Thermodynamics calculating quantities

The authoritative values for physical constants and conversion factors used in thermodynamic calculations are assembled in Table 2.3. Furthermore, information about the proper use of physical quantities, units, and symbols can be found in several additional sources [5]. 

Calculation of the enthalpy of formation from the enthalpy of combustion is common because for most organic compounds, combustion is the most calorimetrically accessible reaction yet the enthalpy of formation is the more useful quantity for additional thermodynamic calculations. A typical example of such a calculation is outlined by Equations (4.18)-(4.21) ... 

A number of important workers who, up to that time, had been working in relative isolation, now became more involved in CALPHAD conferences and publications. The Canadian group, led by Pelton, had evolved is own representation of thermodynamic quantities in a specific set of non-metallic systems (Pelton and Flengas 1969, Pelton and Schmalzried 1973, Bale and Pelton 1974) but found that many of the concepts being outlined for alloys could also be applied in their area. This was to eventually lead to a Facility for Analysis of Chemical Thermodynamics (F A C T) (Bale and Pelton 1979) and the foundation of the Centre of Research for Thermodynamic Calculations at Montreal. In due course there would be further collaboration (Thompson et al. 1983) between F A C T and the SOLGASMIX programme of Eriksson (1975). 

S.5.2.2 Energies Calculating Quantities Relevant to Thermodynamics and to Kinetics... 

Based upon experimentally observed spectroscopic data, statistical thermodynamic calculations provide thermodynamic data which would not be obtained readily from direct experimental measurements for the species and temperature of interest to rocket propulsion. If the results of the calculations are summarized in terms of specific heat as a function of temperature, the other required properties for a particular specie, for example, enthalpy, entropy, the Gibb s function, and equilibrium constant may be obtained in relation to an arbitrary reference state, usually a pressure of one atmosphere and a temperature of 298.15°K. Or alternately these quantities may be calculated directly. Significant inaccuracies in the thermochemical data are not associated generaUy with the results of such calculations for a particular species, but arise in establishing a valid basis for comparison of different species. 

For both hypothetical and pseudo components, physical properties are computed by the same equations, which are based upon the correlations given in the Technical Data Book of the American Petroleum Institute (1). Equivalent molar quantities of these petroleum components are added to the amounts of the discrete (methane, etc.) components, to obtain the complete mixture for the thermodynamic calculations that follow. 

A PVT-data-code was generated to calculate phase equilibria, critical curves and thermodynamic excess quantities of quaternary systems. The program uses the Christoforakis-Franck-equation of state [11]... 

Eor thermodynamic calculations and analyses of phase diagrams of binary systems whose components form a binary compound, partially or totally dissociating at melting, it is necessary to know the enthalpies of fusion of the components of the binary compounds, and of both eutectic mixtures, as input quantities. When these data cannot be found in the literature, it is possible to estimate them using entropy or enthalpy balances. 

We now proceed with the calculations of the thermodynamic adsorption quantities for a surface possessing a lower degree of symmetry, via a surface whose properties vary periodically along one dimension, say x, and do not depend on another lateral coordinate, y. For such a system, expression (1) becomes... 

This result supports our contention that it is the partition function that serves as the analytic engine for calculating quantities of thermodynamic interest. 

While the use of calculated quantities may seem, at first, cumbersome and even counterproductive, it actually simplifies the analysis of chemical reactors with multiple reactions. In fact, calculated quantities such as enthalpy and free energy are commonly used in thermodynamics resulting in simplified expressions. Here too, by using the extents of independent reactions, we formulate the design of chemical reactors by the smallest number of design equations. 

Although thermodynamic calculations show appreciable quantities of di-methylbutanes at equilibrium (about 30-35% of the total hexane isomers at 500°C), such quantities are not observed in reforming. Equilibria are established readily between n-hexane and the methylpentanes, but not between these hydrocarbons and the dimethylbutanes. The reaction kinetics are not favorable for the rearrangement of singly branched to doubly branched isomers (11). This limitation apparently does not exist for the rearrangement of the normal structure to the singly branched structures. 

The problem is to be attacked in quite another manner when our concern is simply to calculate chemical equilibria in this case it will of course be best to derive the chemical constants from actual chemical equilibria. I have naturally worked in both directions in my numerous calculations, of which I have published, of course, only a small fraction. In my publications I have laid less stress on the accurate calculation of equilibria than on the remarkable fact, that quantities like Trouton s coefficient, and in particular certain coefficients in my vapour-pressure formula, bore a dose relation to chemical equilibria. Those who are not very practised in thermodynamical calculations will hardly have recognized this distinction, and for this reason a repetition of the calculation of the ammonia equilibrium will be desirable. 

S.5.2.2 Energies calculating quantities relevant to thermodynamics and to kinetics... 

More extensive and accurate data and additional calculations are necessary to obtain s , e , and from isotherm data over what is required to get the differential energy and entropy from the isosteric equation. The first complete calculation of ss, e and , as well as the differential quantities, has recently been made by Hill, Emmett, and Joyner (95). This paper shows in detail how the methods of this section can be applied in practice. Using heats of immersion, Harkins and Jura (96) made earlier equivalent calculations, but the relationship of their calculated quantities to the thermodynamic functions of the adsorbed molecules was not pointed out until recently by Jura and Hill (92). 

Molar Gibbs Energy Other extensive thermodynamic quantities are dealt with in the same way. In the case of pure substances, they are considered a function of T, p, n, and for a substance in a mixture with other substances, as a function of T, p, n, n, n",. The Gibbs energy G is especially interesting in this context because in the conventional thermodynamic calculations, it is very closely connected with the chemical potential. In the case of a pure substance at fixed T and p, G is proportional to the amount of substance n. Therefore, G itself does not serve as the substance-specific characteristic, but the quotient G/n ... 

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