An Apparatus Based on a Spherical Resonator for Measuring the Speed of Sound in Gases and for Determining the Boltzmann Constant

Segovia, José J.; Vega‐Maza, David; Martín, M. Carmen; Gómez, E.; Tabacaru, C.; Campo, D. del

doi:10.1007/s10765-010-0746-4

Cited by 11 publications

(20 citation statements)

References 16 publications

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“…Since the 1970s, acoustic resonators have been the preferred method for determining k B [2][3][4][5][6][7][8][9], thermodynamic temperatures [10][11][12][13][14], and the thermophysical properties of gases. For determining k B , acoustic resonators rely on kinetic theory to relate the speed of sound in a dilute monatomic gas to the kinetic energy of the gas atoms and, therefore, to the thermodynamic temperature.…”

Section: Introductionmentioning

confidence: 99%

Progress Toward Redetermining the Boltzmann Constant with a Fixed-Path-Length Cylindrical Resonator

et al. 2011

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A single, fixed-path-length cylindrical-cavity resonator was used to measure c 0 = (307.825 2 ± 0.001 2) m · s −1 , the zero-density limit of the speed of sound in pure argon at the temperature of the triple point of water. Three even and three odd longitudinal modes were used in this measurement. Based on the ratio M/γ 0 = (23.968 644 ± 0.000 033) g · mol −1 , determined from an impurity and isotopic analysis of the argon used in this measurement and the measured c 0 , the value k B = 1.380 650 6 × 10 −23 J · K −1 was obtained for the Boltzmann constant. This value of k B has a relative uncertainty u r (k B ) = 7.9 × 10 −6 and is fractionally, (0.12 ± 8.1) × 10 −6 larger than the value recommended by CODATA in 2006. (The uncertainty is one standard uncertainty.) Several, comparatively large imperfections of our prototype cavity affect the even longitudinal modes more than the odd modes. The models for these imperfections are approximate, but they suggest that an improved cavity will significantly reduce the uncertainty of c 0 .

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Section: Introductionmentioning

confidence: 99%

Progress Toward Redetermining the Boltzmann Constant with a Fixed-Path-Length Cylindrical Resonator

et al. 2011

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“…The experimental set-up is described in a previous work [6]. It is equipped with two capsuletype platinum resistance thermometers whose calibration standard uncertainties are ± 2 mK at T = 273.16 K and ± 5 mK at T = 250.00 K. Pressure is measured by means of two resonant quartzcrystal manometers for pressure ranges (0 to 2) MPa and (1 to 20) MPa with a relative standard uncertainty of ± 1•10 -4 Pa/Pa.…”

Section: Methodsmentioning

confidence: 99%

“…R is the ideal gas constant, the adiabatic coefficient as a perfect gas (γ pg ) drives the molar isochoric and isobaric heat capacities (Cv and Cp, respectively) thanks to Mayer's relation, as seen in equations 5and (6).…”

Section: Acoustic Modelmentioning

confidence: 99%

Heat capacities and acoustic virial coefficients for a synthetic coal mine methane mixture by speed of sound measurements at T = (273.16 and 250.00) K

Pérez-Sanz

Martín

Chamorro

et al. 2016

The Journal of Chemical Thermodynamics

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Measurements of speed of sound for a synthetic coal mine methane mixture of ten components are reported. Data were obtained using a spherical resonator for two isotherms T = (273.16 and 250.00) K and pressures up to 8 MPa. The uncertainty study is detailed and the total uncertainty of the speed of sound is no worse than 0.01%. Heat capacities and acoustic virial coefficients were obtained through said measurements. Results are compared with the GERG-2008 equation of state.

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“…is that of a triaxial ellipsoid with axes of length a, a•(1+ε1); a•(1+ε2): [6] and a sketch of our units is shown in [7]. The northern hemisphere is provided with two antennas at positions (θs, ϕs) = (π/4, π/4) and (θd, ϕd) = (π/4, 5π/4).…”

Section: Quasi Spherical Cavity Description and Geometrical Charactermentioning

confidence: 99%

Updated determination of the molar gas constantRby acoustic measurements in argon at UVa-CEM

et al. 2017

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A new determination of the molar gas constant was performed from measurements of the speed of sound in argon at the triple point of water and extrapolation to zero pressure. A new resonant cavity was used. This is a triaxial ellipsoid whose walls are gold-coated steel and which is divided into two identical halves that are bolted and sealed with an O-ring. Microwave and electroacoustic traducers are located in the northern and southern parts of the cavity, respectively, so that measurements of microwave and acoustic frequencies are carried out in the same experiment. Measurements were taken at pressures from 600 kPa to 60 kPa and at 273.16 K. The internal equivalent radius of the cavity was accurately determined by microwave measurements and the first four radial symmetric acoustic modes were simultaneously measured and used to calculate the speed of sound. The improvements made using the new cavity have reduced by half the main contributions to the uncertainty due to the radius determination using microwave measurements which amounts to 4.7 parts in 10 6 and the acoustic measurements, 4.4 parts in 10 6 , where the main contribution (3.7 parts in 10 6) is the relative excess half-widths associated with the limit of our acoustic model, compared with our previous measurements. As a result of all the improvements with the new cavity and the measurements performed, we determined the molar gas constant R = (8.314449  0.000056) J•K-1 •mol-1 which corresponds to a relative standard uncertainty of 6.7 parts in 10 6. The value reported in this paper lies-1.3 parts 2 in 10 6 below the recommended value of CODATA 2014, although still within the range consistent with it.

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An Apparatus Based on a Spherical Resonator for Measuring the Speed of Sound in Gases and for Determining the Boltzmann Constant

Cited by 11 publications

References 16 publications

Progress Toward Redetermining the Boltzmann Constant with a Fixed-Path-Length Cylindrical Resonator

Progress Toward Redetermining the Boltzmann Constant with a Fixed-Path-Length Cylindrical Resonator

Heat capacities and acoustic virial coefficients for a synthetic coal mine methane mixture by speed of sound measurements at T = (273.16 and 250.00) K

Updated determination of the molar gas constantRby acoustic measurements in argon at UVa-CEM

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