Calculating Thermodynamic 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). 

The surface pressure—area and surface dipole moment-area data for both components and a 1 to 1 molar ratio of all but the last mixture were obtained for at least two temperatures in the range 0° to 40 °C. From such data excess thermodynamic quantities were calculated. For reasons... 

Approximate Thermodynamic Quantities. Thermodynamic quantities, not taking into account activity coefficients, can be calculated from the experimental data at constant pH for the exchange reaction,... 

The p0 dependence of oxygen nonstoichiometry (8) was determined by using coulometric titration. The data were analyzed using a simple point defect model and thermodynamic quantities were calculated. From this model, the standard enthalpy for oxidation (AH0f) and disproportionation (A77D) were determined to be -140.7 and 228.7 kJ/mol, respectively. The mobilities of the electron holes, electrons, and oxygen ions were calculated from the conductivity data using the defect concentrations determined from the stoichiometry and point defect model. 

For this fluid model, the chemical potential is one of the most difficult thermodynamic quantities to calculate. Only few SCIETs approximations succeed in obtaining direct accurate results (ZSEP, DHH, BB,. ..). The reader has to be informed that the method developed by Bomont and Bretonnet [96,97] has not yet been applied to the LJ fluid, but works are in progress along these lines. 

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. 

Rodriguez, Luis S.J., "Calculation of Available-Energy Quantities", Thermodynamics Second Law Analysis, A.C.S. Symposium Series, 122, 39-60, 1980. 

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. 

From this equation, the following thermodynamic quantities are calculated... 

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. 

Altogether, 62 >S02 molecules were studied, not counting the atom and small fragment species needed to calculate certain thermodynamic quantities. The calculated results are presented in Tables 1-18 and Figures 1-60. Generally, the tables fall into the following categories. 

So far we have considered only the volume as a partial molar quantity. But calculations involving solutes will require knowledge of all the thermodynamic properties of dissolved substances, such as H, S, Cp, and of course G, as well as the pressure and temperature derivatives of these. These quantities are for the most part derived from calorimetric measurements, that is, of the amount of heat released or absorbed during the dissolution process, whereas V is the result of volume or density measurements. 

At least for this linear fluids mixfure, we (partially) overcome the usual objection to Truesdell s conception how to find fhe thermodynamic partial properties taken as primitives in this theory. Namely, we show that such partial quantities maybe calculated from the dependence of corresponding mixture properties on the composition using the so-called mixture invariance of balances [59], see Sects. 4.5 and 4.6. 

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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