Vapor pressure thermodynamic calculations

Steam), and oi er input from CORCON. It contains a library of thermodynamic properties je energies from bich vapor pressures are calculated) for chemical species (mostly elements, oxides, and hydroxide that might be formed by fission products and other melt constituents. 

Thermodynamic properties of the ideal monatomic gas have been calculated from energy levels listed in the Landolt-Bornstein Tabellen 208), Jones, Langmuir, and Mackay 170) have measured the vapor pressure. We calculate a heat of sublimation at 298 K. of 134,800 cal./gram atom, a normal boiling point of 4100 K., and a heat of vaporization at the normal boiling point of 122,000 cal./gram atom. 

In Example 7.1 we showed that for any pure species, we can calculate the fugacity from an EOS. In Chapters 7 and 9 we used only the little EOS, for which that calculation was easy. For more complex EOSs the mathematics become more complex, as shown in Appendix F, but in principle the procedure is the same. In Figure 10.8 at any value of P we could read the values of the BWR EOS specific volume corresponding to the vapor and the liquid. At the pressure corresponding to the vapor pressure, the calculated fugacities of these two should be equal. That is the method actually used to calculate the values of the saturation vapor pressure in most modem tables of thermodynamic properties. It has the merit that the PvT behavior of the liquid, and that of the vapor, and the vapor-pressure curve are all calculated from the same EOS, with the consequence that at the phase boundaries all the values are internally consistent. We might think that this divorces the calculated vapor pressures from the experimental vapor-pressure measurements, but it does not. The adjustable constants in the EOS are chosen to make the... 

Selected physical properties are given in Table 1 and some thermodynamic properties in Table 2. Vapor pressure (P) and enthalpy of vaporization (H) over the temperature range 178.45 to 508.2 K can be calculated with an error of less than 3% from the following equations wherein the units are P, kPa Pi, mj/ mol T, K and = reduced temperature, T/ T (1) ... 

The physical piopeities of toluene have been well studied expeiimentally. Several physical properties ate presented in Table 1 (1). Thermodynamic and transport properties can also be obtained, from other sources (2—7). The vapor pressure of toluene can be calculated as follows (8), where P is in kPa and T is in K. 

In order to ensure thermodynamic consistency, in almost all cases these properties are calculated from Tr. and the vapor pressure and liquid density correlation coefficients listed in those tables. This means that there will be slight differences between the values listed here and those in the DIPPR tables. Most of the differences are less than 1%, and almost all the rest are less than the estimated accuracy of the quantity in question. 

The pair of Eqs. 12, 13 epitomizes the relation between the equilibrium vapor pressure, composition, and chemical potential of the solvent in a clathrate obeying the present model. These expressions were used in the calculation of the thermodynamic properties of gas hydrates30 and have also been formulated by Barrer and Stuart 4 for a clathrate with a single type of cavity and one occluded component they reduce to the equations of ref. 52. 

Trustworthy thermodynamic data for metal solutions have been very scarce until recently,25 and even now they are accumulating only slowly because of the severe experimental difficulties associated with their measurement. Thermodynamic activities of the component of a metallic solution may be measured by high-temperature galvanic cells,44 by the measurement of the vapor pressure of the individual components, or by equilibration of the metal system with a mixture of gases able to interact with one of the components in the metal.26 Usually, the activity of only one of the components in a binary metallic solution can be directly measured the activity of the other is calculated via the Gibbs-Duhem equation if the activity of the first has been measured over a sufficiently extensive range of composition. 

Fugacity, like other thermodynamics properties, is a defined quantity that does not need to have physical significance, but it is nice that it does relate to physical quantities. Under some conditions, it becomes (within experimental error) the equilibrium gas pressure (vapor pressure) above a condensed phase. It is this property that makes fugacity especially useful. We will now define fugacity, see how to calculate it, and see how it is related to vapor pressure. We will then define a related quantity known as the activity and describe the properties of fugacity and activity, especially in solution. 

Equilibrium vapor pressures were measured in this study by means of a mass spectrometer/target collection apparatus. Analysis of the temperature dependence of the pressure of each intermetallic yielded heats and entropies of sublimation. Combination of these measured values with corresponding parameters for sublimation of elemental Pu enabled calculation of thermodynamic properties of formation of each condensed phase. Previ ly reported results on the subornation of the PuRu phase and the Pu-Pt and Pu-Ru systems are correlated with current research on the PuOs and Pulr compounds. Thermodynamic properties determined for these Pu-intermetallics are compared to analogous parameters of other actinide compounds in order to establish bonding trends and to test theoretical predictions. 

Vapor pressures and vapor compositions in equilibrium with a hypostoichiometric plutonium dioxide condensed phase have been calculated for the temperature range 1500 I H 4000 K. Thermodynamic functions for the condensed phase and for each of the gaseous species were combined with an oxygen-potential model, which we extended from the solid into the liquid region to obtain the partial pressures of O2, 0, Pu, PuO and Pu02 as functions of temperature and of condensed phase composition. The calculated oxygen pressures increase rapidly as stoichiometry is approached. At least part of this increase is a consequence of the exclusion of Pu +... 

This expression provides the basis for vapor-liquid equilibrium calculations on the basis of liquid-phase activity coefficient models. In Equation 4.27, thermodynamic models are required for cf>y (from an equation of state) and y, from a liquid-phase activity coefficient model. Some examples will be given later. At moderate pressures, the vapor phase becomes ideal, as discussed previously, and fj = 1. For... 

In contrast to the effects of temperature, the effect of pressure on c/w is relatively small and can be neglected for reasonable pressure differences. Based on thermodynamics, a change in total pressure of a system affects the vapor pressure. The change in water activity with pressure, at constant moisture content, can be calculated using Eq (8) (Bell and Labuza, 2000) ... 

It is shown that the properties of fully ionized aqueous electrolyte systems can be represented by relatively simple equations over wide ranges of composition. There are only a few systems for which data are available over the full range to fused salt. A simple equation commonly used for nonelectrolytes fits the measured vapor pressure of water reasonably well and further refinements are clearly possible. Over the somewhat more limited composition range up to saturation of typical salts such as NaCl, the equations representing thermodynamic properties with a Debye-Hiickel term plus second and third virial coefficients are very successful and these coefficients are known for nearly 300 electrolytes at room temperature. These same equations effectively predict the properties of mixed electrolytes. A stringent test is offered by the calculation of the solubility relationships of the system Na-K-Mg-Ca-Cl-SO - O and the calculated results of Harvie and Weare show excellent agreement with experiment. 

Correlating ln(Pc /Pc), with vapor pressure data For isotopomer pairs with the vapor pressure and VPIE established near Tc, a thermodynamic consistency test between ln(Tc7Tc) and ln(Pc /Pc), and calculation of ln(Pc7Pc) from ln(Tc7Tc) is possible. The critical pressure of the heavier isotopomer at its critical temperature, Pc(Tc), can be calculated from the lighter, Pc,(Tc7 provided the vapor pressure of the lighter between Tc and Tc, the VPIE, and Tc and Tc are known. For Tc < Tc ... 

Homogeneous Liquids. The physical properties important in determining the suitability of a liquid for propellant application are the freezing point, vapor pressure, density, and viscosity. To a lesser extent, other physical properties are important such as the critical temperature and pressure, thermal conductivity, ability to dissolve nitrogen or helium (since gas pressurization is frequently used to expel propellants) and electrical conductivity. Also required are certain thermodynamic properties such as the heat of formation and the heat capacity of the material. The heat of formation is required for performing theoretical calculations on the candidate, and the heat capacity is desired for calculations related to regenerative cooling needs. 

In this study, a thermodynamic framework has been presented for the calculation of vapor-liquid equilibria for binary solvents containing nonvolatile salts. From an appropriate definition of a pseudobinary system, infinite dilution activity coefficients for the salt-containing system may be estimated from a knowledge of vapor pressure lowering, salt-free infinite dilution activity coefficients, and a single system-dependent constant. Parameters for the Wilson equation may be determined from the infinite dilution activity coefficients. 

Look up thermodynamic data for ethanol (C2H5OH) in Appendix B, estimate the normal boiling point of ethanol, and calculate the vapor pressure of ethanol at 25°C. 

P (c, red). The exact thermodynamic status of the solid forms of phosphorus other than yellow has not yet been determined. The vapor pressure of red phosphorus was measured by Chapman1 and Troost and Hautefeuille1 and the latter calculated, from the difference in the temperature coefficients of the vapor pressures of the yellow and red forms, the heat of transition from yellow to red to be 4.2 at 700°. From the difference in the heats of combustion of the yellow and red forms of phosphorus, Giran1 found T=3.7. A more direct measurement of the heat of transition is that from the data of Giran1 on the heats of reaction of the two forms with bromine in carbon disulfide, (2 = 38.79 and 43.01 for the red and yellow forms, respectively. These data yield T=4.22. Giran1 found that the so-called violet or black phosphorus had a heat of reaction of 38.56 with bromine in carbon disulfide. Apparently this form is thermochemically identical with the red form. 

In the most common thermodynamic case, the Clapeyron equation is used with pure components to obtain the heat of vaporization from pure component two-phase (vapor pressure) data. The Clapeyron equation is one of the primary successes of thermodynamics, because it enables the calculation of AH, which is difficult to measure, from easily available properties of pressure and temperature. 

---