Johnson Noise Thermometry near the Zinc Freezing Point Using Resistance-Based Scaling

Johnson noise thermometry (JNT) is a primary method of measuring temperature which can be applied over wide ranges. The National Institute of Standards and Technology (NIST) is currently using JNT to determine the deviations of the International Temperature Scale of 1990 (ITS-90) from the thermodynamic temperature in the range of 505–933 K, overlapping the ranges of both acoustic gas-based and radiation-based thermometry. Advances in digital electronics have now made viable the computationally intensive and data-volume-intensive processing required for JNT using noise-voltage correlation in the frequency domain. The spectral noise power, and consequently the thermodynamic temperature T, of a high-temperature JNT probe is determined relative to a known reference spectrum using a switched-input digital noise-voltage correlator and simple resistance-scaling relationships. Comparison of the JNT results with standard platinum resistance thermometers calibrated on the ITS-90 gives the deviation of the thermodynamic temperature from the temperature on the ITS-90, T − T ₉₀. Statistical uncertainties under 50 μK·K⁻¹ are achievable in less than 1 day of integration by fitting the effects of transmission-line time constants over bandwidths of 450 kHz. The methods and results in a 3 K interval near the zinc freezing point (T _90-ZnFP ≡ 692.677 K) are described. Preliminary results show agreement between the JNT-derived temperatures and the ITS-90.     

Acoustic Thermometry Results from 271 to 552 K

The NIST acoustic thermometer determines the thermodynamic temperature from measurements of ratios of the speed of sound of argon in a nearly spherical cavity. We report recent results for T − T ₉₀ on 12 isotherms spanning the range 271–552 K. (T is the thermodynamic temperature and T ₉₀ is the temperature on the International Temperature Scale of 1990.) The results are in excellent agreement with recent acoustic thermometry results reported by Benedetto et al. in the range from 273 to 380 K and with our previously reported results at 303, 430, and 505 K. The combined data sets are sufficiently redundant and sufficiently distributed over the temperature range to support a re-determination of the reference function for standard platinum resistance thermometers for a future temperature scale. The isotherms were analyzed using several methods; the T−T ₉₀ results and related uncertainties are insensitive to the method chosen. The thermal expansion of the stainless-steel resonator was deduced from the frequencies of the microwave resonances of the cavity. To clearly identify two nearly degenerate eigenmodes in our nearly axially symmetric resonator, two phased coupling probes were used to control the azimuthal angle of the microwave excitation.     

NMIJ Constant-Volume Gas Thermometer for Realization of the ITS-90 and Thermodynamic Temperature Measurement

The constant-volume gas thermometer (CVGT) of the National Metrology Institute of Japan (NMIJ), AIST with ³He as the working gas is used as an interpolating gas thermometer to realize the International Temperature Scale of 1990 (ITS-90) from 3 K to 24.5561 K and as a relative gas thermometer for thermodynamic temperature measurement calibrated at the triple point (TP) of Ne. The standard uncertainties of the realization and measurement are estimated to be 0.58 mK and 0.86 mK at a maximum in the mentioned temperature range, respectively. The maximum difference between both temperatures is about 1 mK. In the calibration of the CVGT, the TP of equilibrium hydrogen (e-H₂) is corrected for isotopic composition as specified in the Technical Annex for the ITS-90. The ambiguity of the TP of Ne due to the variability in isotopic composition is included in the uncertainty. Although the CVGT was also used in 2004 to realize the ITS-90, it was modified for the present experiment to reduce some measurement uncertainty components and the working gas was replaced with a higher-isotopic-purity gas. The results from 2004 were recalculated by correcting for the isotopic composition of e-H₂ and differ insignificantly from the present results, except for a wider scatter.     

Realisation, Dissemination, and Comparison of the ITS-90 and the PLTS-2000 Below 1 K at PTB

The International Temperature Scale of 1990 (ITS-901 and the Provisional Low Temperature Scale (PLTS-2000)² are the internationally agreed temperature scales in the low temperature range. At temperatures between 0.65 K and 5 K, the ITS-90 is defined by polynomials relating the vapour pressure p _v of ⁴He and ³He to the temperature T ₉₀, whereas the PLTS-2000 is defined by a polynomial relating the ³He megting pressure p _m to the temperature T ₂₀₀₀ in the range from 0.9 mK to 1 K. Here, we describe the methods and the cryogenic facilities used for the realisation and dissemination of the ITS-90 and the PLTS-2000 as well as the level of accuracy, which is achieved at PTB. We focus on how the pressures are measured traceably to the national pressure standard. Using this experimental basis, we plan to compare directly the vapour and megting pressure of ³He in the overlapping temperature range from 0.65 K to 1 K.     

The Limits of a Rayleigh-Scattering Primary Thermometer

Progress in the development of an apparatus to compare the thermodynamic temperature of a gas with the temperature as determined by the International Temperature Scale of 1990 (ITS-90) is reported. The apparatus uses the Rayleigh scattering of light from a gas to provide an intensive measure of gas density, thus avoiding the need for corrections for dead volumes or wall adsorption required by conventional gas thermometry. A laser beam is shone through gas in two cells that are at the same pressure but different temperatures, and the measured ratio of the Rayleigh scattering signals from the two cells can be related to the ratio of the gas density in the cells. From the density ratio, the thermodynamic temperature of one cell can be inferred if the other cell is held close to the triple point of water. However, the Rayleigh scattering is weak and signals are small, making measurements with sufficiently small uncertainty extremely challenging. Since previous reports, the apparatus has been significantly modified, and these changes are described along with indicative results. In this paper, results of measurements in the range from 211 K to 292 K using both argon and xenon are reported. The results suffer from large systematic errors due to contamination in one of the measurement cells. Although the results do not provide reliable estimates of T  − T ₉₀, they indicate that measurements with uncertainties below 1 mK are feasible.     

Measurement of Speed of Sound with a Spherical Resonator: HCFC-22, HFC-152a, HFC-143a, and Propane

A spherical resonator and acoustic signal measurement apparatus have been designed and developed for measuring the speed of sound in the gaseous phase. The inner radius of the spherical resonator, being about 6.177 cm, was determined by measuring the speed of sound in gaseous argon at temperatures between 293 and 323 K and at pressures up to 200 kPa. Measurements of the speed of sound in four halogenated hydrocarbons are presented, the compounds are chlorodifluoromethane (CHClF₂ or HCFC-22), 1,1-difluoroethane (CH₃CHF₂ or HFC-152a), 1,1,1-trifluoroethane (CH₃CF₃ or HFC-143a), and propane (CH₃CH₂CH₃ or HC-290). Ideal-gas heat capacities and acoustic virial coefficients were directly deduced from the present data. The results were compared with those from other studies. In this work, the experimental uncertainties in temperature, pressure, and speed of sound are estimated to be less than ±14 mK, ±2.0 kPa, and ±0.0037%, respectively. In addition, equations for the ideal-gas isobaric specific heat capacity for HFC-152a, HFC-143a, and propane are proposed, which are applicable in temperature ranges 240 to 400 K for HFC-152a, 250 to 400 K for HFC-143a, 225 to 375 K for propane. The purities for each of the samples of HCFC-22, HFC-152a, HFC-143a, and propane are better than 99.95 mass%.     

Present Estimates of the Differences Between Thermodynamic Temperatures and the ITS-90

At the request of the Consultative Committee for Thermometry (CCT), Working Group 4 (WG4) has critically reviewed all available measurements of the differences between thermodynamic and ITS-90 temperatures, (T ? T ₉₀), and documented the conversion of older data to the ITS-90. Particular attention has been given to the uncertainties. Based on this review, we provide consensus estimates of T ? T ₉₀ for selected measurements from 0.65 K to 1358 K. We provide two analytic functions for T ? T ₉₀, one for use from 8 K to the triple point of water (T _TPW) and one for use above T _TPW. The small discontinuity of the derivative dT ₉₀/d T at T _TPW is discussed. We also identify temperature ranges where researchers are encouraged to undertake high-accuracy measurements of T ? T ₉₀.     

A practical vapor pressure equation for helium-3 from 0.01 K to the critical point

A saturation vapor pressure equation, p(T), is an essential component in the ³He state equation currently under development. The state equation is valid over the range 0.01-20 K with pressures from 0 to the melting pressure or 15 MPa. The vapor pressure equation consequently must be valid from 0.01 K to the critical temperature. This paper surveys available ³He critical temperature and pressure measurements, leading to new recommended critical values of 3.3157 K and 114603.91 Pa. The ITS-90 temperature scale is defined by the ³He vapor pressure from 0.65 to 3.2 K. A new vapor pressure equation is developed for the interval from the upper end of the T₉₀ scale to this newly defined critical point, employing a mathematical form in which the second derivative d²p/dT² diverges in agreement with scaling laws at the critical point. Below 0.65 K, an empirical vapor pressure expression is adopted, consistent with a theoretical expression valid in the limit T → 0. These two new components are fitted to be piecewise continuous with the EPT-76 p(T) scale rather than the ITS-90 T(p) scale between 0.65 and 3.2 K. Probable deviations between this vapor pressure scale and PLTS-2000 melting pressure-temperature scale are recognized, but not reconciled.     

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.     

Progress in Noise Thermometry at 505 K and 693 K Using Quantized Voltage Noise Ratio Spectra

Technical advances and new results in noise thermometry at temperatures near the tin freezing point and the zinc freezing point using a quantized voltage noise source (QVNS) are reported. The temperatures are derived by comparing the power spectral density of QVNS synthesized noise with that of Johnson noise from a known resistance at both 505 K and 693 K. Reference noise is digitally synthesized so that the average power spectra of the QVNS match those of the thermal noise, resulting in ratios of power spectra close to unity in the low-frequency limit. Three-parameter models are used to account for differences in impedance-related time constants in the spectra. Direct comparison of noise temperatures to the International Temperature Scale of 1990 (ITS-90) is achieved in a comparison furnace with standard platinum resistance thermometers. The observed noise temperatures determined by operating the noise thermometer in both absolute and relative modes, and related statistics together with estimated uncertainties are reported. The relative noise thermometry results are combined with results from other thermodynamic determinations at temperatures near the tin freezing point to calculate a value of T ? T ₉₀ = +4(18) mK for temperatures near the zinc freezing point. These latest results achieve a lower uncertainty than that of our earlier efforts. The present value of T ? T ₉₀ is compared to other published determinations from noise thermometry and other methods.     

气体声学温度计中声波导管的优化设计研究

声波导管的设计是影响声学信号信噪比的关键因素,导管内径越大、长度越短,越利于声波传输,但同时对声学共鸣腔产生更大的扰动。提出了采用变径声波导管降低声波的能量损耗和扰动方法,建立了变径声波导管的衰减和扰动模型,对比分析声学信号在不同尺寸声波导管内的能量衰减和导管对圆柱轴向非缔合声学共振频率和半宽的扰动,获得了优化的导管尺寸,在声波传输能量损失较小的情况下对内长为80 mm圆柱腔体首个轴向非缔合声学共振频率产生的相对扰动在3×10^-5以内,该声波导管的优化设计可为高温气体声学温度计的深入研究提供理论支持。     

Thermal metrology after the introduction of the ITS-90

The adoption of the international temperature scale of 1990 (ITS-90) is producing significant innovation in thermal metrology. The temperature range of the ITS is wider than that of the previous editions. Also the scale precision and the accuracy of the thermodynamic temperature values forming its base have been improved. A short presentation of the ITS-90 will introduce its most important features, describing briefly the types of interpolating instruments and fixed points. To realize the ITS-90, many national laboratories will have to develop within their premises relatively new techniques of measurement such as gas thermometry to interpolate between fixed points from 3 K and 24.6 K and high-temperature platinum resistance thermometry. The highest precision is acheived in the temperature range –40°C to 30° C, where the ITS-90 combines the most reproducible fixed points with the interpolating instrument exhibiting the highest accuracy and the lowest nonuniqueness. Since a reproducibility better than 0.2 mK can be achieved everywhere in that range, except in the proximity of the triple point of water where it is lower than 0.1 mK (all estimates being at the 1 level), the size of the kelvin is reporoduced to within 7·10^–6 in the worst case, and to within 2·10^–7 at the triple point of water. Some practical problems may result from the dissemination of the iTS-90 to users of temperature measurements in the temperature range 420–1085°C. They are related to the construction and use of high-temperature platinum resistance thermometers (HTPRTs), to the practical exploitation of radiation thermometry, and to the availabiality of suitable transfer standards in this temperature range. Several practical realizations of the ITS-90 that are underway in various national laboratories will enable one to better estimate its precision. Such an operation will essentially be carried out through intercomparisons, which will be successful if highly-reproducible transfer standards like the sealed cells for fixed points will be made available. The basic level of the scale precision, i.e., its irreducible component, is given by the scale nonuniqueness. Some results are already available and some experiments have recently been proposed in order to provide further data in critical areas. Another important aspect is the scale smoothness and its effect on the measured thermal properties. With the introduction of the ITS-90 the projects for the determination of thermodynamic properties have not completely stopped. Radiometric determinations and noise thermometry are mainly carried out at temperatures between 660°C and 1085°C. Other experiments involving gas thermomery may lead to better determinations below 3 K. Thermal noise measurements are presently considered for the redetermination of the Boltzmann constant, k_B. Their uncertainty should be within ± 10ppm, still too high to propose such a method for the definition of the kelvin in terms of k_B and of the SI unit of energy. As regards the determination of thermophysical properties of matter, special importance is now attributed to the temperature dependence of the vapor pressure of sodium. Such an interest in connection with the use of pressure-controlled sodium heat pipes for temperature reference. In addition, some information is provided on methods for the determination of pulsed-energy excitation. There, advantage is taken from improvements in radiation thermometry.Translated from Izmeritel'naya Tekhnika, No. 12, pp. 50–58, December, 1993.     

Indirect Determination of the Thermodynamic Temperature of a Gold Fixed-Point Cell

Since the value T ₉₀(Au) was fixed on the ITS-90, some determinations of the thermodynamic temperature of the gold point have been performed which form, with other renormalized results of previous measurements by radiation thermometry, the basis for the current best estimates of (T ? T ₉₀)_Au = 39.9 mK as elaborated by the CCT-WG4. Such a value, even if consistent with the behavior of T ? T ₉₀ differences at lower temperatures, is quite influenced by the low values of T _Au as determined with few radiometric measurements. At INRIM, an independent indirect determination of the thermodynamic temperature of gold was performed by means of a radiation thermometry approach. A fixed-point technique was used to realize approximated thermodynamic scales from the Zn point up to the Cu point. A Si-based standard radiation thermometer working at 900 nm and 950 nm was used. The low uncertainty presently associated to the thermodynamic temperature of fixed points and the accuracy of INRIM realizations, allowed scales with an uncertainty lower than 0.03 K in terms of the thermodynamic temperature to be realized. A fixed-point cell filled with gold, 99.999 % in purity, was measured, and its freezing temperature was determined by both interpolation and extrapolation. An average T _Au = 1337.395 K was found with a combined standard uncertainty of 23 mK. Such a value is 25 mK higher than the presently available value as derived by the CCT-WG4 value of (T ? T ₉₀)_Au = 39.9 mK.     

Realization of a 3He�C4He Vapor-Pressure Thermometer for Temperatures Between 0.65?K and 5?K at LNE-CNAM

In the temperature range between 0.65 K and 5 K, the International Temperature Scale of 1990 (ITS-90) is based on ³He and ⁴He vapor-pressure thermometers. Between 0.65 K and 1 K, the ITS-90 overlaps with the Provisional Low Temperature Scale of 2000 (PLTS-2000), defined in term of the melting pressure of ³He. Some differences, up to more than 1 mK, exist between the two scales in the overlapping interval. The LNE-CNAM has recently started the construction of a ³He?C⁴He vapor-pressure thermometer to realize the ITS-90 in its lowest subrange at the highest degree of accuracy. The device is provided with two separate vapor-pressure chambers, one for ³He and the other for ⁴He, built in a single copper block, and is installed in the experimental space of a dilution refrigerator. The vapor-pressure thermometer is designed to accommodate on the same copper block several transfer standards, an acoustic thermometer, and the ³He melting-pressure thermometer. This configuration is intended for realizing calibrations of transfer standards down to 0.65 K, for investigating the possibility to extend the acoustic thermometer below 4 K, and to perform a direct comparison between the ITS-90 and the PLTS-2000 in the overlapping temperature range, in order to study their differences. The realization of the system has been recently accomplished, and this report illustrates the characteristics of such an experimental device.     

NRC Microwave Refractive Index Gas Thermometry Implementation Between 24.5 K and 84 K

The implementation of microwave refractive index gas thermometry at the National Research Council between 24.5 K and 84 K is reported. A new gas-handling system for accurate control and measurement of experimental gas pressure has been constructed, and primary thermometry measurements have been taken using a quasi-spherical copper resonator and helium gas at temperatures corresponding to three defining fixed points of the International Temperature Scale of 1990 (ITS-90). These measurements indicate differences between the thermodynamic temperature T and ITS-90 temperature \(T_{90}\) of \(\left( T - T_{90} \right) = -0.60 \pm 0.56\) mK at \(T_{90} = 24.5561\) K, \(\left( T - T_{90} \right) = -2.0 \pm 1.3\) mK at \(T_{90} = 54.3584\) K, and \(\left( T - T_{90} \right) = -4.0 \pm 2.9\) mK at \(T_{90} = 83.8058\) K. The present results at \(T_{90} = 24.5561\) K and \(T_{90} = 83.8058\) K agree with previously reported measurements from other primary thermometry techniques of acoustic gas thermometry and dielectric constant gas thermometry, and the result at \(T_{90} = 54.3584\) K provides new information in a temperature region where there is a gap in other recent data sets.     

Uncertainty Budgets for Calibration of Radiation Thermometers below the Silver Point

Below the freezing point of silver, radiation thermometers are generally calibrated by implementing the multi-point interpolation method using blackbody measurements at three or more calibration points, rather than the ITS-90 extrapolation technique. The interpolation method eliminates the need to measure the spectral responsivity and provides greater accuracy at the longer wavelengths required below the silver point. This article identifies all the sources of uncertainty associated with the interpolation method, in particular, those related to the reference blackbody temperatures (either variable-temperature or fixed-point blackbodies) and to the measured thermometer signals at these points. Estimates are given of the ‘normal’ and ‘best’ uncertainties currently achievable. A model of the thermometer response is used to propagate all the uncertainties at the reference points and provide a total uncertainty at any temperature within the calibration range. The multi-point method has the effect of constraining the total uncertainty over this range, unlike the ITS-90 technique for which the uncertainties propagate as T ². This article is a joint effort of the working group on radiation thermometry of the Consultative Committee for Thermometry (CCT), summarizing the knowledge and experience of all experts in this field.     

Progress Towards an Acoustic Measurement of the Molar Gas Constant at INRIM

Progress in developing an experiment for the determination of the molar gas constant R and the Boltzmann constant k at INRIM is reported. The experiment involves simultaneous measurements of the acoustic and microwave resonance frequencies of a stainless steel spherical resonator for which its hemispheres were deliberately misaligned. For the present work, these frequencies were measured in helium near 273.16 K, in the pressure range from 100 to 800 kPa. From microwave data, the radius of the resonator was determined as a function of pressure with an estimated uncertainty of 6.0 ppm. Using acoustic data and the microwave determination of the resonator radius, the speed of sound in helium was deduced, and these values were compared with those predicted by recent accurate ab initio calculations. Over most of the pressure range, the present values agreed with the ab initio values within the uncertainty of the measurements (standard uncertainty of approximately 7.0 ppm). Many suggestions for reducing the uncertainty are provided.     

SF6及CO2三相点替代Hg三相点内插方法可行性探究

在不改变90国际温标内插方程形式的基础上,针对83.8058 K到273.16 K温区,分析了六氟化硫(SF6)和二氧化碳(CO2)三相点替代汞(Hg)三相点后,导致的内插方程变化带来的温度偏差以及传播不确定度变化规律.研究结果表明:SF6和CO2三相点替代Hg三相点后,该方程在该温区仍具有适用性;在复现不确定度相同的...     

Progress in INRiM Experiment for the Determination of the Boltzmann Constant with a Quasi-spherical Resonator

Current progress in the INRiM experiment for the determination of the Boltzmann constant k _B by means of acoustic thermometry is reported. Particularly, the microwave determination of the volume of a triaxial ellipsoidal resonator with an inner radius of 5 cm which was designed at LNE-CNAM is discussed. For the same cavity, acoustic measurements in helium at T _w over the extended pressure range between 50 kPa and 1.4 MPa are reported and these results are compared with the predictions of a model which accounts for several perturbing effects. The procedures, methods, and results obtained in the calibration of several capsule-type SPRTs used in the experiment are briefly illustrated, together with the estimate of the temperature uniformity of the experiment.