Vaporization equation

With the approximation of ideal vapors, equation (6.78) becomes... 

The analytical expression for a given property can be reparametrized, if desired, to apply to a particular class of compounds. Our tendency is usually to have, as general, a database as possible. But for example, Byrd and Rice desired to optimize the heat of sublimation and heat of vaporization equations specifically for nitro derivatives [46]. They retained the dependence on surface area and vofot, but used a nitro compound database to obtain new coefficients for these quantities. 

Gas formation volume factors are calculated with z-factors measured with the gases removed from the cell at each pressure step during differential vaporization. Equation 6-2 is used. Usually Bg values as calculated are listed in the report. 

The purpose of this paper is to (1) document published studies of vaporization in vacuum of the Group 4 and 5 transition metal carbides and uranium carbide, and determine the temperature dependence of their equilibrium CVCs (C/MeCVC) and vaporization rates (Vecvc, g/cmzs) (2) document published studies on chemical diffusion of these carbides, and develop and compare data to a model describing the concentration dependence of the chemical diffusion coefficients and (3) develop diffusion-coupled vaporization equations which predict changes of surface composition (Cs, units of C/M and g/cm3 of C), average composition (Cavg units of C/M and g/cm3 of C), and C mass loss (M, units of g/cm2 of C). 

Derivation of a diffusion-coupled vaporization equation for protective coatings... 

Assumptions (a) and (b) have been already validated while the purported equality (c) makes use of the additional simple assumptions that the differences of the enthalpies of solution (equation 6) and of vaporization (equation 7) are small. 

In the first experiments to measure the vapor pressure of metallic Bk, using Knudsen effusion target-collection techniques, the preliminary data were fitted with a least-squares line to give a provisional vaporization equation for the temperature range 1326-1582 K, and Ai 298 was calculated to be 382 18 kJ/mol (128). The crystal entropy of berkelium metal at 298 K (S s) had been estimated earlier to be 76.2 1.3 J K 1 mol-1 (129), and later, to be 78.2 1.3 J K 1 mol-1 (124). 

Later data on the vapor pressure of berkelium metal over the temperature range 1100-1500 K, obtained by using combined Knudsen effusion mass spectrometric and target collection techniques, have been published in 1982 (124). The vaporization equations obtained were... 

Before solving the equations, we need system property data, which, in this case, are thermodynamic properties. Equations 3.2.9 and 3.2.11 states that we may obtain vapor pressures for water from steam tables, such as those compiled by Chaar et al. [13]. Equation 3.2.10 also states that we can find the enthalpy of vaporization in the steam tables. We assume that the air-water mixture is ideal to calculate the enthalpy of air, so we can use the mole-fraction average of the pure-component enthalpies. Equations 3.2.12 and 3.2.13 in Table 3.2.1 give the mole fraction average of the inlet and outlet enthalpy. Table 3.2.1 also lists pure component enthalpies for water vapor (Equations 3.2.14 and 3.2.16) and for air (Equa-... 

Despite this success and that enunciated in Reference 32, it is to be noted that experience has shown methyl derivatives are generally poorly treated by our enthalpy of vaporization equations (cf. Reference 30. Supplementary material). 

The mass transfer smdies in AGMD suggest that, the transport of vapor through the membrane can be modeled by molecular diffusion mechanism [57], since the pore size of the membrane used is much bigger than the molecular mean free path of water vapor. Equations 19.23 and 19.27 can be used to calculate the mass transfer through the membrane. 

Gy is the mass velocity (mass flnx) of the entering fluid, defined as the mass flow rate in kg/s (lb j/h) divided by the cross-sectional area of the tube or the flow channel. The snbscript i refers to the physical properties of the condensate and v to the vapor. Equation (6.86a) may be nsed to calcnlate the local condensing heat-transfer coefficient at any quality x by replacing the bracketed term by... 

The dispersion analyses that yielded the EPA tables were based on an averaging time of 6 s as compared with the 10 min and 60 min used for the toxic gas and vapor dispersion analyses. As with toxic materials, the neutral density equations would be used for listed gases and vapors that have a molecular weight <28 or where the product of vapor pressure and molecular weight is <500 millimeters of mercury (mm Hg). In contrast, the dense vapor equations would be used for listed... 

Prausnitz (1,2) has discussed this problem extensively, but the most successful techniques, which are based on either closed equations of state, such as discussed in this symposium, or on dilute liquid solution reference states such as in Prausnitz and Chueh (3), are limited to systems containing nonpolar species or dilute quantities of weakly polar substances. The purpose of this chapter is to describe a novel method for calculating the properties of liquids containing supercritical components which requires relatively few data and is of general applicability. Used with a vapor equation of state, the vapor-liquid equilibrium for these systems can be predicted to a high degree of accuracy even though the liquid may be 30 mol % or more of the supercritical species and the pressure more than 1000 bar. 

The explicit formula pxr — I = (1 — Pr)0 for reduced saturation density as a function of reduced pressure is proposed for the entire liquid-vapor saturation boundary. The expression A 1 depends on Pr p 0.35 depends weakly on Pr, corresponding at Pr = 1 to the critical exponent pc. The parameters A and ft can be related to the Pitzer factor o>. Special cases include the power law pr — 1 = C(1 — Tr)0c. . . and the low-pressure vapor equation prx0 = p0Pr The function A — Ac = g(Pr) is found from data to be a universal function for nonpolar substances. If Ac is correlated with o>, the formula takes on the corresponding-states form pr = /o,(Pr, to). This form predicted the density of saturated liquid and vapor with 0.4% and 0.9% accuracy, respectively, for 38 substances. 

Equations 3.7-3.9 will be referred to in this text as the Langmuir vaporization equations. 

Advantages of the Langmuir Vaporization Equations A comprehensive analysis of these equations lead us to the following conclusions. 

---