Thermochemical data

Thermochemical data

Every computed bound in the library comes from thermochemical data. extensions/chemistry/ reads that data in the three polynomial forms that publishers use. It fits polynomials to a table, writes CHEMKIN files, and carries each enthalpy's uncertainty into the results.

This page is a reference. For the rest of the library, see Process chemistry.

One fit, three forms

A ThermoFit holds the nine-coefficient NASA form of McBride, Zehe and Gordon (NASA TP-2002-211556), one set per temperature segment:

cp/R = a1 T^-2 + a2 T^-1 + a3 + a4 T + a5 T^2 + a6 T^3 + a7 T^4
H/RT = -a1 T^-2 + a2 ln(T)/T + a3 + a4 T/2 + a5 T^2/3 + a6 T^3/4
       + a7 T^4/5 + b1/T
S/R  = -a1 T^-2/2 - a2/T + a3 ln T + a4 T + a5 T^2/2 + a6 T^3/3
       + a7 T^4/4 + b2

Constructor	Form	Source
nasa9(bounds, coefficients)	Nine coefficients per segment	NASA TP-2002-211556, NASA CEA
nasa7(bounds, coefficients)	Seven, with a1 = a2 = 0	NASA TM-4513, CHEMKIN files
shomate(bounds, coefficients)	A to G, with t = T / 1000	The NIST Chemistry WebBook

The Shomate enthalpy coefficient F is in kJ/mol and holds the formation enthalpy. The coefficient H is not needed and is not read. shifted(dh, ds) moves a fit by a constant enthalpy and entropy. The catalog makes diamond from graphite this way.

H is the enthalpy of formation at 298.15 K plus the heat taken up since. So G = H - T S of each species is on one scale, and the sum over a reaction is its change. S is at one bar.

Read, write and fit

Function	Does
read_chemkin_thermo(text)	Reads CHEMKIN records, with the fifth element pair of extended files in columns 74 to 78
write_chemkin_thermo(species)	Writes CHEMKIN records, each coefficient as Fortran's E15.8 writes it
read_cea_thermo(text)	Reads NASA CEA thermo.inp records
fit_nasa7(points, low, common, high)	Fits two NASA-7 segments to a table

The CEA reader leaves out ions, records with no temperature interval, and formulas with a count that is not whole. A record that is short or that cannot be read raises an error with its line number. The writer takes fits of one or two segments in the seven-coefficient form.

fit_nasa7 takes a list of ThermoPoint: a temperature, the heat capacity, the enthalpy and the entropy, as JANAF tables give them. It fits the two heat capacity quartics together by least squares, equal at the common temperature. The enthalpy and entropy constants make H and S continuous there. Each segment needs five points at least.

Uncertainty

Species.set_uncertainty(u) sets the standard uncertainty of a species' enthalpy, as CODATA gives it with the enthalpy of formation. Substance.uncertainty_at(T) reads it for the phase at a temperature.

Reaction.delta_g_uncertainty(T) adds the terms' uncertainties in quadrature, each times its coefficient. Reaction.equilibrium_temperature_uncertainty(T, P) divides that by the change's slope in temperature. The tests check it against moving the data by the uncertainty and solving again.

The catalog

The catalog's 30 substances use NASA TM-4513 data, except Fe(a), which Cantera stores in the NASA-9 form of TP-2002-211556. All coefficients come unchanged from the conversion that Cantera 3.2 ships, and both sources are public domain. See THIRD-PARTY-NOTICES.md.

Checks

Check	Result
NASA-9 O2 from a CEA record and NASA-7 O2 from TM-4513	Agree to the 0.1 % the two fits differ by
NIST Shomate CO2 and NASA CO2	Agree in H, S and G
A table sampled from the CO2 fit, refitted	Gives back the fit
A CHEMKIN file written from species, read back	Gives back the species
Methane read from a CHEMKIN record	Equal to the catalog's G to 1e-6 J/mol

Limits

A fit is valid only over its range, and a computation outside a range raises an error. The NASA data of a condensed phase is for a pure, stoichiometric compound, as the FeO of Process maps shows.