vogl_1972 ========= W\. F\. Vogl and K\. R\. Hall, "Compressibility data and virial coefficients for helium, neon and one mixture", Physica 59, 529 \(1972\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1016/0031\-8914\(72\)90204\-2 `__ **Source kind:** measurement **Recorded technique:** A low\-pressure Burnett apparatus \(University of Virginia; Vogl's 1971 dissertation, their ref\. 1\)\: the cells in a gas\-bath thermostat \(Hallikainen 1053 thermotrol\), the temperature from a calibrated platinum\-resistance thermometer \(Leeds and Northrup 8164\-B\) with a Mueller bridge \(Rubicon 1551\), the pressure from an air\-piston gauge \(Ruska 2465\) with a differential pressure\-cell indicator \(Ruska 2413/2416\)\. Isotherms of two Burnett runs each at 40, 0 and \-40 C, between about 1 and 37 atm, for pure He, pure Ne and one He\-Ne mixture of 49\.4 mole % He\. The Burnett constants and virial coefficients are fitted simultaneously by non\-linear least squares \(Hall and Canfield 1970, their ref\. 2\), the number of virial coefficients chosen by Hall and Canfield's criterion \(their ref\. 3\); a pressure\-distortion correction, Eq\. \(4\), is applied\. **Materials in structured entries:** He, Ne **Dataset quantities:** cross\_second\_virial\_coefficient, mixture\_compressibility\_factor, mixture\_second\_virial\_coefficient, second\_virial\_coefficient **Contents:** 7 datasets; 0 formulas. Curation notes -------------- Identity VALIDATED\_WITH\_WARNINGS by the library \(the PDF's 2002 scan date against the 1972 registry year\); the first page reads 'Physica 59 \(1972\) 529\-535', checked against its image\. Received 6 August 1971\. Printed pp\. 529\-535 \(pdf pages 1\-7\)\. TABLE I \(pp\. 530\-531; the mixture's 51 points checked cell by cell against the image of p\. 530, 2026\-10\-01, every cell agreeing\)\: P \(atm\), Z and sigma\_z \(x 10^5\) at \+40, 0 and \-40 C, for 100\.00 % He, 49\.4 % He and 100\.00 % Ne\. Each isotherm is two Burnett runs, printed one after the other with a blank line between them; the cells file drops the blank line and the script splits the runs where the pressure rises again\. Only the 49\.4 % He mixture is extracted\: three datasets, one per isotherm, 18 points at 40 C and at 0 C \(1\.07\-36\.6 atm\) and 15 at \-40 C \(1\.55\-35\.4 atm\)\. The pure gases' Z \(He 18, 17, 16 points; Ne 18, 17, 16\) are not extracted\: optmat takes pure fluids from reference equations of state\. No pressure cut was needed \(all below 38 atm\)\. TABLE II \(p\. 531, image checked\)\: B\_2 \(sigma\_B2\) of He, the mixture and Ne at the three temperatures, and B\_3 \(sigma\_B3\) where fitted \(He at 40 and 0 C, 153\.7192 \(279\) and 133\.4656 \(132\); Ne at \-40 C, 393\.9654 \(179\)\)\. The table prints no unit; B\_2 is in cm^3/mol \(Table III's unit, and reproduced from Table I below\)\. The page prints seven digits with the imprecise ones staggered \(set as subscripts\: 11\.7\_1858\); the text \(p\. 533\) says all seven are needed to regenerate Z within experimental accuracy, though they are not that accurate\. The digits are kept as printed\. The B\_3 are not extracted\: the vocabulary has no third virial coefficient\. TABLE III \(p\. 532, image checked\)\: B\_12 for the 49\.4 % He\-50\.6 % Ne mixture at \+40, 0 and \-40 C, cm^3/mole, without an uncertainty\. Eq\. \(2\), from which it is computed, is printed with subscripts He and Ar for He and Ne \(a misprint of the labels; no number is affected\)\. Not extracted\: Table IV \(the Burnett cell and run constants\), Tables V and VI \(this work's Z at round pressures and B\_2 at 0 C, compared with other authors' values\)\. REPRODUCED \(computed 2026\-10\-01, R = 82\.0574 cm^3 atm/\(mol K\), T = t \+ 273\.15 K\)\: \- B\_2 of the mixture from the printed Z of both runs by Z = 1 \+ B rho, rho = P/\(Z R T\), weighted by 1/sigma\_z \(Table II fits no B\_3 for the mixture\)\: 12\.306, 12\.000 and 11\.452 cm^3/mol at 40, 0 and \-40 C against the printed 12\.30729, 11\.99564 and 11\.44466, within 0\.01, a tenth of the stated sigma\. He with B and C\: 11\.70 and 11\.93 at 40 and 0 C \(printed 11\.719, 11\.944\), with B alone 12\.214 at \-40 C \(12\.217\); Ne with B alone 12\.340 and 11\.375 at 40 and 0 C \(12\.328, 11\.382\), with B and C 9\.061 at \-40 C \(9\.059\)\. \- B\_12 from Table II by Eq\. \(2\) with x\_He = 0\.494\: 12\.58, 12\.34 and 12\.29 cm^3/mol against the printed 12\.57, 12\.33 and 12\.26; the paper's least\-squares route is not described further\. UNCERTAINTY\: 'All errors tabulated in this article have been calculated by propagation of error analysis' \(p\. 534, Hall and Canfield's method\)\: standard deviations, taken as 1 sigma\. The standard deviations of Z increase with pressure between 0\.001 % and 0\.035 % \(p\. 534; the synopsis says 0\.02 to 0\.04 %\); those of B\_2 range from 0\.8 % to 6 %, which the printed sigma\_B2 \(0\.1 to 0\.6 cm^3/mol\) match as absolute values\. No uncertainty is stated for the mole fraction, for the temperature or for B\_12; propagating the sigma\_B2 through Eq\. \(2\) gives 0\.36, 0\.25 and 0\.48 cm^3/mol at 40, 0 and \-40 C \(computed, not in the paper\)\. The temperature scale is not stated\. DOUBTS \(computed 2026\-10\-01 with CoolProp 8\.0\.0's reference equations, Ortiz Vega et al\. 2019 for He, Thol et al\. 2019 for Ne, B from the equation's zero\-density limit\)\: \- Pure Ne\: B\_2 = 12\.33, 11\.38 and 9\.06 cm^3/mol at 40, 0 and \-40 C against 11\.81, 10\.97 and 9\.73 from Thol et al\.\: \+4 % at 40 and 0 C \(five and four stated sigma\) and \-7 % at \-40 C \(1\.3 sigma\)\. The authors note their neon values 'appear to be consistently larger' than earlier work \(p\. 534; Table VI\: 11\.38 against 10\.90 and 10\.81 at 0 C\)\. The \-40 C neon isotherm is the least precise of Table I \(sigma\_z up to 42 x 10^\-5\) and needed a B\_3 of 394 cm^6/mol^2\. Any such error in B\_Ne enters B\_12 through Eq\. \(2\) with the weight x\_Ne^2/\(2 x\_He x\_Ne\) = 0\.51\. \- Pure He\: 11\.72, 11\.94 and 12\.22 cm^3/mol against 11\.78, 11\.95 and 12\.09 \(\-0\.5 %, 0 %, \+1\.0 %\), within the stated sigma\. \- Hence the mixture's B\_2 and Z, measured directly, are the primary datasets; the pure B\_2 and the B\_12 \(which carries the pure B\_2 of this work\) are kept as checks\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- vogl\_1972/Z\_x0494\_40C ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "Z_x0494_40C", "material": "He", "file": "He/vogl_1972__Z_x0494_40C.csv", "table": "tbl_b47536f1a05a", "quantity": "mixture_compressibility_factor", "unit": "1", "abscissa": "pressure", "abscissa_unit": "atm", "use": "primary", "parameters": { "partner": "Ne", "mole_fraction": 0.494, "temperature_k": 313.15 }, "uncertainty": { "column": true, "level": "1 sigma" } } Table I \(p\. 530\)\: Z of the 49\.4 mole % He\-Ne mixture at \+40 C, two Burnett runs \(rows run1\_k, run2\_k in the printed order\); sigma\_z printed x 10^5, written in units of Z\. vogl\_1972/Z\_x0494\_0C ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "Z_x0494_0C", "material": "He", "file": "He/vogl_1972__Z_x0494_0C.csv", "table": "tbl_b47536f1a05a", "quantity": "mixture_compressibility_factor", "unit": "1", "abscissa": "pressure", "abscissa_unit": "atm", "use": "primary", "parameters": { "partner": "Ne", "mole_fraction": 0.494, "temperature_k": 273.15 }, "uncertainty": { "column": true, "level": "1 sigma" } } Table I \(p\. 530\)\: Z of the 49\.4 mole % He\-Ne mixture at 0 C, two Burnett runs \(rows run1\_k, run2\_k in the printed order\); sigma\_z printed x 10^5, written in units of Z\. vogl\_1972/Z\_x0494\_m40C ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "Z_x0494_m40C", "material": "He", "file": "He/vogl_1972__Z_x0494_m40C.csv", "table": "tbl_b47536f1a05a", "quantity": "mixture_compressibility_factor", "unit": "1", "abscissa": "pressure", "abscissa_unit": "atm", "use": "primary", "parameters": { "partner": "Ne", "mole_fraction": 0.494, "temperature_k": 233.15 }, "uncertainty": { "column": true, "level": "1 sigma" } } Table I \(p\. 530\)\: Z of the 49\.4 mole % He\-Ne mixture at \-40 C, two Burnett runs \(rows run1\_k, run2\_k in the printed order\); sigma\_z printed x 10^5, written in units of Z\. vogl\_1972/B\_mix\_x0494 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_mix_x0494", "material": "He", "file": "He/vogl_1972__B_mix_x0494.csv", "table": "tbl_00584e89d11b", "quantity": "mixture_second_virial_coefficient", "unit": "cm3/mol", "abscissa": "temperature", "abscissa_unit": "C", "use": "primary", "parameters": { "partner": "Ne", "mole_fraction": 0.494 }, "uncertainty": { "column": true, "level": "1 sigma" } } Table II \(p\. 531\)\: B\_2 of the 49\.4 mole % He\-Ne mixture at 40, 0 and \-40 C, seven digits as printed \(the last ones staggered on the page as imprecise\), sigma\_B2 in parentheses\. Reproduced from Table I's Z within 0\.01 cm^3/mol \(the record's notes\)\. vogl\_1972/B12 ~~~~~~~~~~~~~~ .. code-block:: text { "id": "B12", "material": "He", "file": "He/vogl_1972__B12_Ne.csv", "table": "tbl_aa7d07823f8a", "quantity": "cross_second_virial_coefficient", "unit": "cm3/mol", "abscissa": "temperature", "abscissa_unit": "C", "use": "check", "parameters": { "partner": "Ne" }, "uncertainty": { "level": "not stated" } } Table III \(p\. 532\)\: B\_12 of He\-Ne from Table II by Eq\. \(2\); no uncertainty printed \(0\.25\-0\.48 cm^3/mol propagated from Table II's sigma, computed\)\. A check, not fitted beside B\_mix\_x0494, from which it is derived with this work's pure\-gas B\_2 \(the record's doubts on neon\)\. vogl\_1972/B\_He ~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_He", "material": "He", "file": "He/vogl_1972__B_He.csv", "table": "tbl_00584e89d11b", "quantity": "second_virial_coefficient", "unit": "cm3/mol", "abscissa": "temperature", "abscissa_unit": "C", "use": "check", "uncertainty": { "column": true, "level": "1 sigma" } } Table II \(p\. 531\)\: B\_2 of pure He at 40, 0 and \-40 C, as printed, sigma\_B2 in parentheses\. A check\: optmat takes pure\-gas B from the reference equations of state\. vogl\_1972/B\_Ne ~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_Ne", "material": "Ne", "file": "Ne/vogl_1972__B_Ne.csv", "table": "tbl_00584e89d11b", "quantity": "second_virial_coefficient", "unit": "cm3/mol", "abscissa": "temperature", "abscissa_unit": "C", "use": "check", "uncertainty": { "column": true, "level": "1 sigma" } } Table II \(p\. 531\)\: B\_2 of pure Ne at 40, 0 and \-40 C, as printed, sigma\_B2 in parentheses\. A check\: 4 % above Thol et al\. \(2019\) at 40 and 0 C and 7 % below at \-40 C \(the record's doubts\)\. Formulas -------- No formulas are recorded. 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.