Thermodynamic properties, calculated

In some cases the atomic charges are chosen to reproduce thermodynamic properties calculated using a molecular dynamics or Monte Carlo simulation. A series of simulations is performed and the charge model is modified until satisfactory agreement with experiment is obtained. This approach can be quite powerful despite its apparent simplicity, but it is only really practical for small molecules or simple models. 

Table A4.5 summarizes the equations for calculating anharmonicity and nonrigid rotator corrections for diatomic molecules. These corrections are to be added to the thermodynamic properties calculated from the equations given in Table A4.1 (which assume harmonic oscillator and rigid rotator approximations).

Upon insertion of Eq. (82) into Eq. (81) one has an implicit transcendental equation for z that must in general be solved numerically for specified values of x, T, and the interaction coefficients. Then yt and y3 can be obtained with Eq. (57) and various thermodynamic properties calculated. Analytical expressions can be obtained for the various properties in terms of x, , and z. However, these are somewhat cumbersome and in general we shall only write them for... 

Mujtaba (1989) simulated the example considered by Boston et al. (1980) presented in section 4.2.4.1.1 using CMH model. The volume holdups used by Boston et al. were converted to molar holdups at the initial conditions. These were 0.00493 lbmol for each internal plates and 0.0493 lbmol for the condenser. Equilibrium k values were calculated using Antoine s vapour pressure correlation and enthalpies by the same procedure outlined in section 4.2.4.2.I. The simulation results are presented in Table 4.6. Note the slight differences in predictions (Table 4.4 and 4.6) are due to the use of different types of models (CVH and CMH) and thermodynamic property calculations. 

Evaluation of Transports. Using the information given on Figure 2, the composition of the coal, the composition of the stack gases, and the characteristics of the reference environment, typical thermodynamic property calculations serve to evaluate the transport terms (10,12). Thus the exergy transported with the coal is ... 

Thermodynamic property calculations based upon the solution of the molecular OZ equation using spherical harmonic expansions have not been extensive. This is probably due to the computational effort required in the implementation of these methods. However, quite promising results have been obtained for the equation of state of hard sphere diatomics (Chen and Steele, Freasier, Lado ) and for 12-6 diatomics (Lado ). Again, as we noted earlier in Section III.A, more extensive tests of this approach need to be made. 

The selection of a reference base for property tabulations is arbitrary. Whatever base is selected, the base values of the different extensive properties will cancel out of the thermodynamic property calculations--assuming, of course, that the calculations are carried out correctly. (That is, when employing thermochemical property tabulations to make property calculations, it is necessary to assure that the base values cancel out this must be done for all extensive properties--enthalpy, entropy,..., availability, etc.)... 

Here u. j(r,T,P) is the short-range potential for ions, and Eq is the dielectric constant of the solvent. The solvent averaged potentials are thus actually free energies that are functions of temperature and pressure. The thermodynamic properties calculated from the pair correlation functions are summarized below. 

The thermodynamic properties calculated by different routes are different, since the MS solution is an approximation. The osmotic coefficient from the virial pressure, compressibility and energy equations are not the same. Of these, the energy equation is the most accurate by comparison with computer simulations of Card and Valleau [ ]. The osmotic coefficients from the virial and compressibility equations are... 

Thermodynamic properties calculated for the current study are presented in Table 7.5. Enthalpy of formation and entropy values are reported at 298 K, as most experimental data are referenced or available at 298 K. This facilitates the use of these thermodynamic properties and the use of isodesmic reaction set. Entropies and heat capacities are calculated by statistical mechanics using the harmonic-oscillator approximation for vibrations, based on frequencies and moments of inertia of the optimized B3LYP/6-311G(d,p) structures. Torsional frequencies are not included in the contributions to entropy and heat capacities instead, they are replaced with values from a separate analysis on each internal rotor analysis (IR). 

THERMODYNAMIC PROPERTY CALCULATIONS BASED ON P-V-T RELATIONS AND ZERO-PRESSURE SPECIFIC HEATS... 

Significant errors in thermodynamic properties calculated as previously described may arise from the uncertainty in the specific-heat data. These errors may be reduced significantly by using zero-pressure specific heats calculated by the methods of statistical mechanics with spectroscopic data, since ideal-gas properties are generally about an order of magnitude more accurately known than the real-gas properties determined by calorimetric methods. ... 

A comparison of dissolution thermodynamic properties calculated from B and x with condensation for several solutes in n-tetracosane as statio-naiy phase at 76°C, is shown in Table 4.1 [21, 22]. 

Regardless of whether the property formulation for a particular fluid is explicit in pressure, Helmholtz energy, Gibbs energy, or another property, the user must be given an assessment of the uncertainty of the predicted properties so that the equation can be considered practical. The quality of a thermodynamic property formulation is best determined by its ability to model the physical behaviour to represent the measured properties of the fluid. Statistics and deviation plots are used to show how thermodynamic properties calculated from equations of state compare to experimental data. 

To simplify the problem of determining approximate potential functions for the internal rotation of asymmetric tops, Scott and McCullough have tabulated contributions to thermodynamic properties calculated within the classical approximation for potential functions consisting of segments of (1 - cos 3 ) curves. In certain favourable cases these tables can be used to derive potential functions that are consistent with calorimetric data. 

The results for tetrahydrofuran are important since there is substantial evidence for pseudo-rotation from both far-i.r. and microwave spectroscopy. A series of absorptions between 20 and 100 cm can be fitted to equation (34) with mq% — (8.56 0.13) x 10 and (8.48 0.15) X 10 gem for the vibrational states y = 0 and y = 1, respectively. For a fit to the measured thermodynamic properties a value for mql of 8 X 10 g cm had previously been required, so the agreement is extremely satisfactory. Microwave spectroscopy has since afforded values for the first 15 energy levels for pseudo-rotation and shown that the barrier is very low. Additional levels have been estimated from these, their contributions to the thermodynamic properties calculated, and the total values of the latter obtained and shown to be in excellent agreement with the observed values. A calculation of the barrier to pseudo-rotation gave a value of 10.5 kJ mol . But it has been shown that if, for this calculation, the barrier height is transferred from dimethyl ether (11.4kJmol 0 rather than from methanol (4.48 kJmol ), then the... 

The thermodynamic properties calculated through the virial and compressibility equations (Waismann and Lebowitz, 1970, 1972) are ... 

Normal mode frequencies that have been refined in the above fashion can also be employed to calculate thermodynamic properties. In the xfin 31 study, TSv and //vib at 300 K were calculated using (1) the original set of normal modes, (2) the set of adjusted 250 normal modes, (3) the set of adjusted 35 normal modes, and (4) the quasi-harmonic normal modes derived from the MD simulation, Both sets of adjusted normal modes were seen to be an improvement over the original set of normal modes in terms of reproducing the low frequency distribution of modes as well as the thermodynamic properties calculated from the quasi-harmonic modes derived from the MD trajectory. 

The process flow sheet is performed using shortcut distillation and utilizing Antoine package for thermodynamic properties calculations. 

P2 vapor pressure measurements over liquid alloys of the ternary system and thermodynamic property calculations were carried out by [1983Ban]. The mixing parameter of the B-Fe-P liquid was calculated by [1993Din] using Miedema s method. 

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