Construction and Start-up of a Large-Volume Thermostat for Dielectric-Constant Gas Thermometry

A liquid-bath thermostat with a volume of about 800  L was designed to provide a suitable thermal environment for a dielectric-constant gas thermometer (DCGT) in the range from the triple point of mercury to the melting point of gallium. In the article, results obtained with the unique, huge thermostat without the DCGT measuring chamber are reported to demonstrate the capability of controlling the temperature of very large systems at a metrological level. First tests showed that the bath together with its temperature controller provide a temperature variation of less than ±0.5mK peak-to-peak. This temperature instability could be maintained over a period of several days. In the central working volume (diameter—500mm, height—650mm), in which the vacuum chamber containing the measuring system of the DCGT will be placed later, the temperature inhomogeneity has been demonstrated to be also well below 1mK.     

Capabilities for Dielectric-Constant Gas Thermometry in a Special Large-Volume Liquid-Bath Thermostat

Dielectric-constant gas thermometry is being further developed at PTB to measure thermodynamic temperature and the Boltzmann constant at the triple point of water. For this purpose, a huge liquid-bath thermostat with a liquid volume of about 800 L has been built to provide a suitable thermal environment in the central working volume (diameter 0.5 m, height 0.65 m), in which the vacuum chamber containing the measuring system is placed. Measurements of the temperature field in the working volume have been performed with and without the chamber using a mesh of 12 platinum resistance thermometers at appropriate positions. The results verify that the temperature inhomogeneity in the bath is well below 1 mK as necessary. The uncertainty of the temperature measurement inside the measuring system must be of the order of 0.1 mK. Its thermal conditions have been, therefore, investigated in detail, too. Special emphasis was given to the thermalization after temperature changes.     

Acoustic and Volumetric Virial Coefficients of Nitrogen

Speeds of sound in nitrogen were measured at temperatures between 170 and 400 K at amount-of-substance densities between 40 and 400 mol·m^–3. From these measurements, second and third acoustic virial coefficients were obtained. The parameters of two- and three-body isotropic intermolecular potential-energy models were optimized in a simultaneous fit to the second and third acoustic virial coefficients and the ordinary second and third virial coefficients of nitrogen reported by Nowak et al. The results, which shows that the acoustic and ordinary virial coefficients are mutually consistent, may be used to predict second and third virial coefficients, and their acoustic counterparts, over a wide range of temperatures. The parameters of an anisotropic site-site potential-energy model were also obtained from a fit to the acoustic and ordinary second virial coefficients alone.     

Second and Third Virial Coefficients for Hydrogen

Second and third virial coefficients for parahydrogen have been derived from closely spaced PVT data from 24 to 100 °K. They are in good agreement at 100 °K with published data for normal hydrogen. Analytical representations of the combined data from about 20 to 423 °K are presented which may be useful in computation of thermodynamic functions of the gas. These formulas are related to those resulting from the use of the Lennard-Jones potential.     

Ideal-Gas Heat Capacities and Virial Coefficients of HFC Refrigerants

Thermodynamic properties of HFC (hydrofluorocarbon) compounds have been extensively studied with worldwide interest as alternative refrigerants. Both quality and quantity in the experimental data far exceed those for the CFC and HCFC refrigerants. These data now provide a great opportunity to examine the validity of theoretical models, and vice versa. Among them, the ideal-gas heat capacity C _p ⁰ and virial coefficients derived from the experimental data are of particular interest, since they are directly related to the intramolecular and intermolecular potentials through the statistical mechanical procedure. There have been some discrepancies reported in the observed and theoretical C _p ⁰ for HFC compounds. We have performed new calculations of C _p ⁰ for several HFCs. The present results are consistent with the selected experimental values. The second (B) and third (C) virial coefficients have been reported for these HFC refrigerants from speed of sound data and Burnett PVT data. Often, a square well-type intermolecular potential is employed to correlate the data. However, the model potential cannot account consistently for both B and C coefficients with the same potential parameters. We have analyzed the data with the Stockmayer potential and obtained self-consistent results for various HFC (R-23, R-32, R-125, R-134a, R-143a, and R-152a) compounds with physically reasonable potential parameters.     

Accurate Effective Potentials of Real Substances from Acoustic Virial Coefficients

Accurate second acoustic virial coefficients have been employed to determine parameters of an effective intermolecular potential for nine pure substances: argon, nitrogen, carbon dioxide, carbon tetrafluoride, and the first five alkanes (methane, ethane, propane, butane, and pentane). The values used for the second acoustic virial coefficients were taken from data reported in the literature. To obtain the form and parameters of the effective potential, we employed an inversion method recently introduced for volumetric second virial coefficients of nonconformal potentials. The potential parameters determined in this way are useful in predicting various gas properties. The model reproduces the experimental second virial data within their uncertainty, including volumetric second virial coefficients that were not used in the potential determination.     

基准声学温度计的研究进展

热力学温度是一切温度测量(包括国际实用温标)的基准,是国际上公认的最基本的温度.声学温度计是测量中低温区热力学温度精度最高的方法之一,也是定容理想气体温度计最有效的替代方法之一.综述了声学温度计测量热力学温度的研究进展,分析了目前建立声学温度计的最主要方法-球共鸣声学法的测量原理及其进展,并对声学温度计的未来发展进行了展望.     

Path-Integral Calculation of Cross Second Virial Coefficients for Hydrogen Isotopologues

The path-integral Monte Carlo technique and a recent high-accuracy six-dimensional potential are used to compute the cross second virial coefficients for all unlike pairs among the hydrogen isotopologues $\mathrm{H}_{2}, \mathrm{D}_{2}, \mathrm{T}_{2}$ H 2 , D 2 , T 2 , HD, HT, and DT. Values are calculated from 15 K to 2000 K for these quantities where experimental information is almost completely absent. It is found that the commonly assumed arithmetic mean of the pure-component values does not provide a good approximation for the cross coefficients below approximately 50 K, especially for pairs containing $\mathrm{H}_{2}$ H 2 .     

Burnett Measurements and Virial Coefficients for the R32 + N2O System

Experimental results for the difluoromethane (R32) + nitrous oxide (N₂O) system are presented in this paper. The Burnett apparatus was calibrated using helium, and its performance was confirmed by measurements for pure N ₂O. The values of the virial coefficients for R32 were adopted from previous measurements as the same sample was used in the present study. PVTx measurements were performed for the binary R32 + N₂O system for four isotherms (303, 323, 343, and 364 K). Twenty Burnett expansions were performed in a pressure range from 5000 to 150 kPa. The second and third virial coefficients along with the cross second and third virial coefficients were derived from experimental results. Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui, P. R. China An erratum to this article can be found at     

NBS/NIST Gas Thermometry From 0 to 660 °C

In the NBS/NIST Gas Thermometry program, constant-volume gas thermometers, a unique mercury manometer, and a highly accurate thermal expansion apparatus have been employed to evaluate temperatures on the Kelvin Thermodynamic Temperature Scale (KTTS) that correspond to particular temperatures on the 1968 International Practical Temperature Scale (IPTS-68). In this paper, we present a summary of the NBS/NIST Gas Thermometry project, which originated with planning activities in the late 1920s and was completed by measurements of the differences t(KTTS)-t(IPTS-68) in the range 0 to 660 °C. Early results of this project were the first to demonstrate the surprisingly large inaccuracy of the IPTS-68 with respect to the KTTS above 0 °C. Advances in several different measurement techniques, development of new, specialized instruments, and two distinct sets of gas thermometry observations have resulted from the project.     

Corresponding-States Correlation and Prediction of Third Virial Coefficients for a Wide Range of Substances

An extended corresponding-states model is developed that is capable of correlating and predicting the third virial coefficients for a wide range of substances. The present method only requires substance-dependent parameters, such as the critical temperature, critical volume, acentric factor, and aspherical factor, which are based on the simple extended corresponding-states principle. Comparisons with experimental data and existing models show that the present model is more general in that it not only is equivalent to the existing method for nonpolar gases, but also can represent the third virial coefficients of polar substances.     

Virial Coefficients from Burnett Measurements for the R23 + N2O System

This paper presents experimental results for the trifluoromethane (R23) + nitrous oxide (N₂O) system, which has been chosen as a working fluid for low-temperature applications since it might be a valid option for the low-temperature stage in a cascade cycle. The thermodynamic properties of the binary mixture’s constituents are well known from the literature, but no experimental results have been published to date on the PVTx properties of this binary system. PVTx measurements were obtained for the binary R23 + N₂O system for three isotherms (303, 323, and 343 K), performing 15 Burnett expansions in a range of pressures from about 4400 to 80 kPa. The second and third virial coefficients were derived from experimental results together with the second and third cross virial coefficients. The experimental uncertainties in the second and third virial coefficients were estimated to be within ±1 cm³·mol⁻¹ and ±500 cm⁶·mol⁻², respectively.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September, 5-8, 2005, Bratislava, Slovak Republic.     

An Investigation of the Relation Between Contact Thermometry and Dew-Point Temperature Realization

Precision optical dew-point hygrometers are the most commonly used transfer standards for the comparison of dew-point temperature realizations at National Metrology Institutes (NMIs) and for disseminating traceability to calibration laboratories. These instruments have been shown to be highly reproducible when properly used. In order to obtain the best performance, the resistance of the platinum resistance thermometer (PRT) embedded in the mirror is usually measured with an external, traceable resistance bridge or digital multimeter. The relation between the conventional calibration of miniature PRTs, prior to their assembly in the mirrors of state-of-the-art optical dew-point hygrometers and their subsequent calibration as dew-point temperature measurement devices, has been investigated. Standard humidity generators of three NMIs were used to calibrate hygrometers of different designs, covering the dew-point temperature range from ?75 °C to + 95 °C. The results span more than a decade, during which time successive improvements and modifications were implemented by the manufacturer. The findings are presented and discussed in the context of enabling the optimum use of these transfer standards and as a basis for determining contributions to the uncertainty in their calibration.     

Determination of Second Virial Coefficients and Virial Equations of R-32 (Difluoromethane) and R-125 (Pentafluoroethane) Based on Speed-of-Sound Measurements

The second virial coefficients, B, for difluoromethane (R-32, CH₂F₂) and pentafluoroethane (R-125, CF₃CHF₂) are derived from speed-of-sound data measured at temperatures from 273 to 343 K with an experimental uncertainty of ±0.0072%. Equations for the second virial coefficients were established, which are valid in the extensive temperature ranges from 200 to 400 K and from 240 to 440 K for R-32 and R-125, respectively. The equations were compared with theoretically derived second virial coefficient values by Yokozeki. A truncated virial equation of state was developed using the determined equation for the virial coefficients. The virial equation of state represents our speed-of-sound data and most of the vapor PT data measured by deVries and Tillner-Roth within ±0.01 and ±0.1%, respectively.     

CO2 + R23 Binary System: Virial Coefficients Derived from Burnett Measurements

Burnett PVT measurements were performed on trifluoromethane (R23) and mixtures of R23 with carbon dioxide (CO₂). The Burnett apparatus was calibrated using helium. Fourteen expansions were performed for 5 isotherms and in a pressure range from 130 kPa to 6 MPa for R23. Second and third virial coefficients were derived from the collected data and compared with literature values; good agreement was found between them. PVTx measurements for the binary CO₂+R23 system were carried out for five isotherms (303, 313, 323, 333, and 343 K). In all, 18 runs were performed in a pressure range from 150 kPa to 5.9 MPa. The composition of the mixtures was measured with a gas chromatograph after it had been calibrated using samples prepared gravimetrically. Second and third virial coefficients for the system were derived, together with the second and third cross virial coefficients, from experimental results using virial coefficients for CO₂ from previous measurements (for the same sample as used in the present study). Samples for composition measurements were collected during the first Burnett expansion. Second virial coefficients for the system showed positive deviations from ideal values, while the third virials were negative. No previous experimental results were found for the PVTx properties of this binary system.     

Constant-Volume Gas Thermometry with Different Helium-3 Gas Densities at NMIJ/AIST

Constant-volume gas thermometer (CVGT) measurements are conducted using ³He of three different densities as the working gas to obtain the thermodynamic temperature T _CVGT and the second virial coefficient of ³He, B, at temperatures down to 3 K, using the triple point of Ne as a reference temperature. Densities of 127 mol ?? m^?3 and 278 mol ?? m^?3 are used in addition to the density of 168 mol ?? m^?3 used in the measurement reported previously, where T _CVGT was obtained using the virial coefficient adopted by the International Temperature Scale of 1990 (ITS-90), B _ITS-90. T _CVGT is obtained by two methods, by the single- and multi-isotherm fitting of B to the three densities and by the method used in the previous work using one of the three densities and B _ITS-90. B obtained from the isotherm fitting agrees with B _ITS-90 within the uncertainty of the data used to derive B _ITS-90. Moreover, B obtained from a multi-isotherm fit agrees with that of recent theoretical ab initio calculations within 0.05?cm³ ?? mol^?1 at 5 K and above, and within 0.3?cm³ ?? mol^?1 down to 3 K. The values of T _CVGT obtained from the multi-isotherm fits assuming different forms for the temperature dependence of B agree with each other within 0.1?mK. T _CVGT obtained from the multi-isotherm fitting agrees with that obtained from the method in the previous report within 0.22?mK. The tendency of the difference between T _CVGT and the ITS-90 temperature reported in the previous work is confirmed in the present work.     

Installation of Relative Acoustic Gas Thermometry in the Low Temperature Range from 4.2 to 80 K

Measurement Techniques - A relative acoustic gas thermometry unit for reproducing and transmitting the unit of thermodynamic temperature, i.e., kelvin, in the low temperature range 4.2–80 K...     

The Second and Third Virial Coefficients of 3He from 3.3 K to 13 K from Experimental Data

International Journal of Thermophysics - The triple points of carbon dioxide (CO2 TP) and sulfur hexafluoride (SF6 TP) are candidate substitutes for the triple point of mercury from the set of...     

Progress Report on NMIJ Acoustic Gas Thermometry at the Triple Point of Water

Herein, progress in the development of an acoustic gas thermometry (AGT) system at the National Metrology Institute of Japan is reported. This AGT system is an initial low-cost version that uses a 1-l quasi-spherical resonator (QSR) made of oxygen-free copper. The system was tested by measuring the speed of sound in argon at the temperature of triple point of water. Measurements were conducted at ten different pressures, ranging from 60 kPa to 420 kPa. The ideal gas limit of the squared speed of sound was obtained through extrapolation, and a preliminary calculation of the Boltzmann constant, which was 12 ppm below the CODATA2014 value, was made. Large inconsistencies among microwave and acoustic modes were observed, which are dominant sources of uncertainty in speed of sound measurements. The system will be improved by replacing the present QSR with another one that is more precisely fabricated.