Analytic Expressions for the Virial CoefficientsB(T) andC(T) of4He between 2.6 K and 300 K

Steur, P. P. M.; Durieux, M.; McConville, G. T.

doi:10.1088/0026-1394/24/2/003

Cited by 27 publications

(29 citation statements)

References 34 publications

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“…The second virial coefficient error calculated in the present work is within 0.1 cm 3 mol -1 for temperatures above 10 K, but this result increases to 0.63 cm 3 mol -1 for T = 3 K. Guided by the experimental error of 0.6 cm 3 mol -1 for lower temperatures, one may conclude that the potential used in the present calculation is appropriate in this temperature range. 8,38 Term contribution…”

Section: Resultsmentioning

confidence: 99%

“…The second virial coefficient experimental error will be assumed to be ± 0.01 cm 3 mol -1 , 8 which is below the average experimental error. One might then ask what will the allowed error in the potential parameter be, at a given temperature, to give this experimental error.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…[2][3][4][5] The potential refinement is very important in chemistry and is performed whenever new reliable data become available. Accurate values of helium properties, such as the low-temperature experimental virial coefficient, can be determined [6][7][8] and experimental 4 He 2 dimers can be identified. [9][10][11][12][13][14][15] Thus, a comparison between theory and experiment is an important test for the quality of the interatomic He potential.…”

Section: Introductionmentioning

confidence: 99%

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Quantum second virial coefficient calculation for the 4He dimer on a recent potential

Costa¹,

Lemes²,

Alves³

et al. 2013

J. Braz. Chem. Soc.

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Este trabalho concentra-se no cálculo do segundo coeficiente virial quântico, a partir de um potencial desenvolvido recentemente. Este coeficiente foi determinado com 4-5 algarismos significativos na faixa de temperatura de 3 a 100 K. Nossos resultados estão dentro do erro experimental. Três contribuições para o valor total deste coeficiente são o espalhamento quântico (contribuição de estados no contínuo), o estado ligado (contribuição de estados discretos) e o gás ideal quântico; discutimos estas contribuições separadamente. A contribuição mais importante é do espalhamento quântico, enquanto que as contribuições menores são dos estados discretos. Uma análise da sensibilidade foi realizada em função da temperatura para um parâmetro na região de curto alcance do potencial e para três parâmetros na região de longo alcance do potencial. Para ambas as temperaturas consideradas, 10 e 100 K, o coeficiente de dispersão C 6 foi o mais significativo, e o termo dispersão C 10 foi o menos significativo para o resultado total. Em geral, a precisão exigida para descrever os potenciais diminui com o aumento da temperatura. A precisão total e a relação dos parâmetros com os erros experimentais são discutidas. This paper focuses on the calculation of the quantum second virial coefficient, under a recently developed potential. This coefficient was determined to within 4-5 significant figures in the temperature range from 3 to 100 K. Our results are within experimental error. The three contributions to the overall value of the coefficient are the quantum scattering (continuum state contribution), the bound state (discrete state contribution) and the quantum ideal gas; we discuss these contributions separately. The most significant contribution is from the scattering states, whereas the smaller contributions are from the discrete states. A sensitivity analysis was performed as a function of temperature for one parameter in the short-range region of the potential and for three parameters in the long-range regions of the potential. For both temperatures considered, 10 and 100 K, the C 6 dispersion coefficient was the most significant, and the C 10 dispersion term was the least significant to the overall result. In general, the precision required to describe the potential decays as the temperature increases. The overall accuracy and the relationship of the parameters to the experimental errors are discussed.

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Section: Resultsmentioning

confidence: 99%

Section: Sensitivity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

Costa¹,

Lemes²,

Alves³

et al. 2013

J. Braz. Chem. Soc.

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show abstract

“…In the past, many different expressions were used. For the range between 2.6 K and 300 K, Steur et al [10] deduced for B(T ):…”

Section: Theory For the Virial Coefficients Of 4 Hementioning

confidence: 99%

“…As in [15], Eqs. 3 and 4 suggested by Steur et al [10] were applied with and without the high-temperature term b 7 T 2 . In addition, the expression C Pais (T ) proposed by Pais and Uhlenbeck [12] (Eq.5) for C(T ) has been tested.…”

Section: Multi-isotherm Fits-dcgt Scalementioning

confidence: 99%

Primary Dielectric-Constant Gas Thermometry in the Range from 2.4 K to 26 K at PTB

2008

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New dielectric-constant gas-thermometry (DCGT) measurements were performed at PTB from 2.4 K to 26 K in order to establish a temperature scale with reduced uncertainty. The progress concerning the measurement of capacitance changes, temperature, and pressure compared with the results published in 1996 is described. This is the first step on the way to determine the Boltzmann constant at the triple point of water. At more than 20 temperatures, isotherms were measured and evaluated performing both single-and multi-isotherm fits. Based on this evaluation, a more accurate DCGT scale has been established that is compared with the constant-volume gas-thermometry scale NPL-75, being one basis of the International Temperature Scale of 1990. Coincidence has been found within only a few tenths of a millikelvin above 3.3 K. This gives, together with literature data, confidence with respect to thermodynamic temperature at this level. Emphasis is also given to the results obtained for the virial coefficients, especially below 3.3 K, where the 1996 DCGT results show strong deviations from the expected behavior. The new experimental data for the second virial coefficient are compared with ab initio calculations.

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Berechnung des zweiten Virialkoeffizienten B(T) für gasförmigen molekularen Wasserstoff im Temperaturintervall von 1 K bis 3000 K

Artym¹,

Kliem²

1991

Ber Bunsenges Phys Chem

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The second virial coefficient B(T) of hydrogen (H2) has been calculated at temperatures over the range 1 K to 3000 K using the Woolley potential function. The potential constants ε/k = 28,79 K, rm = 0,34473 nm, e1 = 0,01 have been determined from the B(T)‐data of Michels et al. (1959). The calculated second virial coefficients B(T) agree very well with the available experimental data over the whole temperature range from 13 K to 3000 K. A new method of calculating second virial coefficients has been suggested for low temperatures based on the representation of (y–y0)/(x–x0) vs x by a straight line (x = T1/2, y = T5/4 B).

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Analytic Expressions for the Virial CoefficientsB(T) andC(T) of⁴He between 2.6 K and 300 K

Cited by 27 publications

References 34 publications

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

Primary Dielectric-Constant Gas Thermometry in the Range from 2.4 K to 26 K at PTB

Berechnung des zweiten Virialkoeffizienten B(T) für gasförmigen molekularen Wasserstoff im Temperaturintervall von 1 K bis 3000 K

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