Calculation of thermodynamic properties

DESCRIPTIONS AND LISTINGS OF SUBROUTINES FOR CALCULATION OF THERMODYNAMIC PROPERTIES... 

McDonald I R and Singer K 1967 Calculation of thermodynamic properties of liquid argon from Lennard-Jones parameters by a Monte Carlo method Discuss. Faraday Soc. 43 40-9... 

Equations 175 through 179 allow calculation of thermodynamic properties from volume-expHcit equations of state, ie, equations expHcitiy solvable for volume. If an equation of state is solvable expHcitiy for pressure but not for volume, then alternative formulas must be used, where p is molar density and subscript p/n = 1/E indicates constancy of total volume. Eor equations 180, 181, and 183, T and x are constant for equation 182, Tis constant. 

Calculation of Thermodynamic Properties We note that the translational contributions to the thermodynamic properties depend on the mass or molecular weight of the molecule, the rotational contributions on the moments of inertia, the vibrational contributions on the fundamental vibrational frequencies, and the electronic contributions on the energies and statistical weight factors for the electronic states. With the aid of this information, as summarized in Tables 10.1 to 10.3 for a number of molecules, and the thermodynamic relationships summarized in Table 10.4, we can calculate a... 

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. 

McDonald, I. R. Singer, K., Machine calculation of thermodynamic properties of a simple fluid at supercritical temperatures, J. Chem. Phys. 1967, 47, 4766-4772... 

In the last decade, quantum-chemical investigations have become an integral part of modern chemical research. The appearance of chemistry as a purely experimental discipline has been changed by the development of electronic structure methods that are now widely used. This change became possible because contemporary quantum-chemical programs provide reliable data and important information about structures and reactivities of molecules and solids that complement results of experimental studies. Theoretical methods are now available for compounds of all elements of the periodic table, including heavy metals, as reliable procedures for the calculation of relativistic effects and efficient treatments of many-electron systems have been developed [1, 2] For transition metal (TM) compounds, accurate calculations of thermodynamic properties are of particularly great usefulness due to the sparsity of experimental data. 

In table 9.14, for the sake of completion, we list the thermodynamic parameters of the HKF model concerning neutral molecules in solution (Shock et al., 1989). Calculation of partial molal properties of solutes (see section 8.11), combined with calculation of thermodynamic properties in gaseous phases (Table 9.5), allows rigorous estimates of the various equilibrium constants at all P and T of interest. 

Virtual Substance simulations can be run using either periodic boundary conditions or fixed walls. In a fixed wall calculation, the simulation box has physical walls. The resulting system is a droplet , albeit a rectangular droplet, and as a result, the thermodynamic properties differ from those of the bulk substance. One can create a bulk substance by using periodic boundary conditions where the simulation box interacts with copies of itself repeated in three dimensions. (5) This approximates the extended nature of a bulk material, making it appear infinite, and results in better accuracy in the calculation of thermodynamic properties. 

The three-dimensional particle in a box corresponds to the real life problem of gas molecules in a container, and is also sometimes used as a first approximation for the free conduction electrons in a metal. As we found for one dimension (Section 2.3), the allowed energy levels are extremely closely spaced in macroscopically sized boxes. For many purposes they can be regarded as a continuum, with no discernible energy gaps. Nevertheless, there are problems, for example in the theory of metals and in the calculation of thermodynamic properties of gases, where it is essential to take note of the existence of discrete quantized levels, rather than a true continuum. 

Brendeng, E. Grini, P. G. Jorslad. O. Melaaen, I. S. Maehlum, H.S. Owren, G.A. Puntervold, S. Measurement and Calculation of Thermodynamic Properties of Natural Gas Mixtures, NTNU-SINTEF 1993. 

The accurate calculation of thermodynamic properties for construction of a table or diagram is an exacting task, seldom required of an engineer. However engineers do make practical use of thermodynamic properties, and an understand ing of the methods used for their calculation leads to an appreciation that some, uncertainty is associated with every property value. There are two major reasons for inaccuracy. First, the experimental data are difficult to measure and are subject to error. Moreover, data are frequently incomplete, and are extended by interpolation and extrapolation. Second, even when reliable PVT data are available, a loss of accuracy occurs in the differentiation process required in the calculation of derived properties. This accounts for the fact that data of a high order of accuracy are required to produce enthalpy and entropy values suitable for engineering calculations. 

The generalized correlations of Pitzer provide an alternative to the use of a cubic equation of state for the calculation of thermodynamic properties. However, no adequate general method is yet known for the extension of the Pitzer correlations based on the compressibility factor to mixtures. Nevertheless, Z, as given by... 

Equations of state have a much wider application. In this chapter we first present a general treatment of the calculation of thermodynamic properties of fluids and fluid mixtures from equations of state. Then the use of an equation of state for VLE calculations is described. For this, the fugacity of each species in both liquid and vapor phases must be determined. These calculations are illustrated with the Redlich/Kwong equation. Provided that the equation of state is suitable, such calculations can extend to high pressures. 

A new correction function for quantum effects in fluids is proposed, which can be coupled to any van der Waals type equation of state. With the new quantum correction, calculations of thermodynamic properties of hydrogen and hydrogen-containing mixtures are significantly improved. 

For the calculation of thermodynamic properties the cubic equations of state have become the workhorse of the process simulation business. In particular, the equations of state of Soave (1972) [SRK] and of Peng and Robinson (1976) [PR] and modifications of these original forms are the most commonly used. 

It is, however, possible to replace the phase integral of Gibbs by a sum-over-statos or partition function, which in quantum statistics plays the same role for the calculation of thermodynamic properties that Gibbs phase integral plays in classical statistics. The partition function Q is defined as... 

The calculation of thermodynamic properties is difficult using MD techniques. The case of defects is especially problematic and both formation and migration energies are far more effectively calculated using static simulation techniques. 

Two important objectives of statistical mechanics are (1) to verify the laws of thermodynamics from a molecular viewpoint and (2) to make possible the calculation of thermodynamic properties from the molecular structure of the material composing the system. Since a thorough discussion of the foundations, postulates, and formal development of statistical mechanics is beyond the scope of this summary, we shall dispose of objective (1) by merely stating that for all cases in which statistical mechanics has successfully been developed, the laws quoted in the preceding section have been found to be valid. Furthermore, in discussing objective (2), we shall merely quote results the reader is referred to the literature [3-7] for amplification. 

R. A. Alberty, Calculation of thermodynamic properties of species of biochemical reactants using the inverse Legendre transform, J. Phys. Chem. 109 B, 9132-9139 (2005). 

Tabulated data for experimental adsorption isotherms are fitted with analytical equations for the calculation of thermodynamic properties by integration or differentiation. These thermodynaunic properties expressed as a function of temperature, pressure, and composition are input to process simulators of atdsorption columns. In addition, anaJytical equations for isotherms are useful for interpolation and cautious extrapolation. Obviously, it is desirable that the Isotherm equations agree with experiment within the estimated experimental error. The same points apply to theoretical isotherms obtained by molecular simulation, with the requirement that the analytical equations should fit the isotherms within the estimated statistical error of the molecular simulation. 

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