Thermodynamic data polynomials

Tables 3 and 4 contain values of the log water activity and log sulfuric acid activity in molarity units. These can be obtained at any temperature by using the polynomial coefficients supplied by Zeleznik,45 which are based on all of the preexisting thermodynamic data obtained for this medium. The numbers were converted to the molarity scale using the conversion formula given in Robinson and Stokes 46 Molarity-based water activities are given for HCIO4 in Tables 5 and 6. These are calculated from data obtained at 25°C by Pearce and Nelson,17...

Burcat [ Thermochemical Data for Combustion Calculations, in Combustion Chemistry. (W. C. Gardiner, Jr., ed.), Chapter 8. John Wiley Sons, New York, 1984] discusses in detail the various sources of thermochemical data and their adaptation for computer usage. Examples of thermochemical data tit to polynomials for use in computer calculations are reported by McBride, B. J Gordon, S., and Reno, M. A., Coefficients for Calculating Thermodynamic and Transport Properties of Individual Species, NASA, NASA Langley, VA, NASA Technical Memorandum 4513, 1993, and by Kee, R. J., Rupley, F. M and Miller, J. A., The Chemkin Thermodynamic Data Base, Sandia National Laboratories, Livermore, CA, Sandia Technical Report SAND87-8215B, 1987. 

FITDAT Kee, R. J., Rupley, F. and Miller, J. A. Sandia National Laboratories, Livermore, CA 94550. A Fortran computer code (fitdat.f) that is part of the CHEMKIN package for fitting of species thermodynamic data (cp, h, s) to polynomials in NASA format for usage in computer programs. 

MECHMOD A utility program written by Turanyi, T. (Eotvos University, Budapest, Hungary) that manipulates reaction mechanisms to convert rate parameters from one unit to another, to calculate reverse rate parameters from the forward rate constant parameters and thermodynamic data, or to systematically eliminate select species from the mechanism. Thermodynamic data can be printed at the beginning of the mechanism, and the room-temperature heat of formation and entropy data may be modified in the NASA polynomials. MECHMOD requires the usage of either CHEMK1N-TT or CHEMKIN-III software. Details of the software may be obtained at either of two websites http //www.chem.leeds.ac.uk/Combustion/Combustion.html or http //garfield. chem.elte.hu/Combustion/Combustion. html. 

A. Burcat. Ideal Gas Thermodynamic Data in Polynomial Form for Combustion and Air Pollution Use. http //garfield.chem.elte.hu/Burcat/burcat.html or ftp //-ftp.technion.ac.il/pub/supported/aetdd/thermodynamics, 2002. 

The proper analysis of experimental data requires careful consideration of the numerical techniques used. Real data are subject to experimental error which can have an effect on results derived from the analysis. Often, this analysis involves fitting a curve to experimental data over the whole range or over part of the range in which experimental observations have been made. When thermodynamic data are involved, the relationship between the independent and dependent variable is usually not known. Then, arbitrary functions such as polynomials in the independent variable are often used in the data analysis. This type of data analysis requires consideration of the level of error in both variables, and of the effects of the error on derived results. 

Brechignaz, C., Cahuzac, P. et al., AlP Conf. Proc., Vol. 561,184-195, 2001. Broadus, K. M. and Kass, S. R., /. Am. Chem. Soc., 123, 4189-4196, 2001. Burcat, A., Ideal Gas Thermodynamic Data in Polynomial Form for Combustion and Air-Pollution Use, ftp //ftp.technion.ac.il/pub/supported/aetdd/ther-modynamics, or http //garfield.chem.elte.hu/Burcat/burcat.html, updated on May 2005. 

This computer program calculates the coefficients of the NASA polynomials from thermodynamic data supplied by the user. 

THERMDAT is a base of thermodynamic data of the CHEMKIN system, in the form of NASA polynomials. 

How to Change A, HzgsK Without Recalculating NASA Polynomials Sometimes better enthalpies of formation values are available for a substance and the polynomials need to be adapted. This can be done in the polynomial form without changing the remaining of the thermodynamic data of the species, if the other molecular properties of the substance need no update. In this case, we shall refer to Eq. (1.35) for NASA seven-term polynomials. The term that includes the information on the enthalpy of formation is a. To change, write... 

JANAF data were used to form polynomial expansions of the partition function for the range 1000 to 6000 K (of astrophysical interest) [33]. The dissociation function computed from thermodynamic data was presented graphically for the range 1000 to 6000 K [34]. 

Thermodynamic data which exists for anhydrous citric acid is given in the form of relative values. De Kruif et al. [8] reported not absolute values of thermodynamic functions, but changes in the Gibbs free energy, enthalpy and entropy, A[G(7)-G(90 K)], A[H(7)-H(90K)] and A[S(7)-S(90K)]. They can be represented in the 90Ktemperature range by the following polynomials... 

As well as rate coefficient information, thermodynamic data are required for the description of many chemical systems. A number of software packages are available to calculate thermodynamic data such as THERM (Ritter and Bozzelli 1991) or THERGAS (Muller et al. 1995). NASA polynomials are often used as a starting point for the calculation of thermod3niamic properties (see Sect. 2.2.3) and have been made available for many years via the data base of Alexander Burcat (Burcat 1984 Burcat and Ruscic 2005 Burcat) as well as in recent evaluations (Ruscic et al. 2003). 

Extrapolating a polynomial outside the temperature range where it was fitted calls for caution. Not only does the uncertainty increase, but the curve often deviates in a direction opposite to the normal trend. This may be a serious drawback, since most thermodynamic data tabulations, as discussed in the next section, cover temperature ranges too low for combustion calculations. Thus, when these data have to be extrapolated to higher temperatures, the polynomials usually used for this purpose may give improper results (see Fig. 1). 

The thermodynamic properties of single-component condensed phases are traditionally given in tabulated form in large data monographs. Separate tables are given for each solid phase as well as for the liquid and for the gas. In recent years analytical representations have been increasingly used to ease the implementation of the data in computations. These polynomial representations typically describe the thermodynamic properties above room temperature (or 200 K) only. 

D.B. Marsland, Data fitting by orthogonal polynomials, in. CACHE Thermodynamics (ed. R.V. Jelinek), Sterling Swift, Manchaca TX, 1971. 

Since the degree of coupling is directly proportional to the product Q (D/k)in, the error level of the predictions of q is mainly related to the reported error levels of Q values. The polynomial fits to the thermal conductivity, mass diifusivity, and heat of transport for the alkanes in chloroform and in carbon tetrachloride are given in Tables C1-C6 in Appendix C. The thermal conductivity for the hexane-carbon tetrachloride mixture has been predicted by the local composition model NRTL. The various activity coefficient models with the data given in DECHEMA series may be used to estimate the thermodynamic factors. However, it should be noted that the thermodynamic factors obtained from various molecular models as well as from two sets of parameters of the same model might be different. 

Exchange constants for low-dimensional magnets are most commonly obtained via comparison of experimental data to the predicted behavior of a thermodynamic property for a given model, usually the magnetic susceptibility. Johnston et al. showed that the molar susceptibility xm of the uniform chain can be expressed as a ratio of polynomials in powers ofthe reduced temperature t t = hgT/ 2J ). The coefficients N and D are listed in Table 1. 

The expansions in even powers of normal frequencies are of special interest, because they provide means for obtaining explicit relations between the equations of motion and the thermodynamic quantities, through the use of the method of moments The sum of over all the normal vibrations can be expressed as the trace, or the sum of all the diagonal elements, of a matrix H" obtained by multiplying the Hamiltonian matrix H of the system by itself (n — 1) times. Such expansions thus enable us to estimate the thermodynamic functions and their isotope effects from known force fields and structures without solving the secular equations, or alternatively, to estimate the force fields from experimental data on the thermodynamic quantities and their isotope effects. The expansions explicitly correlate the motions of particles with the thermodynamic quantities. They can also be used to evaluate analytically a characteristic temperature associated with the system, such as the cross-over temperature of an isotope exchange equilibrium. Such possible applications, however, are useful only if the expansion yields a sufficiently close approximation. The precision of results obtainable with orthogonal polynomial expansions will be explored later. 

As for volume variations with pressure, there is no fundamental thermodynamic basis for specifying the form of cell parameter variations with pressure. It is therefore not unusual to find in the literature cell parameter variations with pressure fitted with a polynomial expression such as a= aQ+a P+ a P, even when the P-V data have been fitted with a proper EoS function. Use of polynomials in P is not only inconsistent, it is also unphysical in that a linear expression implies that the material does not become stiffer under pressure, while a quadratic form will have a positive coefficient for implying that at sufficiently high pressures the material will expand with increasing... 

The polynomial coefficients of Cp(T) are obtained from numerical evaluations to the best possible approximation, and in many cases have no physical meaning. For certain substance phases several polynomials with up to 6 coefficients are necessary, which would require the use of up to 10 characters to present as figures. All basic thermochemical values including alpha-numerical information are stored in databases. For personal use only, they can be requested from the publisher or the author. These data are also included in the thermodynamic software system equiTherm, which is a very useful supplement to this book. 

In this problem, we compare the temperature dependence of the specific heat of triatomic ideal gases based on statistical thermodynamics and classical/empirical polynomials. Locate the appropriate molecular data for carbon dioxide (CO2) and nitrogen dioxide (NO2) that will allow you to compute and graph the specific heat at constant pressure Cp for both gases from 300 to 800 K at atmospheric pressure. The graphs that are generated should be based on calculations from statistical thermodynamics. 

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