Phase change vapor pressure

A V = volume change accompanying the phase change / = vapor pressure... 

The establishment of an equilibrium vapor pressure, as described in Section 12.2, involved two of the.se phase changes vaporization and condensation. Figure 12.31 summarizes the various types of phase changes. 

Gas or vapor removal is more complex than particulate removal because the constituent removed from the air stream is dissolved in the liquid phase and may change the liquid properties. A solution of any volatile material exhibits a vapor pressure of the solute above the liquid phase. This vapor pressure increases with solute concentration and liquid temperature. Contaminant removal continues only as long as the partial pressure of that constituent in the gas phase exceeds the vapor pres-... 

Frequently, vapor-phase supersaturation is studied not by varying the vapor pressure P directly but rather by cooling the vapor and thus changing If To is the temperature at which the saturation pressure is equal to the actual pressure P, then at any temperature T, Pjf = x is given by... 

Reaction 1 is highly exothermic. The heat of reaction at 25°C and 101.3 kPa (1 atm) is ia the range of 159 kj/mol (38 kcal/mol) of soHd carbamate (9). The excess heat must be removed from the reaction. The rate and the equilibrium of reaction 1 depend gready upon pressure and temperature, because large volume changes take place. This reaction may only occur at a pressure that is below the pressure of ammonium carbamate at which dissociation begias or, conversely, the operating pressure of the reactor must be maintained above the vapor pressure of ammonium carbamate. Reaction 2 is endothermic by ca 31.4 kJ / mol (7.5 kcal/mol) of urea formed. It takes place mainly ia the Hquid phase the rate ia the soHd phase is much slower with minor variations ia volume. 

In most utibty boilers, steam pressure regulation is achieved by the throttling of turbine control values where steam generated by the boiler is admitted into the steam turbine. Some modem steam generators have been designed to operate at pressures above the critical point where the phase change between Hquid and vapor does not occur. 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

In terms of the solubilities of solutes in a supercritical phase, the following generalizations can be made. Solute solubiUties in supercritical fluids approach and sometimes exceed those of Hquid solvents as the SCF density increases. SolubiUties typically increase as the pressure is increased. Increasing the temperature can cause increases, decreases, or no change in solute solubiUties, depending on the temperature effect on solvent density and/or the solute vapor pressure. Also, at constant SCF density, a temperature increase increases the solute solubiUty (16). 

Because extractive solvents work by altering the relative volatihty between the components to be distilled, a good solvent causes a substantial change in relative volatihty when present at moderate compositions. As seen from equation 3, the solvent modifies the relative volatihties by affecting the ratio of the hquid-phase activity coefficients yWhereas it is possible to find solvents which increase or decrease this ratio, it is usually preferable to select a solvent which accentuates the natural difference in vapor pressures between the components to be separated that is, a solvent that increases relative to when is favored, over one that increases relative to y. In the latter case, adding small amounts of the solvent actually makes the separation... 

If the temperature of a two-phase system is changed and if the two phases continue to coexist in equilibrium, then the vapor pressure must also change in accord with its temperature dependence. Since Eq. (4-149) holds throughout this change,... 

Boiling point The temperature at which the vapor pressure of a liquid is equal to the external pressure, and the liquid changes phase into the vapor state. 

In the three areas of the phase diagram labeled solid, liquid, and vapor, only one phase is present. To understand this, consider what happens to an equilibrium mixture of two phases when the pressure or temperature is changed. Suppose we start at the point on AB... 

We have encountered equilibrium before—in our we considered the liquid-gas equilibrium that consideration of phase changes. In Section 5-1.2 fixes the vapor pressure of a liquid, and in Sec-142... 

Yet, it is reasonable to suppose that water molecules from the liquid are still evaporating, even at equilibrium. Molecules in the liquid have no way of knowing that the partial pressure of the vapor is equal to the vapor pressure. In the gas phase, the randomly moving molecules continue to strike the surface of the liquid and condense. Equilibrium corresponds to a perfect balance between this continuing evaporation and condensation. Then no net changes can be detected. ... 

Whenever we see the symbol it means that the species on both sides of the symbol are in dynamic equilibrium with each other. Although products (water molecules in the gas phase) are being formed from reactants (water molecules in the liquid phase), the products are changing back into reactants at a matching rate. With this picture in mind, we can now define the vapor pressure of a liquid (or a... 

To find how vapor pressure changes with temperature we make use of the fact that, when a liquid and its vapor are in equilibrium, there is no difference in the molar Gibbs free energies of the two phases ... 

The vapor pressure, density and temperature practically do not change along the evaporation region in physieally realistic systems. The latter allows one to simplify the system of governing equations and reduce the problem to a successive solution of the shortened system of equations to determine the velocity, liquid pressure and gaseous phases as well as the interface shape in a heated capillary. 

The temperature distribution has a characteristic maximum within the liquid domain, which is located in the vicinity of the evaporation front. Such a maximum results from two opposite factors (1) heat transfer from the hot wall to the liquid, and (2) heat removal due to the liquid evaporation at the evaporation front. The pressure drops monotonically in both domains and there is a pressure jump at the evaporation front due to the surface tension and phase change effect on the liquid-vapor interface. 

---