5% SmCl2) was determined in the end of... 

Types IV and V suggest that the complete or almost complete filling of the pores and capillaries of the adsorbent occurs at a pressure lower than the vapor pressure of the gas indeed, sometimes at a considerably lower pressure. This lowering of the vapor pressure indicates that as the pressure of the gas is increased some additional forces appear. There is additional heat of evaporation and the term g appears in the equation (Equation 8.6) which is a function of that additional heat. Therefore, for Type IV and V BET isotherms, the term g in Equation 8.6 is temperature dependent. The term decides the shape. When B2 1 one obtains Type IV isotherm and for B2 < 1 Type V isotherm. 

Once the heel has been established in the carbon bed, the adsorption of the fuel vapor is characterized by the adsorption of the dominant light hydrocarbons composing the majority of the hydrocarbon stream. Thus it is common in the study of evaporative emission adsorption to assume that the fuel vapor behaves as if it were a single light aliphatic hydrocarbon component. The predominant light hydrocarbon found in evaporative emission streams is n-butane [20,33]. Representative isotherms for the adsorption of n-butane on activated carbon pellets, at two different temperatures, are shown in Fig. 8. The pressure range covered in the Fig. 8, zero to 101 kPa, is representative of the partial pressures encountered in vehicle fuel vapor systems, which operate in the ambient pressure range. 

The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). 

The working fluid for vapor cycles is alternately condensed and vaporized. When a working fluid remains in the saturation region at constant pressure, its temperature is also constant. Thus, the condensation or evaporation of a fluid in a heat exchanger is a process that closely approximates the isothermal heat-transfer processes of the Carnot cycle. Owing to this fact, vapor cycles closely approximate the behavior of the Carnot cycle. Thus, in general, they tend to perform efficiently. 

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