Phase changes solid-vapor

In the forward process, called sublimation, iodine molecules change directly from the solid phase to the gas phase. In the reverse process, gaseous iodine molecules return to the solid phase. A solid-vapor equilibrium is established in each flask. 

The pressure-temperature phase diagrams also serve to highlight the fact that the polymorphic transition temperature varies with pressure, which is an important consideration in the supercritical fluid processing of materials in which crystallization occurs invariably at elevated pressures. Qualitative prediction of various phase changes (liquid/vapor, solid/vapor, solid/liquid, solid/liquid/vapor) at equilibrium under supercritical fluid conditions can be made by reference to the well-known Le Chatelier s principle. Accordingly, an increase in pressure will result in a decrease in the volume of the system. For most materials (with water being the most notable exception), the specific volume of the liquid and gas phase is less than that of the solid phase, so that... 

Vapor pressure Partitioning between phases solubility of a gas in a liquid sorption of a solute in a fluid onto a sorbent Chemical reaction equilibrium Electric charge Phase change solid/liquid liquid/gas Diffusivity Ionic mobility Molecular size and shape... 

Analytical solutions for cases of temperature-dependent thermal conductivity are available [22, 23]. In cases where the solid s thermophysical properties vary significantly with temperature, or when phase changes (solid-liquid or solid-vapor) occur, approximate analytical, integral, or numerical solutions are oftentimes used to estimate the material thermal response. In the context of the present discussion, the most common and useful approximation is to utilize transient onedimensional semi-infinite solutions in which the beam impingement time is set equal to the dwell time of the moving solid beneath the beam. The consequences of this approximation have been addressed for the case of a top hat beam, p 1 = K = 0 material without phase change [29] and the ratios of maximum temperatures predicted by the steady-state 2D analysis. Transient ID analyses have also been determined. Specifically, at Pe > 1, the diffusion in the x direction is negligible compared to advection, and the ID analysis yields predictions of Umax to within 10 percent of those associated with the 2D analysis. 

Consider the following sequence of phase changes solid liquid vapor. Solids must absorb heat in order to melt, and Uquids must absorb heat in order to vaporize. Both are endothermic processes. When a soUd melts, there isn t very much change in volnme (maybe 10 percent or so), so the work done when the solid expands is usually ignored. (Of course, in the case of water, the solid contracts as it melts—more about that in Chapter 24.) On the other hand, there is a big change in volume when a liquid vaporizes—the increase in volume is on the order of a factor of 1,000. 

Notice from the figure that the effect of temperature on entropy is due almost entirely to phase changes. The slope of the curve is small in regions where only one phase is present. In contrast, there is a large jump in entropy when the solid melts and an even larger one when the liquid vaporizes. This behavior is typical of all substances melting and vaporization are accompanied by relatively large increases in entropy. 

Fusion and vaporization are the most familiar phase changes, but sublimation is also common. Sublimation is a phase change in which a solid converts directly to a vapor without passing through the liquid phase. Dry ice (solid CO2) sublimes at 195 K with A ii/subl — 25.2 kJ/mol. Mothballs contain naphthalene (Cio Hg,... 

The dashed lines on Figure 11-39 show two paths that involve phase changes for water. The horizontal dashed line shows what happens as the temperature increases at a constant pressure of 1 atm. As ice warms from a low temperature, it remains in the solid phase until the temperature reaches 273.15 K. At that temperature, solid ice melts to liquid water, and water remains liquid as the temperature increases until the temperature reaches 373.15 K. At 373.15 K, liquid water changes to water vapor. When the pressure is 1 atm, water is most stable in the gas phase at all higher temperatures. The vertical dashed line shows what happens as the pressure on water is reduced at a constant temperature of 298 K (approximately room temperature). Water remains in the liquid phase until the... 

Phase changes, which convert a substance from one phase to another, have characteristic thermodynamic properties Any change from a more constrained phase to a less constrained phase increases both the enthalpy and the entropy of the substance. Recall from our description of phase changes in Chapter 11 that enthalpy increases because energy must be provided to overcome the intermolecular forces that hold the molecules in the more constrained phase. Entropy increases because the molecules are more dispersed in the less constrained phase. Thus, when a solid melts or sublimes or a liquid vaporizes, both A H and A S are positive. Figure 14-18 summarizes these features. 

In pharmaceutical systems, both heat and mass transfer are involved whenever a phase change occurs. Lyophilization (freeze-drying) depends on the solid-vapor phase transition of water induced by the addition of thermal energy to a frozen sample in a controlled manner. Lyophilization is described in detail in Chapter 16. Similarly, the adsorption of water vapor by pharmaceutical solids liberates the heat of condensation, as discussed in Chapter 17. 

This is the fundamental distillation equation, often referred to as the Rayleigh law when in its integrated form (Rayleigh, 1896). As far as Dt is considered to be a function of F, this equation applies to the change of any species concentration in the course of phase separation. Liquid-vapor or solid-solid fractionations are liable to the same formulation. 

The physical nature of the process stream. Is it single-phase or two-phase Is it liquid, solid, vapor or slurry What is its temperature and pressure at the sampling point, and how far can these be allowed to change during sampling What is its viscosity at the appropriate sample measurement temperature The chemical nature of the process stream. Is it at equilibrium (a final product) or is it to be measured mid-reaction Is sample transport possible, or must the sample be measured in situ Is it corrosive, and what material and metallurgical constraints exist ... 

The liquid state exists only below the critical point pressure and above the triple point pressure. When a vapor below the triple point pressure is cooled down, we encounter a discontinuous and abrupt phase change to solid but, above the critical point pressure, a cooled vapor turns into the supercritical state where the properties of the fluid... 

At the right combination of pressure and temperature, matter can move directly from a solid to a gas, or vapor. This type of phase change is called sublimation, and it s the kind of phase change responsible for the white mist that emanates from dry ice, the common name for solid carbon dioxide. Movement in the opposite direction, from gas directly into solid phase, is called deposition. 

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