Gas Thermometry Research Articles

Realization of an ultra-high precision temperature control in a cryogen-free cryostat.

Single-pressure refractive-index gas thermometry (SPRIGT) is a new type primary thermometry jointly developed by TIPC of CAS in China and LNE-Cnam in France. To realize a competitive uncertainty of 0.25 mK for the thermodynamic temperature measurement, a cryogen-free cryostat with high-stability better than 0.2 mK should be designed. This paper presented the first experimental results of temperature control for this cryostat. To realize this objective, multi-layer radiation shields combined with a thermal-resistance method were used to isolate the thermal-noise from surroundings. Besides, a new temperature control method based on a gas-type heat switch and proportional-integral-derivative control method was proposed, which was applicable to different temperature ranges by changing the working modes of the heat switch. After optimizing, the ultra-high precision temperature control in the range of 5-25 K has been fully realized, which was the temperature instability (with standard deviation) of 0.021 mK at 5.0 K, 0.05 mK at 5.7 K, 0.042 mK at 7.4 K, 0.029 mK at 14.3 K, and 0.022 mK at 25 K with the sampling time of 0.8 s. This was almost the best reporting result in the world and showed its great potential in SPRIGT.

Development of absolute acoustic gas thermometer for the state primary standard of the temperature unit – kelvin in the range 0.3-273.16 K in VNIIFTRI and the total standard uncertainty of the thermodynamic temperature measurements near the triple point of water

An absolute primary acoustic gas thermometer has been developed and successfully tested in VNIIFTRI. The acoustic gas thermometer is planned to be included in the Russian state primary standard of the temperature unit – kelvin in the range 0.3-273.16 K. The uncertainty of the thermodynamic temperature measurements with the acoustic gas thermometer near the triple point of water was experimentally researched.

Investigating the adequacy of a low-cost vector network analyser for microwave measurements in quasispherical resonators

Microwave measurements in quasispherical resonators (QSRs) have enabled remarkable improvements in primary gas thermometry, but the expense of vector network analysers (VNAs) restricts wider use of the technique. In this work we compare the performance of a commercially available, low-cost VNA with a fully-featured VNA in microwave resonance measurements in a QSR. For acoustic gas thermometry (AGT) where a relative uncertainty in frequency measurement in an order of 10−7 is required, we have found that the accuracy of the low-cost VNA is easily sufficient. The use of a +20 dB amplifier was also tested for both VNAs and allowed statistical uncertainties to be reduced by a factor of 5 to 12. The two VNAs showed agreement within 20 × 10−9 of the absolute frequency of microwave resonances. However, when the low-cost VNA was used with the amplifier, some spurious systematic effects were found which biased the measured resonance frequency at levels below 20 × 10−9. These effects were apparent only when the amplifier was used with the low-cost VNA, because, when the amplifier was not used, the statistical uncertainty was much larger than the magnitude of these effects. While the physical cause of these systematic effects is not investigated in the present work, we made observations that could help to estimate their magnitudes. The comparison showed that the low-cost VNA, although being perfectly suitable for the AGT, may not be sufficiently accurate for applications where the required relative uncertainty in the frequency determination is of an order of 10−9.

Noble gas based temperature reconstruction on a Swiss stalagmite from the last glacial–interglacial transition and its comparison with other climate records

Here we present the results of a first application of a “Combined Vacuum Crushing and Sieving (CVCS)” system to determine past (cave/soil) temperatures from dissolved noble gas concentrations in stalagmite samples grown under ‘cold’ climatic conditions (e.g. close to freezing point of water) during the last glacial–interglacial transition. To establish noble gas temperatures (NGTs) also for stalagmites grown in cold regions, we applied the CVCS system to samples from stalagmite M2 precipitated in the Milandre Cave, located in the Swiss Jura Mountains. The investigated stalagmite M2 covers the Allerød–Younger Dryas–Holocene transitions. Noble gas temperatures are determined by using a new algorithm based on noble gas and water abundances and not from concentrations. Noble gas results indicate annual mean temperatures in the Milandre Cave were 2.2±1.8 °C during the late stages of the Allerød, then dropping to 0(−)+2.6°C at the onset of the Younger Dryas. Such temperatures indicate conditions near to the freezing point of water during the first part of the Younger Dryas. During the last part of the Younger Dryas, the temperature increased to 6.3±2.3 °C. No early Holocene temperature could be determined due the non-detectable water abundances in these samples, however one late Holocene sample indicates a cave temperature of 8.7±2.7 °C which is close to the present day annual mean temperature. NGTs estimated for the Allerød–Younger Dryas–Holocene are in good agreement with paleo-temperature reconstructions from geochemical and biological proxies in lake sediments. The observed deviations between the different paleo-temperature reconstructions are minor if the according temperatures are rescaled to annual mean temperatures and are primarily attributed to the chronological tuning of the different records. As in other stalagmites, NGT reconstructions of the recently precipitated stalagmite (‘young’) samples again are biased, most likely due to diffusive gas loss during sample processing. We speculate that a reduced retentivity of noble gases during experimental sample processing is a general feature of recently precipitated stalagmite fabrics. Therefore, the recently precipitated stalagmite samples do not allow the reliable NGT determination given the currently available experimental methods. Nevertheless, this study makes the case that noble gas thermometry can be applied to stalagmites for paleo-temperature reconstruction based on a physical method including stalagmites that grew during cold climatic conditions.

Identification of prospective significance levels for potential geothermal fields of India

Abstract This study aims to predict prospective significance levels of potential geothermal fields already identified by Geological Survey of India (GSI) and National Geophysical Research Institute (NGRI) by field investigations. Wide range of criteria's are considered in determining the relative significance level of each geothermal field in terms of cumulative score. These criteria's include useful resource base (URBfield), Areal extent (Afield), Minimum temperature as per geothermometry (Tmin), Maximum temperature as per geothermometry (Tmax), Utilization score (USfield), Cumulative discharge of thermal springs (Q), Minimum electrical resistivity (Rmin), Maximum electrical resistivity (Rmax) and Representative reservoir temperature as per Gas thermometry (Tgas). Fuzzy Analytical Hierarchy Process (Fuzzy AHP) is used to study the dominance of each geothermal field, evaluated over the aforementioned criteria to find cumulative score. URBfield depends on possible extraction temperature of reservoir estimated by COMSOL Multiphysics® modelling and simulation software. The geothermal fields are conceptualized as shallow homogenous reservoirs with injection and extraction wells. The attributes of remaining criteria are collected from published works of NGRI and GSI. The results of this study ratify that Puga geothermal field is the most significant site among the identified potential geothermal fields, to conduct further developmental works and for commercial extraction of geothermal energy.

Molecular gas thermometry on acetylene using dual-comb spectroscopy: analysis of rotational energy distribution

We propose and demonstrate a novel method for temperature determination using dual-comb spectroscopy and a novel analysis technique, “Rotational-state Distribution Thermometry: RDT.” We obtained the spectral profile of a vibration–rotation band of 12C2H2 using dual-comb spectroscopy at room temperature. The line-center absorbance was determined for each transition by fitting the line profile to a Gaussian function. A model function that relates the rotational temperature of the molecule to the distribution of the line-center absorbance was introduced; the gas temperature was determined by fitting the distribution to the model function. The determined temperature agrees to within 0.6 K with the cell-wall temperature measured with a platinum resistance thermometer. In addition, using the spectral profile obtained in this study, we compare the present analysis with two conventional methods for determining the gas temperature; one is based on the line-center absorbance ratio, and the other on the Doppler width. The present method takes full advantage of the supreme characteristics of dual-comb spectroscopy and has the potential to offer fast and precise thermometry.

Polarizability of Helium, Neon, and Argon: New Perspectives for Gas Metrology.

With dielectric-constant gas thermometry, the molar polarizability of helium, neon, and argon has been determined with relative standard uncertainties of about 2 parts per million. A series of isotherms measured with the three noble gases and two different experimental setups led to this unprecedented level of uncertainty. These data are crucial for scientists in the field of gas metrology, working on pressure and temperature standards. Furthermore, with the new benchmark values for neon and argon, theoretical calculations, today about 3 orders of magnitude larger in uncertainty, can be checked and improved.

Constructing a Device for Calculating the Atmospheric Correction Factor for the Calibration the Radiation-Absorbed Dose in Radiotherapy

The purpose of this study was to measure the air temperature and the air pressure, develop an atmospheric correction factor calculation device (ACFCD), and utilize it. Because the radiation dose varies with the temperature, pressure, and humidity, is essential calibrating doses after calculating the atmospheric correction factor. In this study, we constructed an ACFCD by using a micro controller, an air thermometer, and an air pressure sensor. We measured the temperature and the air pressure in nine different spaces and confirmed the changes in the factors. We obtained the measured data as comma-separated-values files, and we created a Microsoft Excel macro for the analysis to calculate the average temperature, pressure, and atmospheric correction factor; we determined trends by using graphs. As a result of the performance evaluation, we confirmed that the space temperature and the air pressure measurement were the same (p > 0.05). In addition, we confirmed that the micro controller unit measured the heating, which we observed to be 3.9 ◦ C. The ACFCD that we developed in this study confirmed the possibility of replacing existing air thermometers and barometers and can contribute to improving work efficiency. In addition, in light of the basic concept of the ACFCD, we consider that the device will be useful for ensuring safe, accurate use of radiation once it is made more practical through additional studies.

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.

Determination of the Boltzmann constant with cylindrical acoustic gas thermometry: new and previous results combined

We report a new determination of the Boltzmann constant kB using a cylindrical acoustic gas thermometer. We determined the length of the copper cavity from measurements of its microwave resonance frequencies. This contrasts with our previous work (Zhang et al 2011 Int. J. Thermophys. 32 1297, Lin et al 2013 Metrologia 50 417, Feng et al 2015 Metrologia 52 S343) that determined the length of a different cavity using two-color optical interferometry. In this new study, the half-widths of the acoustic resonances are closer to their theoretical values than in our previous work. Despite significant changes in resonator design and the way in which the cylinder length is determined, the value of kB is substantially unchanged. We combined this result with our four previous results to calculate a global weighted mean of our kB determinations. The calculation follows CODATA’s method (Mohr and Taylor 2000 Rev. Mod. Phys. 72 351) for obtaining the weighted mean value of kB that accounts for the correlations among the measured quantities in this work and in our four previous determinations of kB. The weighted mean is 1.380 6484(28) × 10−23 J K−1 with the relative standard uncertainty of 2.0 × 10−6. The corresponding value of the universal gas constant is 8.314 459(17) J K−1 mol−1 with the relative standard uncertainty of 2.0 × 10−6.

Emission properties and temperature quenching mechanisms of rare-earth elements doped in garnet hosts

Thermographic phosphors continue to be investigated for gas thermometry in combustion applications due to their relative non-intrusiveness and ability to survive harsh environments. To further develop this technology, the mechanisms leading to their temperature-sensitive emission must be understood in greater detail. As a result, this work focuses on the quenching mechanisms of four different thermographic phosphors: Pr:YAG, Pr:LuAG, Ce:YAG, and Ce:LuAG. Spectrally- and temporally-resolved emission measurements were performed in a tube furnace, providing data on the emission properties of the phosphors at elevated temperatures. A quantum mechanical single configurational coordinate (QMSCC) model is used to understand the temperature sensitivity of the emission spectrum and of the nonradiative intersystem crossing. Energy diagrams for each phosphor are constructed to understand the likelihood of nonradiative ionization to the conduction band as a thermal-quenching mechanism. Configurational coordinate diagrams for each phosphor are constructed and used to interpret the mechanism responsible for thermal quenching. It is found that intersystem crossing is responsible for thermal quenching of Pr:YAG and Pr:LuAG, whereas ionization to the conduction band is the likely mechanism for Ce:YAG and Ce:LuAG. The ability to understand and model the mechanisms associated with the temperature-sensitive emission properties will be a valuable tool towards choosing appropriate thermographic phosphors for specific gas thermometry applications.

A methodology for identifying thermographic phosphors suitable for high-temperature gas thermometry: application to Ce3+ and Pr3+ doped oxide hosts

A methodology is presented that utilizes configurational coordinate diagrams in combination with energy level diagrams to select new potential thermographic phosphors for high-temperature gas thermometry applications. Oxide hosts doped with trivalent ions were investigated, and based on the analysis Ce3+ doped ortho-phosphates (GdPO4, LuPO4, YPO4) were selected for testing. All three phosphors had high measured quenching temperatures ( $$T_{50} > 800\, K$$ ), partially validating the methodology used. Additionally, the quenching temperature for Ce:GdPO4 of $$T_{50} = 1000\, K$$ was more than $$150\, {\text{K}}$$ larger than previously seen for trivalent ions doped in oxide hosts. The encouraging results demonstrate that this analysis may be applied to aid in finding thermographic phosphors for gas thermometry at combustion relevant temperatures.

An improved electronic determination of the Boltzmann constant by Johnson noise thermometry

Recent measurements using acoustic gas thermometry have determined the value of the Boltzmann constant, k, with a relative uncertainty less than 1 × 10−6. These results have been supported by a measurement with a relative uncertainty of 1.9 × 10−6 made with dielectric-constant gas thermometry. Together, the measurements meet the requirements of the International Committee for Weights and Measures and enable them to proceed with the redefinition of the kelvin in 2018. In further support, we provide a new determination of k using a purely electronic approach, Johnson noise thermometry, in which the thermal noise power generated by a sensing resistor immersed in a triple-point-of-water cell is compared to the noise power of a quantum-accurate pseudo-random noise waveform of nominally equal noise power. The experimental setup differs from that of the 2015 determination in several respects: a 100 Ω resistor is used as the thermal noise source, identical thin coaxial cables made of solid beryllium–copper conductors and foam dielectrics are used to connect the thermal and quantum-accurate noise sources to the correlator so as to minimize the temperature and frequency sensitivity of the impedances in the connecting leads, and no trimming capacitors or inductors are inserted into the connecting leads. The combination of reduced uncertainty due to spectral mismatches in the connecting leads and reduced statistical uncertainty due to a longer integration period of 100 d results in an improved determination of k = 1.380 649 7(37) × 10−23 J K−1 with a relative standard uncertainty of 2.7 × 10−6 and a relative offset of 0.89 × 10−6 from the CODATA 2014 recommended value. The most significant terms in the uncertainty budget, the statistical uncertainty and the spectral-mismatch uncertainty, are uncorrelated with the corresponding uncertainties in the 2015 measurements.

Time-resolved gas thermometry by laser-induced grating spectroscopy with a high-repetition rate laser system

Thermometry using laser-induced grating spectroscopy (LIGS) is reported using a high-repetition rate laser system, extending the technique to allow time-resolved measurements of gas dynamics. LIGS signals were generated using the second harmonic output at 532 nm of a commercially available high-repetition rate Nd:YAG laser with nitrogen dioxide as molecular seed. Measurements at rates up to 10 kHz were demonstrated under static cell conditions. Transient temperature changes of the same gas contained in a cell subjected to rapid compression by injection of gas were recorded at 1 kHz to derive the temperature evolution of the compressed gas showing temperature changes of 50 K on a time-scale of 0.1 s with a measurement precision of 1.4%. The data showed good agreement with an analytical thermodynamic model of the compression process.

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.

Reproducibility of the Helium-3 Constant-Volume Gas Thermometry and New Data Down to 1.9 K at NMIJ/AIST

This study confirms reproducibility of the International Temperature Scale of 1990 (ITS-90) realized by interpolation using the constant-volume gas thermometer (CVGT) of National Metrology Institute of Japan (NMIJ)/AIST with \(^{3}\)He as the working gas from 3 K to 24.5561 K by comparing the newly obtained results and those of earlier reports, indicating that the CVGT has retained its capability after renovation undertaken since strong earthquakes struck Japan. The thermodynamic temperature T is also obtained using the single-isotherm fit to four working gas densities (\(127\,\hbox {mol}\cdot \hbox {m}^{-3}\), \(145\,\hbox {mol}\cdot \hbox {m}^{-3}\), \(171\,\hbox {mol}\cdot \hbox {m}^{-3}\) and \(278\,\hbox {mol}\cdot \hbox {m}^{-3})\) down to 1.9 K, using the triple point temperature of Ne as a reference temperature. In this study, only the second virial coefficient is taken into account for the single-isotherm fit. Differences between T and the ITS-90 temperature, \(T-T_{90}\), reported in earlier works down to 3 K were confirmed in this study. At the temperatures below 3 K down to 2.5 K, \(T-T_{90}\) is much smaller than the standard combined uncertainty of thermodynamic temperature measurement. However, \(T- T_{90}\) seems to increase with decreasing temperature below 2.5 K down to 1.9 K, although still within the standard combined uncertainty of thermodynamic temperature measurement. In this study, T is obtained also from the CVGT with a single gas density of \(278\,\hbox {mol}\cdot \hbox {m}^{-3}\) using the triple-point temperature of Ne as a reference temperature by making correction for the deviation from the ideal gas using theoretical values of the second and third virial coefficients down to 2.6 K, which is the lowest temperature of the theoretical values of the third virial coefficient. T values obtained using this method agree well with those obtained from the single-isotherm fit. We also found that the second virial coefficient obtained by the single-isotherm fit to experimental results agrees well with that obtained by the single-isotherm fit to the theoretically expected behavior of \(^{3}\)He gas with the theoretical second and third virial coefficients at four gas densities used in the present work.

Calibration of Air Thermometers in a Climatic Chamber and Liquid Baths

The paper deals with calibration of digital indication thermometers designed for air temperature measurements. These were calibrated by comparison with a reference thermometer in two different calibration media: in the air when a climatic chamber was used and in a liquid when a calibration bath was used. The main difference between the media was thermal conductivity, which was more than ten times lower in the air. To compare both methods, we calibrated two sets of air thermometers twice. The first set comprised of small temperature loggers with an internal sensor, whereas the second set was a group of temperature probes connected to the measurement unit. The temperature ranges for the loggers were from 0 \(^{\circ }\)C to 40 \(^{\circ }\)C and for the probes from −20 \(^{\circ }\)C to 60 \(^{\circ }\)C. The results showed that the measured temperature errors were smaller in the bath as well as less scattered. Furthermore, the assigned measurement uncertainty was lower, if calibration was performed in a calibration bath, mostly due to better thermal homogeneity of a liquid compared to the air in a climatic chamber. Calibration shall assure traceability of a measurement equipment in such a way that a calibration procedure simulates an actual use of equipment; otherwise, the corrections and associated measurement uncertainty could be misleading. Therefore, when air thermometers, which are designed to measure a gaseous medium, are calibrated, they should be calibrated under similar conditions as they are used. The paper presents the differences in results of calibration of air thermometers under different calibration conditions.

Final determination of the Boltzmann constant by dielectric-constant gas thermometry

Gaiser et al published in 2013 (Metrologia 50 L7–11) a second, improved value of the Boltzmann constant k determined by dielectric-constant gas thermometry at the triple point of water (k = 1.380 6509 × 10−23 J K−1, relative standard uncertainty 4.3 parts per million (4.3 ppm)). Subsequently, the uncertainty was able to be reduced to 4.0 ppm by reanalysing the pressure measurement. Since 2013, further progress regarding this primary-thermometry method has been achieved in terms of the design and the assembly of the measuring capacitors, the determination of their effective compressibility, the sensitivity of the capacitance bridge, and the scattering and the evaluation of the data. Based on a huge amount of data, two new k values have been obtained by applying two different capacitors. The combination of these two values with the 2013 result, fully taking into account the correlations, has yielded a final result of k = 1.380 6482 × 10−23 J K−1 with a relative standard uncertainty of 1.9 ppm. This value is about 0.2 ppm smaller than the CODATA 2014 one, which has a relative standard uncertainty of 0.57 ppm.

Kinetic temperature of massive star-forming molecular clumps measured with formaldehyde

The Large Magellanic Cloud (LMC), the closest star forming galaxy with low metallicity, provides an ideal laboratory to study star formation in such an environment. The classical dense molecular gas thermometer NH3 is rarely available in a low metallicity environment because of photoionization and a lack of nitrogen atoms. Our goal is to directly measure the gas kinetic temperature with formaldehyde toward six star-forming regions in the LMC. Three rotational transitions of para-H2CO near 218 GHz were observed with the APEX 12m telescope toward six star forming regions in the LMC. Those data are complemented by C18O 2-1 spectra. Using non-LTE modeling with RADEX, we derive the gas kinetic temperature and spatial density, using as constraints the measured para-H2CO 321-220/303-202 and para-H2CO 303-202/C18O 2-1 ratios. Excluding the quiescent cloud N159S, where only one para-H2CO line could be detected, the gas kinetic temperatures derived from the preferred para-H2CO 321-220/303-202 line ratios range from 35 to 63 K with an average of 47 K. Spatial densities of the gas derived from the paraH2CO 303-202/C18O 2-1 line ratios yield 0.4-2.9x10^5 cm^-3 with an average of 1.5x10^5 cm^-3. Temperatures derived from the para-H2CO line ratio are similar to those obtained with the same method from Galactic star forming regions and agree with results derived from CO in the dense regions of the LMC. A comparison of kinetic temperatures derived from para-H2CO with those from the dust also shows good agreement. This suggests that the dust and para-H2CO are well mixed in the studied star forming regions. A correlation between the gas kinetic temperatures derived from para-H2CO and infrared luminosity, represented by the 250um flux, suggests that the kinetic temperatures traced by para-H2CO are correlated with the ongoing massive star formation in the LMC.

Temperature observations in Bologna, Italy, from 1715 to 1815: a comparison with other contemporary series and an overview of three centuries of changing climate

The observations taken in Bologna, Italy, from 1715 to 1815, three times a day, with a number of thermometers (i.e., Stancari air thermometers, Little Florentine thermometer, Florentine stick thermometer and a number of Reaumur spirit and mercury thermometers) some of them operating in parallel, have been recovered and analysed. The early thermometers had unknown scales and temperature units, with deviations due to the bulb shape or the thermometric liquid, but it is possible to interpret them after comparison between parallel readings. Historical sources and the analysis of the data fingerprints and their variability permit recognition of where instruments were located and who the observers were. It is also possible to relate the indoor climate of historical buildings to the outdoor one, and transform indoor readings as they were taken outdoors, expressed in Celsius. The Bologna series has been compared with the contemporary observations in Padua, Venice and Milano. The climate analysis shows that the temperature fluctuated but with an increasing trend. The 1730–1770 decades constituted the coldest period and 1980—today the warmest one. The eighteenth century was generally cold and had an impressive frequency of extremely severe winters that exceeded the rest of the series. The whole dataset (i.e. 1715–2015) of daily temperatures has been included to allow further use for scientific purposes. Finally, the paper provides a methodological example of procedures to recover and analyse early instrumental series.