picard_2008 =========== A\. Picard, R\. S\. Davis, M\. Gläser and K\. Fujii, "Revised formula for the density of moist air \(CIPM\-2007\)", Metrologia 45, 149 \(2008\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1088/0026\-1394/45/2/004 `__ **Source kind:** compilation **Recorded technique:** The CIPM\-2007 equation of state for moist air, approved by the 96th CIPM meeting \(November 2007\)\: the CIPM\-81/91 equation with two constants amended, the mole fraction of argon \(from the KRISS mass\-spectrometric and LNE gas\-chromatographic determinations against gravimetric standards\) and the molar gas constant \(CODATA\), and an uncertainty evaluation following the GUM\. The composition of dry air is a reference \(conventional\) composition, the mole fractions of the US Standard Atmosphere 1976 with new argon, the default carbon dioxide and the oxygen that follows from it \(pp\. 149\-151\)\. **Materials in structured entries:** Ar, CH4, CO, CO2, H2, He, Kr, N2, N2O, Ne, O2, Xe **Dataset quantities:** mole\_fraction **Contents:** 12 datasets; 3 formulas. Curation notes -------------- Identity checked against the first page \(Metrologia 45 \(2008\) 149\-155, published 18 February 2008\)\. Page numbers are the journal's\: p\. = pdf page \+ 148\. THE COMPOSITION \(Table 1, p\. 151; image checked digit by digit\)\. Mole fractions of the twelve constituents of dry air, recorded as mole\_fraction datasets with parameters\.mixture = 'dry air \(CIPM\-2007\)', one per constituent \(all twelve are registered gases; no material is registered for air, which is a mixture, TC\-543\)\. N2 0\.780848, O2 0\.209390, Ar 0\.009332, CO2 0\.00040, Ne 18\.2e\-6, He 5\.2e\-6, CH4 1\.5e\-6, Kr 1\.1e\-6, H2 0\.5e\-6, N2O 0\.3e\-6, CO 0\.2e\-6, Xe 0\.1e\-6\. Every printed contribution x\_i M\_i is reproduced by the printed x\_i and M\_i to the last digit \(e\.g\. 0\.780848 x 28\.0134 = 21\.874207\), which confirms each digit of the major fractions; sum x\_i = 1 \- 2\.9e\-6, as the paper says \(p\. 150\: 'presumably due to minor rounding errors in \[12\]', hence the normalisation in Eq\. 3\); M\_a = sum x\_i M\_i/sum x\_i = 28\.96546 g/mol, as printed \(computed 2026\-09\-27\)\. Which values are whose\: N2, O2, CO2 and Ar are set by this paper \(Ar measured by KRISS and LNE, N2 the remainder, CO2 the conventional default, O2 = S \- x\_CO2\); the eight minor constituents are the US Standard Atmosphere 1976's, unchanged \(reproduced\)\. Water vapour is not a constituent of dry air\: moist air enters through x\_v \(Eq\. 1, Appendix A\)\. THE MOLAR MASSES of Table 1 \(10^\-3 kg/mol\: N2 28\.0134, O2 31\.9988, Ar 39\.948, CO2 44\.01, Ne 20\.18, He 4\.0, CH4 16\.0, Kr 83\.8, H2 2, N2O 44, CO 28, Xe 131\) are IUPAC 2005's \[17\], 'rounded for convenience' from CO2 on \(p\. 150\); no quantity, kept here and in the formula eq3\_molar\_mass\. UNCERTAINTY \(Table 2, p\. 152, standard uncertainties per the GUM, assuming x\_CO2 known exactly\)\. Parameter, standard uncertainty \(1e\-6 of its unit\), relative contribution to u\(rho\_a\)/rho\_a \(1e\-6\)\: R, 15 \(in 8\.314472\), 1\.7; M\_N2, 200 \(in g/mol\), 5\.4; M\_O2, 300, 2\.2; M\_Ar, 500, 0\.2; M\_CO2, 500, 0\.0; x\_Ar, 3 umol/mol, 1\.2; S = x\_O2 \+ x\_CO2, 60 umol/mol, 8\.3; Delta x\_O2, 60, 8\.3 \(type A\); Delta x\_CO2, 60, 8\.3 \(type A\); Z, 15 \(1e\-6\), 15\. Quadratic sums 18\.2 \(type B\), 11\.7 \(type A\); combined standard uncertainty of the formula itself 22e\-6 relative\. Only x\_Ar has a standard uncertainty of its own \(the dataset x\_Ar\); the oxygen components are in x\_O2's notes\. The sensitivities to the measured inputs \(Eq\. 6, p\. 152\)\: \+1e\-5 Pa^\-1 u\(p\), \-4e\-3 K^\-1 u\(T\), \-9e\-3 u\(h\), \-3e\-4 K^\-1 u\(t\_d\), \+0\.4 u\(x\_CO2\) \(relative\)\. THE DENSITY FORMULA \(Eqs\. 1\-5, p\. 150\-151; Appendix A, pp\. 153\-154\) is recorded as formulas without a form\: the composition's molar mass \(Eqs\. 3\-4\), the density \(Eqs\. 5a/5b\), and Appendix A's saturation vapour pressure \(A1\.1\), enhancement factor \(A1\.2\), water\-vapour mole fraction \(A1\.3\) and compressibility factor \(A1\.4\), valid for 600\-1100 hPa and 15\-27 degrees C \(Appendix A\.3\)\. R = 8\.314472\(15\) J/\(mol K\), 'recommended by CODATA 2006 \[15\]' \(p\. 150; the reference list's \[15\] is Mohr and Taylor's CODATA 2002, whose R is the same number\)\. The formula omits a term of about 0\.26 rho\_a x\_v \(0\.0004 \- x\_CO2\) \(p\. 152\)\. CIPM\-2007 against CIPM\-81/91 \(3\.48349 in Eq\. 5b\)\: \+72e\-6 relative, from x\_Ar \(\+67\.7e\-6\) and R \(\+4\.6e\-6\) \(p\. 152\); 3\.483740/3\.48349 \- 1 = 71\.8e\-6 \(computed\)\. OTHER VALUES \(notes only\)\: the gravimetric\-minus\-formula air density difference that prompted the revision, 6\.4e\-5 with standard uncertainty 1\.2e\-5 \(p\. 149; Picard et al\. 2004, Euromet project 144, Madec et al\. 2007\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- picard\_2008/x\_N2 ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_N2", "material": "N2", "file": "N2/picard_2008__x_N2.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "abscissa": "none", "use": "primary", "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_N2 = 0\.780848 mol/mol in the reference composition of dry air of the CIPM\-2007 equation\. N2\: 'not directly measured\. It is simply determined as the remainder when the mole fractions of all other components of dry air have been subtracted from 1' \(p\. 150\); it changed with the new argon value\. No uncertainty of its own is given \(Table 2 budgets S, x\_Ar and the molar masses\)\. picard\_2008/x\_O2 ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_O2", "material": "O2", "file": "O2/picard_2008__x_O2.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "abscissa": "none", "use": "primary", "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_O2 = 0\.209390 mol/mol in the reference composition of dry air of the CIPM\-2007 equation\. O2\: x\_O2 = S \- x\_CO2 with S = x\_O2 \+ x\_CO2 = 0\.20979 mol/mol \(Eq\. 2, p\. 150; Appendix B\), the value of S accepted from CIPM\-81 and \-81/91 \[1, 2\], so 0\.209390 = 0\.20979 \- 0\.00040 \(checked\)\. Uncertainty \(Table 2, Appendix B\)\: u\(S\) = 60 umol/mol \('each determination is within 50 umol/mol of the accepted value for S', KRISS's two air samples of different continents and elevations, each with u = 60 umol/mol\) and a further u\(Delta x\_O2\) = 60 umol/mol for oxygen changes not anticorrelated with CO2 \(standard uncertainties; the earlier estimate of 170 umol/mol rested on unconfirmed nineteenth\-century data\)\. No single u\(x\_O2\) is printed\: not recorded as the dataset's uncertainty\. picard\_2008/x\_Ar ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_Ar", "material": "Ar", "file": "Ar/picard_2008__x_Ar.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "abscissa": "none", "use": "primary", "uncertainty": { "absolute": 3e-06, "level": "standard" }, "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_Ar = 0\.009332 mol/mol in the reference composition of dry air of the CIPM\-2007 equation\. Ar\: 'x\_Ar = 9\.332\(3\) mmol/mol' \(pp\. 150, 153\), the new value of CIPM\-2007\: 'A weighted average gives essentially the KRISS result' \(KRISS 2002, Park et al\. \[11\]\: 9\.332\(3\) mmol/mol by mass spectrometry; LNE 2006, Sutour et al\. \[14\]\: 9\.330\(16\) by gas chromatography; both calibrated with gravimetric synthetic standards\)\. CIPM\-81 and \-81/91 used 9\.17 mmol/mol; atmospheric science had kept Moissan's 1903 9\.34\. The change raises the CIPM air density by 67\.7e\-6 \(p\. 152\)\. Standard uncertainty 3 umol/mol \(Table 2, the GUM evaluation\)\. picard\_2008/x\_CO2 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_CO2", "material": "CO2", "file": "CO2/picard_2008__x_CO2.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "abscissa": "none", "use": "primary", "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_CO2 = 0\.00040 mol/mol in the reference composition of dry air of the CIPM\-2007 equation\. CO2\: 'the average mole fraction of carbon dioxide in laboratory air, x\_CO2, has a default value of 0\.00040' \(p\. 150\), 'as in the previous CIPM formulas'\: a conventional reference value, not a measurement\. The formula is to be used with a measured x\_CO2 where available \(Eq\. 4\); otherwise an uncertainty for the assumption must be added \(Eq\. 6, 0\.4 u\(x\_CO2\) relative in density\)\: Euromet project 503 found 440 umol/mol on average among twelve laboratories, with maxima averaging 660 and reaching 1000 umol/mol \(p\. 152\)\. No uncertainty given for the default\. picard\_2008/x\_Ne ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_Ne", "material": "Ne", "file": "Ne/picard_2008__x_Ne.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "scale": 1e-06, "abscissa": "none", "use": "reproduced", "reproduced_from": [ "US Standard Atmosphere 1976 (Washington, DC: US Government Printing Office) pp. 3, 33" ], "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_Ne = 18\.2 x 10^\-6 mol/mol \(printed with its factor; scale 1e\-6\), a minor constituent of the CIPM\-2007 reference composition of dry air, taken unchanged from the mole fractions of \[12\], the US Standard Atmosphere 1976 \(p\. 150\: 'based on the mole fractions found in \[12\] with the following exceptions'\: argon, carbon dioxide and oxygen\)\. No uncertainty given; the minor constituents' molar masses are rounded \(p\. 150\)\. Adopted by CIPM\-2007 as part of its definition of dry air; the US Standard Atmosphere is not in the library\. picard\_2008/x\_He ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_He", "material": "He", "file": "He/picard_2008__x_He.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "scale": 1e-06, "abscissa": "none", "use": "reproduced", "reproduced_from": [ "US Standard Atmosphere 1976 (Washington, DC: US Government Printing Office) pp. 3, 33" ], "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_He = 5\.2 x 10^\-6 mol/mol \(printed with its factor; scale 1e\-6\), a minor constituent of the CIPM\-2007 reference composition of dry air, taken unchanged from the mole fractions of \[12\], the US Standard Atmosphere 1976 \(p\. 150\: 'based on the mole fractions found in \[12\] with the following exceptions'\: argon, carbon dioxide and oxygen\)\. No uncertainty given; the minor constituents' molar masses are rounded \(p\. 150\)\. Adopted by CIPM\-2007 as part of its definition of dry air; the US Standard Atmosphere is not in the library\. picard\_2008/x\_CH4 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_CH4", "material": "CH4", "file": "CH4/picard_2008__x_CH4.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "scale": 1e-06, "abscissa": "none", "use": "reproduced", "reproduced_from": [ "US Standard Atmosphere 1976 (Washington, DC: US Government Printing Office) pp. 3, 33" ], "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_CH4 = 1\.5 x 10^\-6 mol/mol \(printed with its factor; scale 1e\-6\), a minor constituent of the CIPM\-2007 reference composition of dry air, taken unchanged from the mole fractions of \[12\], the US Standard Atmosphere 1976 \(p\. 150\: 'based on the mole fractions found in \[12\] with the following exceptions'\: argon, carbon dioxide and oxygen\)\. No uncertainty given; the minor constituents' molar masses are rounded \(p\. 150\)\. Adopted by CIPM\-2007 as part of its definition of dry air; the US Standard Atmosphere is not in the library\. picard\_2008/x\_Kr ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_Kr", "material": "Kr", "file": "Kr/picard_2008__x_Kr.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "scale": 1e-06, "abscissa": "none", "use": "reproduced", "reproduced_from": [ "US Standard Atmosphere 1976 (Washington, DC: US Government Printing Office) pp. 3, 33" ], "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_Kr = 1\.1 x 10^\-6 mol/mol \(printed with its factor; scale 1e\-6\), a minor constituent of the CIPM\-2007 reference composition of dry air, taken unchanged from the mole fractions of \[12\], the US Standard Atmosphere 1976 \(p\. 150\: 'based on the mole fractions found in \[12\] with the following exceptions'\: argon, carbon dioxide and oxygen\)\. No uncertainty given; the minor constituents' molar masses are rounded \(p\. 150\)\. Adopted by CIPM\-2007 as part of its definition of dry air; the US Standard Atmosphere is not in the library\. picard\_2008/x\_H2 ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_H2", "material": "H2", "file": "H2/picard_2008__x_H2.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "scale": 1e-06, "abscissa": "none", "use": "reproduced", "reproduced_from": [ "US Standard Atmosphere 1976 (Washington, DC: US Government Printing Office) pp. 3, 33" ], "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_H2 = 0\.5 x 10^\-6 mol/mol \(printed with its factor; scale 1e\-6\), a minor constituent of the CIPM\-2007 reference composition of dry air, taken unchanged from the mole fractions of \[12\], the US Standard Atmosphere 1976 \(p\. 150\: 'based on the mole fractions found in \[12\] with the following exceptions'\: argon, carbon dioxide and oxygen\)\. No uncertainty given; the minor constituents' molar masses are rounded \(p\. 150\)\. Adopted by CIPM\-2007 as part of its definition of dry air; the US Standard Atmosphere is not in the library\. picard\_2008/x\_N2O ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_N2O", "material": "N2O", "file": "N2O/picard_2008__x_N2O.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "scale": 1e-06, "abscissa": "none", "use": "reproduced", "reproduced_from": [ "US Standard Atmosphere 1976 (Washington, DC: US Government Printing Office) pp. 3, 33" ], "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_N2O = 0\.3 x 10^\-6 mol/mol \(printed with its factor; scale 1e\-6\), a minor constituent of the CIPM\-2007 reference composition of dry air, taken unchanged from the mole fractions of \[12\], the US Standard Atmosphere 1976 \(p\. 150\: 'based on the mole fractions found in \[12\] with the following exceptions'\: argon, carbon dioxide and oxygen\)\. No uncertainty given; the minor constituents' molar masses are rounded \(p\. 150\)\. Adopted by CIPM\-2007 as part of its definition of dry air; the US Standard Atmosphere is not in the library\. picard\_2008/x\_CO ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_CO", "material": "CO", "file": "CO/picard_2008__x_CO.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "scale": 1e-06, "abscissa": "none", "use": "reproduced", "reproduced_from": [ "US Standard Atmosphere 1976 (Washington, DC: US Government Printing Office) pp. 3, 33" ], "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_CO = 0\.2 x 10^\-6 mol/mol \(printed with its factor; scale 1e\-6\), a minor constituent of the CIPM\-2007 reference composition of dry air, taken unchanged from the mole fractions of \[12\], the US Standard Atmosphere 1976 \(p\. 150\: 'based on the mole fractions found in \[12\] with the following exceptions'\: argon, carbon dioxide and oxygen\)\. No uncertainty given; the minor constituents' molar masses are rounded \(p\. 150\)\. Adopted by CIPM\-2007 as part of its definition of dry air; the US Standard Atmosphere is not in the library\. picard\_2008/x\_Xe ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "x_Xe", "material": "Xe", "file": "Xe/picard_2008__x_Xe.csv", "table": "tbl_b2ed47a88f5d", "quantity": "mole_fraction", "unit": "1", "scale": 1e-06, "abscissa": "none", "use": "reproduced", "reproduced_from": [ "US Standard Atmosphere 1976 (Washington, DC: US Government Printing Office) pp. 3, 33" ], "parameters": { "mixture": "dry air (CIPM-2007)" } } Table 1 \(p\. 151\)\: x\_Xe = 0\.1 x 10^\-6 mol/mol \(printed with its factor; scale 1e\-6\), a minor constituent of the CIPM\-2007 reference composition of dry air, taken unchanged from the mole fractions of \[12\], the US Standard Atmosphere 1976 \(p\. 150\: 'based on the mole fractions found in \[12\] with the following exceptions'\: argon, carbon dioxide and oxygen\)\. No uncertainty given; the minor constituents' molar masses are rounded \(p\. 150\)\. Adopted by CIPM\-2007 as part of its definition of dry air; the US Standard Atmosphere is not in the library\. Formulas -------- picard\_2008/eq3\_molar\_mass ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq3_molar_mass", "equation": "Eqs. (2)-(4), p. 150, with Table 1", "printed": "M_a = sum x_i M_i / sum x_i (Eq. 3) = 28.96546 x 10^-3 kg mol^-1; with a measured x_CO2: M_a = [28.96546 + 12.011 (x_CO2 - 0.0004)] x 10^-3 kg mol^-1 (Eq. 4); x_O2 + x_CO2 = 0.20979 mol mol^-1 = S (Eq. 2)", "variable": "x_CO2: mole fraction of carbon dioxide in dry air (mol/mol); M_a: molar mass of dry air", "range": "dry air of the Table 1 composition, x_CO2 near 0.0004", "coefficients": { "M_a": "28.96546e-3", "dM_dxCO2": "12.011e-3", "x_CO2_ref": "0.0004", "S": "0.20979" }, "check": "Table 1's x_i and M_i give sum x_i M_i/sum x_i = 28.965456 x 10^-3 kg/mol (sum x_i = 0.9999971), the printed 28.96546; 12.011 = M_CO2 - M_O2 = 44.01 - 31.9988 = 12.0112 (checked 2026-09-27)." } The molar mass of the CIPM\-2007 dry air; Eq\. \(4\) moves CO2 against O2 at fixed S \(Eq\. 2\)\. Air is not a material\: this formula is recorded for review \(solprop's air\)\. picard\_2008/eq5\_density ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq5_density", "equation": "Eqs. (1), (5a), (5b), pp. 150-151", "printed": "rho_a = (p M_a/(Z R T)) [1 - x_v (1 - M_v/M_a)] (Eq. 1); rho_a/(10^-3 kg m^-3) = [28.96546 + 12.011 (x_CO2 - 0.0004)]/8.314472 x (p/(Z T)) (1 - 0.3780 x_v) (Eq. 5a) = [3.483740 + 1.4446 (x_CO2 - 0.0004)] (p/(Z T)) (1 - 0.3780 x_v) (Eq. 5b); R = 8.314472(15) J mol^-1 K^-1; M_v = 18.01528(17) x 10^-3 kg mol^-1; 1 - M_v/M_a = 0.3780", "variable": "p: pressure in Pa; T = 273.15 + t/degrees C, the thermodynamic temperature in K; x_v: mole fraction of water vapour (Appendix A, formula appendix_a); Z: compressibility factor (Appendix A); rho_a in 10^-3 kg m^-3 as written (i.e. g m^-3 for p in Pa)", "range": "600-1100 hPa, 15-27 degrees C (Appendix A.3)", "coefficients": { "M_a": "28.96546", "dM_dxCO2": "12.011", "R": "8.314472", "R_sigma": "0.000015", "c0": "3.483740", "c1": "1.4446", "x_CO2_ref": "0.0004", "water": "0.3780", "M_v": "18.01528" }, "check": "28.96546/8.314472 = 3.483740 (5b's constant, checked); 12.011/8.314472 = 1.4446; 1 - 18.01528/28.96546 = 0.37803 (0.3780 printed). At 20 degrees C, 101 325 Pa, x_v = 0, x_CO2 = 0.0004, with appendix_a's Z = 0.99964: rho_a = 1.20456 kg/m^3 (computed; the paper prints no worked example). Checked 2026-09-27." } Combined relative standard uncertainty of the formula itself 22e\-6 \(Table 2\), to which the measured inputs' uncertainties are added with Eq\. \(6\)'s sensitivities\. The coefficient 0\.3780 is treated as constant; the missing term is about 0\.26 rho\_a x\_v \(0\.0004 \- x\_CO2\) \(p\. 152\)\. The density of moist air, not an optical quantity\: recorded for the air model\. picard\_2008/appendix\_a ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "appendix_a", "equation": "Eqs. (A1.1)-(A1.4), Appendix A, pp. 153-154", "printed": "p_sv = 1 Pa x exp(A T^2 + B T + C + D/T), A = 1.2378847 x 10^-5 K^-2, B = -1.9121316 x 10^-2 K^-1, C = 33.93711047, D = -6.3431645 x 10^3 K (A1.1); f = alpha + beta p + gamma t^2, alpha = 1.00062, beta = 3.14 x 10^-8 Pa^-1, gamma = 5.6 x 10^-7 K^-2 (A1.2); x_v = h f(p, t) p_sv(t)/p = f(p, t_d) p_sv(t_d)/p (A1.3); Z = 1 - (p/T)[a0 + a1 t + a2 t^2 + (b0 + b1 t) x_v + (c0 + c1 t) x_v^2] + (p^2/T^2)(d + e x_v^2), a0 = 1.58123 x 10^-6 K Pa^-1, a1 = -2.9331 x 10^-8 Pa^-1, a2 = 1.1043 x 10^-10 K^-1 Pa^-1, b0 = 5.707 x 10^-6 K Pa^-1, b1 = -2.051 x 10^-8 Pa^-1, c0 = 1.9898 x 10^-4 K Pa^-1, c1 = -2.376 x 10^-6 Pa^-1, d = 1.83 x 10^-11 K^2 Pa^-2, e = -0.765 x 10^-8 K^2 Pa^-2 (A1.4)", "variable": "T in K, t in degrees C, p in Pa; h the relative humidity (0-1), t_d the dew-point temperature", "range": "600-1100 hPa, 15-27 degrees C (Appendix A.3)", "coefficients": { "A": "1.2378847e-5", "B": "-1.9121316e-2", "C": "33.93711047", "D": "-6.3431645e3", "alpha": "1.00062", "beta": "3.14e-8", "gamma": "5.6e-7", "a0": "1.58123e-6", "a1": "-2.9331e-8", "a2": "1.1043e-10", "b0": "5.707e-6", "b1": "-2.051e-8", "c0": "1.9898e-4", "c1": "-2.376e-6", "d": "1.83e-11", "e": "-0.765e-8" }, "check": "No worked values are printed. Computed (2026-09-27): p_sv(20 degrees C) = 2339 Pa; Z(20 degrees C, 101 325 Pa, x_v = 0) = 0.999643. The constants are unchanged from CIPM-81/91 (p. 153); not checked against a printed value." } The interpolating formulas for x\_v and Z of the CIPM\-81/91 equation, 'listed here for completeness' \(p\. 153\)\. Z's uncertainty is dominated by the second virial coefficient of dry air \(15e\-6, Table 2\)\. 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.