Thermodynamic saturation conditions

The effect of the medium (solvent) on the dissolved substance can best be expressed thermodynamically. Consider a solution of a given substance (subscript i) in solvent s and in another solvent r taken as a reference. Water (w) is usually used as a reference solvent. The two solutions are brought to equilibrium (saturated solutions are in equilibrium when each is in equilibrium with the same solid phase—the crystals of the dissolved substance solutions in completely immiscible solvents are simply brought into contact and distribution equilibrium is established). The thermodynamic equilibrium condition is expressed in terms of equality of the chemical potentials of the dissolved substance in both solutions, jU,(w) = jU/(j), whence... 

Prior to a discussion on the impact of processing air dew point and temperature on the drying rate behavior of a product, it is necessary to consider heat and mass transfer. Water will move from the granule to air in an attempt to reach an equilibrium, or saturated condition, determined by thermodynamics, which can be read from a phase diagram or psychrometric chart. The rate at which water will move from liquid in the granule to vapor in the air increases the further away the system is from equilibrium. When the water evaporates, it requires an amount of energy, the heat of vaporization, in order to change from liquid to vapor. Because of this, we must also consider transfer of heat as well as movement of material. These concepts can be described by equations shown in Table 5. 

There is a saturation value of the concentration of non-aggregated amphiphile at which phase separation occurs. The nonaggregated amphiphile and aggregates in solution are in this case in thermodynamic equilibrium with a bulk amphiphilar phase. The corresponding thermodynamic equilibrium condition introduces an upper limit, n,Sx> fur . The equilibrium condition leads to... 

From thermodynamics we recall that the relative humidity is defined as the ratio of concentration of vapor to the concentration at saturation conditions for the airstream. We therefore calculate the actual water-vapor concentration in the airstream from... 

Figure 8.13 The function G (A) for water at 300 K at the liquid saturation conditions (Ashbaugh and Pratt, 2004). The points are obtained by direct Monte Carlo calculation, and the solid line by matching an empirical thermodynamic model for the large solute case. The dashed lines are the classic scaled-particle model (Pierotti, 1976) predictions for several solvent hard-sphere diameter parameters between cr = 2.6 A and 3.0 A in 0.1 A increments. Notice that the parameter value that provides the best fit of the classic scaled-particle model for small radii is not the same as that for the large radii results.

Since they are thermodynamic variables, specific entropy and specific enthalpy may be regarded as functions of the two variables temperature and pressure. However, pressure is a single-valued function of temperature along the saturated boundary, and so the specific entropy and enthalpy of saturated steam are themselves single-valued functions of temperature. Hence specific enthalpy may be plotted as a singlevalued function of specific entropy in saturated conditions. This has been done in Figure 16.1. 

Despite widespread use of the ideal K-value concept in industrial calculations, particularly during years prior to digital computers, a sound thermodynamic basis does not exist for calculation of the fugacity coefficients for pure species as required by (4-85). Mehra, Brown, and Thodos discuss the fact that, for vapor-liquid equilibrium at given system temperature and pressure, at least one component of the mixture cannot exist as a pure vapor and at least one other component cannot exist as a pure liquid. For example, in Fig. 4.3, at a reduced pressure of 0.5 and a reduced temperature of 0.9, methane can exist only as a vapor and toluene can exist only as a liquid. It is possible to compute vl or f v for each species but not both, unless vl = vy, which corresponds to saturation conditions. An even more serious problem is posed by species whose critical temperatures are below the system temperature. Attempts to overcome these difficulties via development of pure species fugacity correlations for hypothetical states by extrapolation procedures are discussed by Prausnitz. ... 

Very negative potentials can be found in saturated conditions where there is no oxygen to form a passive layer but with no oxygen there can be no corrosion (see Section 2.2). This shows the weakness of potential measurements. It is a measure of the thermodynamics of the corrosion, not of the rate of corrosion. Corrosion potentials can be misleading, their interpretation is based on empirical observation, not rigorously accurate scientific theory. The problem is that the potential is not purely a function of the corrosion condition but also other factors, and that the corrosion condition is not the corrosion rate. 

Vapor permeation differs from pervaporation, as stated above, insofar as the feed mixture to be separated is supplied as a vapor. At least the more-permeable component is kept as close to saturation conditions as possible. Thermodynamically there is no difference between a liquid and ifs equilibrium vapor, the partial vapor pressure and thus the driving force for the transport through the membrane are identical and the same solution-diffusion mechanism is valid. However, the density of the vaporous feed and thus the concentration of molecules per volume is lower by two to three orders of magnitude than that of the liquid. As a consequence the membrane is usually less swollen than when in contact with a liquid feed. As the feed mixture getting in contact with the membrane is already in the vapor phase no phase change occurs across the membrane and thus no temperature polarization will be observed. Concentration polarization, however, is still an issue. Although the diffusion coefficient is much higher in a vapor than in a liquid, this is at least partially outbalanced by the lower density of the vapor, and therefore concentration polarization effects may be observed at all concentrations of the component to be removed. Minimum... 

If co-crystals are to solve solubility problems one must assess their true or thermodynamic solubility so that development strategies are guided by the fundamental properties of co-crystals. Measuring the solubility of co-crystals that generate supersaturation of the parent drug is often experimentally impossible due to conversion. Eutectic points, described in Section 11.4, provide a measure of co-crystal solubility under thermodynamic equilibrium conditions. The solution at the eutectic point is saturated with co-crystal and solution concentrations represent experimentally accessible thermodynamic solubility values. Once co-crystal solubility is determined at the eutectic, the solubility under different solution conditions (pH, co-former, micelle concentration) can be obtained from solubility models that consider the appropriate solution phase equilibrium expressions. 

For illustration. Figure 1.2 plots the temperature and pressure ranges over which the four fluids exist as liquids between the saturation curve and triple line. Temperature/ pressure (T/P) plots are used throughout the text to illustrate how the LAD performs as a function of the thermodynamic state of the liquid. For comparison. Table 1.1 lists the four primary cryogenic fluids along with thermophysical properties at the NBP saturation conditions relevant in the current work, such as the saturation temperature, heat of vaporization hfg, liquid density pf, kinematic viscosity v, and surface tension j lv- Clearly, advanced systems are required to store, maintain, and transfer such cold liquids. 

According to the classical nucleation theory, the free energy barrier for bubble nucleation and thereby the nucleation rate are functions of the bubble pressiu e, PbubUe-In computer simulations of polymeric foaming processes, almost all previous research has approximated the value of Pbubbie by the saturation pressure, P at- In this paper, the thermodynamic equilibrium condition and the Sanchez-Lacombe (SL) equations of state (EOS) are enployed to determine the value of PbubUe- It is shown that the Pbubbk approximation using Psat will lead to significant overestimations of the nucleation rate and the final cell density. 

Nucleation is the growth of clusters of molecules that become a thermodynamically stable nucleus. This process is dependent on the vapor pressure of the condensable species. The molecular clusters undergo growth when the saturation ratio, S, is greater than 1, where saturation ratio is defined as the actual pressure of the gas divided by its equilibrium vapor pressure. S > 1 is referred to as a supersaturated condition (14). 

Saturated hydrocarbons are stable. Only cycloalkanes with a tight ring are unstable. Alkenes and alkynes have a strong endothermic character, especially the first homologues and polyunsaturated conjugated hydrocarbons. This is also true for aromatic compounds, but this thermodynamic approach does not show up their real stability very well. Apart from a few special cases, the decomposition of unsaturated hydrocarbons requires extreme conditions, which are only encountered in the chemical industry. 

---