schmidt_2003 ============ J\. W\. Schmidt and M\. R\. Moldover, "Dielectric Permittivity of Eight Gases Measured with Cross Capacitors", Int\. J\. Thermophys\. 24, 375 \(2003\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1023/A\:1022963720063 `__ **Source kind:** measurement **Recorded technique:** Relative dielectric permittivity eps\(p, T\) from a four\-ring toroidal cross capacitor \(superinvar electrodes, sapphire\-ball insulators; the capacitor, bridge, thermometers and pressure instruments of Moldover and Buckley 2001, 'MB'\), eps\_expt = \[C\_x\(p\)/C\_x\(0\)\]\(1 \+ k\_T p/3\) with the measured superinvar compressibility k\_T = \(9\.43 \+\- 0\.38\)e\-12 Pa^\-1 \(Eq\. 4\); capacitance ratios with sub\-ppm resolution \(a commercial bridge\)\. The deformation model is tested absolutely against the ab initio eps\(p, T\) of helium \(\ = \(\-0\.05 \+\- 0\.21\)e\-6, Fig\. 3\), and argon was measured simultaneously with a 16\-rod stainless\-steel cross capacitor \(\ \- \ = \(0\.161 \+\- 0\.025\)e\-6 \(p/MPa\), 3e\-5 A\_eps of argon; Sect\. 4\)\. Isotherms at 0, 23, 29\.3 and 40 degrees C \(and MB's 50 degrees C data, included in the fits\), pressures to 7 MPa in 1 MPa steps up and down, 3 to 7 h per step; temperatures within 2 mK \(ITS\-90\), pressure uncertainty 3e\-5 p \+ 84 Pa\. Densities from the reference equations of state\: Tegeler et al\. 1999 \(Ar\), Span et al\. 2000 \(N2\), Schmidt and Wagner 1985 \(O2\), Setzmann and Wagner 1991 \(CH4\), Span and Wagner 1996 \(CO2\) \(pp\. 3\-19\)\. **Materials in structured entries:** Ar, CH4, CO2, N2, O2 **Dataset quantities:** molar\_refractivity **Contents:** 9 datasets; 9 formulas. Curation notes -------------- Identity checked against the first page \(the pdf is an author copy titled 'EightGasEpsValues'; journal pages 375\-403 = pdf pages 1\-29\)\. Page numbers below are pdf pages\. WHAT A\_eps IS\. Molar polarizability wp = \[\(eps \- 1\)/\(eps \+ 2\)\]/rho = A\_eps\(1 \+ b rho \+ c rho^2 \+ \.\.\.\) \(Eq\. 5\); the fits use Eq\. \(9\)\: \(eps \- 1\)/\(eps \+ 2\) = A\_eps,273 rho \(1 \+ b rho \+ c rho^2\) \+ A\_tau rho \(T/273\.16 K \- 1\) \+ q rho^2 \(273\.16 K/T \- 1\), 'at most four coefficients' per fit, all data weighted equally \(p\. 18\)\. A\_eps,273 is the zero\-density molar polarizability at 273\.16 K where A\_tau is fitted, and a temperature\-independent A\_eps over 0\-50 degrees C where it is not\. It is the static \(bridge\-frequency\) value\: for Ar, N2 and O2 \(no infrared\-active vibration, no dipole\) the electronic polarizability; for CH4 and CO2 it includes the static vibrational polarizability \(hohm\_2013 subtracts 0\.23 au from CH4 and 2\.18 au from CO2, i\.e\. 0\.086 and 0\.81 cm^3/mol\)\. b, c, A\_tau and q are dielectric virial and temperature coefficients whose uncertainties 'from the equations of state are much larger than the indicated uncertainties' \(Table V caption\); b is 'determined via subtraction\: b ~ B \- A\_eps \+ a\_2/\(3 A\_eps\)' and its uncertainty 'is dominated by the uncertainty of B' \(p\. 20\)\. They are recorded only in the formulas \(no quantity holds b, a virial per unit A\_eps; B\_eps = A\_eps b\)\. UNCERTAINTY \(pp\. 19\-20, 25\)\. Table V caption\: 'For the more satisfactory fits, the uncertainty of the last two digits of each coefficient is shown in parentheses\. The uncertainty of A\_eps,273 from the elastic properties of the capacitor is 1\.1e\-4 cm^3 mol^\-1\.' No level is stated for the parentheses \(fit uncertainties\); stored as the sigma column, level 'not stated'\. The accuracy is larger\: 'the uncertainty of A\_eps,273 is the quadrature sum of three terms\: delta x A\_eps,273, 1e\-6 A\_eps,273/\(eps\_max \- 1\), and 1\.1e\-4 cm^3 mol^\-1' with delta ~ 3e\-5 from the pressure measurements \(p\. 19\), and for N2 \(p\. 25\) 'The error from the fit must be augmented by the three contributions \.\.\. 1\.3e\-4 cm^3 mol^\-1 from pressure measurements, 1\.1e\-4 from capacitance measurements, and 1\.1e\-4 from the deformation of the ring capacitor'\. Computed here from that budget \(not printed; eps\_max from the 0 degrees C column of Table IV\)\: the three terms add in quadrature to about 1\.9e\-4 \(Ar, O2\), 2\.0e\-4 \(N2\) and 2\.4e\-4 cm^3/mol \(CH4\); with the printed fit uncertainty, about 2\.7e\-4 \(Ar\), 2\.7e\-4 \(N2, two\-parameter fit\), 2\.1e\-4 \(O2, A\_tau fit\), 3\.9e\-4 cm^3/mol \(CH4, four\-parameter fit\), i\.e\. 50\-65 ppm\. The p\. 25 text gives N2 'A\_eps = \(4\.3878 \+\- 0\.0009\) cm^3 mol^\-1 where our uncertainty is from the two\-parameter fit in Table V', five times Table V's \(18\) in the last digits\: unexplained \(0\.0009 is also not the budget above\)\. Temperature dependence\: 'the three parameters A\_eps,273, A\_tau and b in Eq\. \(9\) are of interest to theory' \(p\. 19\); A\_tau of O2 0\.0065 cm^3/mol \(Younglove's \-0\.0059 inconsistent, p\. 22\), of N2 0\.0017 \(lowers sigma from 0\.91 to 0\.69\), of CH4 ~6e\-3 \(four parameters\) or ~11e\-3 with a fifth parameter b\_tau, bracketing Wong et al\.'s calculated 8\.4e\-3 and below Bose et al\.'s \(1972\) 17e\-3 \(p\. 22\)\. PREFERRED FITS\. N2\: the text quotes the two\-parameter value \(p\. 25\)\. O2\: the A\_tau fit \(Fig\. 5d; 'This is evidence that A\_eps is temperature\-dependent', p\. 21\)\. CH4\: the four\-parameter fit \('All four parameters are statistically significant', p\. 22\)\. CO2\: the four\-parameter fit with q \(Fig\. 7b; 'a temperature\-dependent A\_eps was much less significant than a rho^3 term', p\. 25\)\. Every A\_eps is recorded, use = check\. COMPARISONS \(pp\. 25\-27\)\. Ewing and Royal \(2002\), N2 at 300 K\: A\_eps = 4\.3921 \+\- 0\.0019, differing by 0\.0043 \+\- 0\.0021 cm^3/mol, 'the known uncertainties are too small to explain the small inconsistency'\. Straty and Goodwin's CH4 wp lies 0\.11\-0\.17 % below; Malbrunot et al\. A\_eps \+\- 0\.002; Bose et al\. \(bose\_1972\) at 280, 323, 373 K; CO2's q agrees with Bose and Cole's B\_eps decrease of 6\.9 \+\- 1\.3 cm^6/mol^2 from 29\.4 to 49\.7 degrees C \('our value for the decrease is 6\.5'\)\. Oxygen agrees with Younglove within scatter \(Fig\. 9\)\. Not extracted \(no quantity, or not a curated species\)\: Tables I\-IV, the raw 100\(eps \- 1\) against p \(kPa\)\: He at 29\.3 and 0\.019 degrees C \(Table I, the helium test\), propane and ethane \(Table II\), and CH4, N2, CO2, Ar, O2 at 29\.3 degrees C \(Table III, whose Methane and Nitrogen columns are merged into shared cells in the CSV, with N2's two extra points 3244\.67/1\.71409 and 2269\.70/1\.19627 merged into the last row\) and 0\.019 degrees C \(Table IV\)\. They are used below only to check the Eq\. \(9\) formulas\. The propane, ethane and CO2 three\-parameter rows of Table V; the propane dipole term \(Eq\. 10, mu = 0\.0848 D\)\. Helium\: no A\_eps is fitted here \(MB's recommended helium values are used for the theory comparison, p\. 9\)\. Reproductions of this paper\: may\_2008 \(schmidt\_moldover\_2003\_O2, its alpha\_e 1\.7461e\-40 F m^2 = 3 eps0 A\_eps/N\_A of the O2 A\_tau fit, 3\.95875\) and yang\_2025 \(schmidt\_moldover\_2003\_N2, 4\.3877\(2\)\) cite it\. May et al\. \(2008\) also REFIT these O2 eps\(p, T\) data together with theirs \(their Eq\. 19\)\: may\_2008's recommended O2 value is not independent of the O2 rows here \(double\-counting risk\)\. hohm\_2013 cites it for N2 \(11\.7379 au, the mean of the two N2 fits, 4\.38765 cm^3/mol\), O2 \(with may\_2008\), CO2 \(19\.652 au = 7\.34590\) and CH4 \(in a mean\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- schmidt\_2003/A\_eps\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_eps_Ar", "material": "Ar", "file": "Ar/schmidt_2003__A_eps_Ar.csv", "table": "tbl_d4ad17b1acdf", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "nm", "use": "check", "uncertainty": { "column": true, "level": "not stated" } } Table V\: A\_eps,273 = 4\.14203 \(19\) cm^3 mol^\-1, the two\-parameter fit \(A\_eps, b; Tegeler et al\. EoS; 10^6 sigma = 0\.98\), independent of temperature over 0\-50 degrees C\. Static dielectric, electronic polarizability \(argon\)\. Parenthesised fit uncertainty as sigma \(level not stated\); the budget of the source notes gives about 2\.7e\-4 cm^3/mol in all\. schmidt\_2003/A\_eps\_two\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_eps_two_N2", "material": "N2", "file": "N2/schmidt_2003__A_eps_two_N2.csv", "table": "tbl_d4ad17b1acdf", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "nm", "use": "check", "uncertainty": { "column": true, "level": "not stated" } } Table V\: A\_eps,273 = 4\.38782 \(18\) cm^3 mol^\-1, two\-parameter fit \(A\_eps, b; Span et al\. EoS; 10^6 sigma = 0\.91\), independent of temperature over 0\-50 degrees C\: the value the text quotes \(4\.3878 \+\- 0\.0009, p\. 25; the \+\- there is five times the parentheses\)\. Static dielectric, electronic\. Budget about 2\.7e\-4 cm^3/mol \(source notes\)\. schmidt\_2003/A\_eps\_tau\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_eps_tau_N2", "material": "N2", "file": "N2/schmidt_2003__A_eps_tau_N2.csv", "table": "tbl_d4ad17b1acdf", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "nm", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "temperature_k": 273.16 } } Table V\: A\_eps,273 = 4\.38748 \(15\) cm^3 mol^\-1 at 273\.16 K, three\-parameter fit with A\_tau = 0\.00170 \(30\) \(10^6 sigma = 0\.69\)\. Not independent of A\_eps\_two\_N2 \(the same data\)\. Static dielectric, electronic\. schmidt\_2003/A\_eps\_two\_O2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_eps_two_O2", "material": "O2", "file": "O2/schmidt_2003__A_eps_two_O2.csv", "table": "tbl_d4ad17b1acdf", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "nm", "use": "check" } Table V\: A\_eps,273 = 3\.95945 cm^3 mol^\-1, two\-parameter fit \(A\_eps, b; Schmidt and Wagner EoS; 10^6 sigma = 1\.86\), no uncertainty printed\: the fit the authors reject for O2 \(the isotherm deviations have opposite slopes, p\. 21\)\. Static dielectric, electronic\. schmidt\_2003/A\_eps\_tau\_O2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_eps_tau_O2", "material": "O2", "file": "O2/schmidt_2003__A_eps_tau_O2.csv", "table": "tbl_d4ad17b1acdf", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "nm", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "temperature_k": 273.16 } } Table V\: A\_eps,273 = 3\.95875 \(09\) cm^3 mol^\-1 at 273\.16 K, three\-parameter fit with A\_tau = 0\.00648 \(27\) \(10^6 sigma = 0\.39\)\: the preferred O2 fit \(Fig\. 5d\)\. may\_2008 refits these data with its own and reprints alpha\_e = 1\.7461e\-40 F m^2 \(= this value\); its recommended 3\.9576 is not independent of this one\. Static dielectric, electronic\. Budget about 2\.1e\-4 cm^3/mol \(source notes\)\. schmidt\_2003/A\_eps\_two\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_eps_two_CH4", "material": "CH4", "file": "CH4/schmidt_2003__A_eps_two_CH4.csv", "table": "tbl_d4ad17b1acdf", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "nm", "use": "check", "parameters": { "includes": "electronic + vibrational static polarizability" } } Table V\: A\_eps,273 = 6\.54787 cm^3 mol^\-1, two\-parameter fit \(A\_eps, b; Setzmann and Wagner EoS; 10^6 sigma = 2\.95\), no uncertainty printed \(Fig\. 6a; superseded by the four\-parameter fit\)\. Static dielectric\: electronic plus vibrational\. schmidt\_2003/A\_eps\_four\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_eps_four_CH4", "material": "CH4", "file": "CH4/schmidt_2003__A_eps_four_CH4.csv", "table": "tbl_d4ad17b1acdf", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "nm", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "temperature_k": 273.16, "includes": "electronic + vibrational static polarizability" } } Table V\: A\_eps,273 = 6\.54467 \(31\) cm^3 mol^\-1 at 273\.16 K, four\-parameter fit \(b = 1\.250 \(34\), c = \-44\.7 \(68\), A\_tau = 0\.00622 \(36\); 10^6 sigma = 0\.86\)\: the preferred CH4 fit \(Fig\. 6b\)\. Static dielectric\: electronic plus vibrational \(the vibrational part is about 0\.086 cm^3/mol, 1\.3 %\)\. Budget about 3\.9e\-4 cm^3/mol \(source notes\)\. schmidt\_2003/A\_eps\_three\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_eps_three_CO2", "material": "CO2", "file": "CO2/schmidt_2003__A_eps_three_CO2.csv", "table": "tbl_d4ad17b1acdf", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "nm", "use": "check", "parameters": { "includes": "electronic + vibrational static polarizability" } } Table V\: A\_eps,273 = 7\.3797 cm^3 mol^\-1, three\-parameter fit \(A\_eps, b, A\_tau = 0; Span and Wagner EoS; 10^6 sigma = 12\.6\), no uncertainty printed\. The authors replace it by the four\-parameter fit \(quadrupole term q, p\. 25\); this row does not reproduce Tables III\-IV \(formula eq9\_CO2\_three\)\. Static dielectric\: electronic plus the large vibrational part of CO2\. schmidt\_2003/A\_eps\_four\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "A_eps_four_CO2", "material": "CO2", "file": "CO2/schmidt_2003__A_eps_four_CO2.csv", "table": "tbl_d4ad17b1acdf", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "nm", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "includes": "electronic + vibrational static polarizability" } } Table V\: A\_eps,273 = 7\.34590 \(63\) cm^3 mol^\-1, four\-parameter fit \(b = 10\.023 \(80\), c = \-557\. \(20\), q = 114\.21 \(61\); 10^6 sigma = 1\.3\), independent of temperature \(no A\_tau\)\: the preferred CO2 fit \(Fig\. 7b\)\. The CO2 data used the older bath and are less precise; for CO2 the capacitance term dominates the A\_eps budget \(p\. 19\)\. Static dielectric\: electronic plus vibrational \(hohm\_2013 subtracts 2\.18 au = 0\.81 cm^3/mol, 11 %\)\. hohm\_2013 reprints it as 19\.652 \+\- 0\.002 au\. Formulas -------- schmidt\_2003/eq9\_Ar ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq9_Ar", "material": "Ar", "equation": "Eq. (9), p. 18; Table V, p. 20", "printed": "(eps - 1)/(eps + 2) = A_eps,273 rho (1 + b rho + c rho^2) + A_tau rho (T/273.16 K - 1) + q rho^2 (273.16 K/T - 1); Ar [13]: A_eps,273 = 4.14203 (19), b = 0.281 (15), 10^6 sigma = 0.98", "variable": "rho: molar density in mol/cm^3 (from the Tegeler et al. 1999 equation of state); T: temperature in K; A_eps,273, b in cm^3/mol; eps: static relative permittivity", "range": "0-50 degrees C, 0-7 MPa (the fitted isotherms, with MB's 50 degrees C data)", "coefficients": { "A_eps_273": "4.14203", "b": "0.281" }, "check": "With CoolProp's Tegeler equation of state (the paper's Ref. 13), reproduces the 26 non-zero points of Tables III (29.3 C) and IV (0.019 C) to 1.39 ppm rms in eps (mean -0.88 ppm), against the printed fit standard deviation 0.98 ppm over all isotherms. Checked 2026-09-26." } Two\-parameter fit; c, A\_tau, q zero\. schmidt\_2003/eq9\_N2\_two ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq9_N2_two", "material": "N2", "equation": "Eq. (9), p. 18; Table V, p. 20", "printed": "Eq. (9); N2 [14]: A_eps,273 = 4.38782 (18), b = 0.399 (14), 10^6 sigma = 0.91", "variable": "rho: molar density in mol/cm^3 (Span et al. 2000 equation of state); T in K; A_eps,273, b in cm^3/mol", "range": "0-50 degrees C, 0-7 MPa", "coefficients": { "A_eps_273": "4.38782", "b": "0.399" }, "check": "With CoolProp's Span et al. equation of state (Ref. 14), reproduces the 28 non-zero points of Tables III-IV to 1.31 ppm rms (mean -0.69 ppm); printed sigma 0.91 ppm. Checked 2026-09-26." } Two\-parameter fit\. schmidt\_2003/eq9\_N2\_tau ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq9_N2_tau", "material": "N2", "equation": "Eq. (9), p. 18; Table V, p. 20", "printed": "Eq. (9); N2 [14]: A_eps,273 = 4.38748 (15), b = 0.417 (11), A_tau = 0.00170 (30), 10^6 sigma = 0.69", "variable": "rho: molar density in mol/cm^3 (Span et al. 2000); T in K; A_eps,273, b, A_tau in cm^3/mol", "range": "0-50 degrees C, 0-7 MPa", "coefficients": { "A_eps_273": "4.38748", "b": "0.417", "A_tau": "0.00170" }, "check": "Reproduces the 28 non-zero points of Tables III-IV to 0.80 ppm rms (mean -0.25 ppm); printed sigma 0.69 ppm. Checked 2026-09-26." } A\_tau lowers sigma from 0\.91 to 0\.69 \(p\. 21\)\. schmidt\_2003/eq9\_O2\_two ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq9_O2_two", "material": "O2", "equation": "Eq. (9), p. 18; Table V, p. 20", "printed": "Eq. (9); O2 [15]: A_eps,273 = 3.95945, b = -0.113, 10^6 sigma = 1.86", "variable": "rho: molar density in mol/cm^3 (Schmidt and Wagner 1985); T in K; A_eps,273, b in cm^3/mol", "range": "0-50 degrees C, 0-7 MPa", "coefficients": { "A_eps_273": "3.95945", "b": "-0.113" }, "check": "Reproduces the 26 non-zero points of Tables III-IV to 2.00 ppm rms (mean -0.46 ppm); printed sigma 1.86 ppm. Checked 2026-09-26." } Rejected by the authors in favour of eq9\_O2\_tau \(Fig\. 5c\-d\)\. schmidt\_2003/eq9\_O2\_tau ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq9_O2_tau", "material": "O2", "equation": "Eq. (9), p. 18; Table V, p. 20", "printed": "Eq. (9); O2 [15]: A_eps,273 = 3.95875 (09), b = -0.077 (07), A_tau = 0.00648 (27), 10^6 sigma = 0.39", "variable": "rho: molar density in mol/cm^3 (Schmidt and Wagner 1985); T in K; A_eps,273, b, A_tau in cm^3/mol", "range": "0-50 degrees C, 0-7 MPa", "coefficients": { "A_eps_273": "3.95875", "b": "-0.077", "A_tau": "0.00648" }, "check": "Reproduces the 26 non-zero points of Tables III-IV to 0.49 ppm rms (mean -0.10 ppm); printed sigma 0.39 ppm. Checked 2026-09-26." } The preferred O2 fit\. may\_2008 refits these data with its own \(its Eq\. 19\: A\_eps,273 = 3\.95760, A\_tau = 0\.0037\)\. schmidt\_2003/eq9\_CH4\_two ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq9_CH4_two", "material": "CH4", "equation": "Eq. (9), p. 18; Table V, p. 20", "printed": "Eq. (9); CH4 [19]: A_eps,273 = 6.54787, b = 0.981, 10^6 sigma = 2.95", "variable": "rho: molar density in mol/cm^3 (Setzmann and Wagner 1991); T in K; A_eps,273, b in cm^3/mol", "range": "0-50 degrees C, 0-7 MPa", "coefficients": { "A_eps_273": "6.54787", "b": "0.981" }, "check": "Reproduces the 26 non-zero points of Tables III-IV to 5.12 ppm rms (mean -3.93 ppm); printed sigma 2.95 ppm (Fig. 6a shows structured residuals). Checked 2026-09-26." } Superseded by eq9\_CH4\_four\. schmidt\_2003/eq9\_CH4\_four ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq9_CH4_four", "material": "CH4", "equation": "Eq. (9), p. 18; Table V, p. 20", "printed": "Eq. (9); CH4 [19]: A_eps,273 = 6.54467 (31), b = 1.250 (34), c = -44.7 (68), A_tau = 0.00622 (36), 10^6 sigma = 0.86", "variable": "rho: molar density in mol/cm^3 (Setzmann and Wagner 1991); T in K; A_eps,273, b, A_tau in cm^3/mol; c in cm^6/mol^2", "range": "0-50 degrees C, 0-7 MPa", "coefficients": { "A_eps_273": "6.54467", "b": "1.250", "c": "-44.7", "A_tau": "0.00622" }, "check": "Reproduces the 26 non-zero points of Tables III-IV to 1.86 ppm rms (mean -0.53 ppm); printed sigma 0.86 ppm over all isotherms. Checked 2026-09-26." } The preferred CH4 fit \(Fig\. 6b\)\. Adding a fifth parameter b\_tau gives A\_tau ~ 11e\-3 \(p\. 22; not tabulated\)\. schmidt\_2003/eq9\_CO2\_three ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq9_CO2_three", "material": "CO2", "equation": "Eq. (9), p. 18; Table V, p. 20", "printed": "Eq. (9); CO2 [26]: A_eps,273 = 7.3797, b = 6.230, A_tau = 0, 10^6 sigma = 12.6", "variable": "rho: molar density in mol/cm^3 (Span and Wagner 1996); T in K; A_eps,273, b, A_tau in cm^3/mol", "range": "0-50 degrees C (CO2: 0.90 < T/T_c < 1.06, rho/rho_c < 0.26), to about 5 MPa", "coefficients": { "A_eps_273": "7.3797", "b": "6.230", "A_tau": "0" }, "check": "DOES NOT reproduce Tables III-IV: residuals -20 to -36 ppm (and +34 at the highest density) on the 0.019 C isotherm and -27 to -175 ppm, growing with density, on the 29.3 C isotherm (73 ppm rms), against the printed sigma 12.6 ppm. The fitted data include isotherms not tabulated (23, 40 C and MB's 50 C), but no single misprint explains the 29.3 C trend; unresolved (checked 2026-09-26). The four-parameter fit (eq9_CO2_four) reproduces the same points to 1.6 ppm." } Rejected by the authors \('a factor of 5 larger' sigma than ethane's, p\. 25\)\. schmidt\_2003/eq9\_CO2\_four ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq9_CO2_four", "material": "CO2", "equation": "Eq. (9), p. 18; Table V, p. 20", "printed": "Eq. (9); CO2 [26]: A_eps,273 = 7.34590 (63), b = 10.023 (80), c = -557. (20), q = 114.21 (61), 10^6 sigma = 1.3", "variable": "rho: molar density in mol/cm^3 (Span and Wagner 1996); T in K; A_eps,273, b in cm^3/mol; c, q in cm^6/mol^2", "range": "0-50 degrees C (0.90 < T/T_c < 1.06, rho/rho_c < 0.26)", "coefficients": { "A_eps_273": "7.34590", "b": "10.023", "c": "-557.", "q": "114.21" }, "check": "Reproduces the 22 non-zero points of Tables III-IV to 1.61 ppm rms (mean -0.13 ppm); printed sigma 1.3 ppm. Its q gives the decrease of B_eps = A_eps b + q (273.16/T - 1) from 29.4 to 49.7 C as 6.48 cm^6/mol^2, the text's 'our value for the decrease is 6.5' (p. 25). Checked 2026-09-26." } The preferred CO2 fit \(Fig\. 7b\); q allows for the quadrupole \(1/T\) term of the dielectric second virial\. Corrections ----------- No dataset errata are recorded in this source record. Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register ` for the checks and decisions.