Acoustic Thermometry Research Articles

Determinations of the Boltzmann constant

Abstract We review measurements of the Boltzmann constant, k, the value of which is soon to be fixed at exactly 1.380 649 × 10 − 23 J⋅K−1 for the future revised Systeme international of units. In addition to a description of the theoretical background and of diverse experimental techniques (acoustic thermometry, Johnson noise thermometry, dielectric constant gas thermometry, and Doppler broadened molecular spectroscopy), the article highlights the decisive role of ab initio calculations of the thermophysical properties of gases, especially helium-4. Perspectives for improvements in thermometry are outlined in the wake of the new definition.

Results from the "Arctic ocean under melting ice" acoustic thermometry experiment

The Fram Strait is the main gateway for heat exchange between the Arctic Ocean and the Atlantic Ocean, hence estimating the heat transport is important to understand the on-going climate change. An acoustic system for acoustic thermometry was developed under the ACOBAR project. Results from this experiment showed that it was important to monitor the heat content in the north-going West-Spitzbergen current and the south-going East-Greenland current separately. Additionally, the complex oceanographic conditions in this region make it difficult to separate the different arrivals of the acoustic signals in the time domain. The UNDER-ICE experiment, funded by the Research Council of Norway, is the third acoustic thermometry experiment carried out by NERSC in the Fram Strait. Five moorings were deployed from 2014 to 2016, monitoring the north-going and the south-going currents separately. Transmissions were made every third hour for two years along 8 transects, and two moorings were augmented with additional oceanographic sensors. Results from the processing and analysis of the acoustic data are presented, including time series of the depth-range average temperature along the different transects. Oceanographic measurements and a comparison between acoustic observations and modeling results are also presented.

Acoustics on the roadmap for an Integrated Arctic Observing System

The current status of the ocean in situ observing system in the Arctic are addressed in the EU funded Integrated Arctic Observation System (INTAROS). We describe how multipurpose acoustic systems can contribute to fill gaps and to establish an optimized Pan Arctic Ocean Observing System. A brief presentation of the steps from a series of experiments in the Eastern Arctic towards the upcoming pan-arctic Coordinated Arctic Acoustic Thermometry Experiment are given. How we can use this experience to ensure that multipurpose Arctic observation system will get on in roadmap for an Arctic Observing System? Any sustainable ocean observing systems in the Arctic depend on long-term funding, and that funding mechanisms other than research programs should be used for this. To achieve this, we need to engage with stakeholder groups outside the scientific community. How can this be done?

Information content of ship noise on a drifting volumetric array for passive environmental sensing

This study investigates the information content of ship noise received on a drifting volumetric array of hydrophones in shallow water marine environments for the purposes of conducting acoustic thermometry or other environmental inversions. Passive inversions for physical oceanographic parameters are conducted using travel time differences, determined by cross-correlating ship noise received on hydrophones suspended beneath drifting buoys. Ships are tracked using the Automatic Identification System (AIS). Information content gained from the inversion is assessed using traditional a-posteriori error analysis. Numerical simulations using a standard normal mode propagation model are used to test limitations of the proposed approach with respect to frequency band, drifting receiver configuration, precision and accuracy of the inversion results, along with sensitivity to environmental and position mismatch. Performance predictions using this model are compared with results from a field experiment using at-sea data collected off the coast of New London, CT in Long Island Sound. Information gathered using passive acoustic inversion methods on drifting arrays can be used to constrain general circulation models (GCMs), in coastal environments, where ship noise is ubiquitous, environmental data are sparse, and the oceanography is dynamic and important for understanding large-scale ocean processes.

The feasibility of a multipurpose acoustic network in Baffin Bay

Operating autonomous underwater vehicles at high latitudes is a challenge because ice cover prevents the use of GPS or data communications. As a result, our scientific observations are biased towards late spring, summer, and early autumn when ships can navigate and autonomous platforms can safely surface. To address this problem, we studied the feasibility of a basin-scale multipurpose acoustic network called the “Baffin Bay Acoustic Navigation and Communication System” (BBANC). BBANC would deploy broadband low frequency sources and receivers, offering one-way communication, acoustic positioning, and acoustic thermometry services. Passive acoustic listening elements would support the study of marine mammal communication and ambient noise from ships, ocean-based resource exploitation, and ice dynamics, as well as gate acoustic source operation in the presence of marine mammals. We describe the challenges and design parameters for such a system, as well as define additional acoustic and remote sensing measurements required to complete a system design. Drawing from a large database of Baffin Bay hydrography, we present simulations of under-ice sound speed conditions, ice properties derived from satellite remote sensing and upward looking sonar data, and modelled acoustic propagation paths in an ice-covered Baffin Bay. We also assess the feasibility of non-coherent and coherent communication.

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.

Beamforming using chip-scale atomic clocks in a controlled environment

Recently developed low-power Chip-Scale Atomic Clocks (CSACs) hold promise for underwater acoustics applications because they enable time-coherent processing, critical for estimating the directionality of the sound field, when acoustic array elements cannot share a timing reference. Controlled, tank-based experiments with a small acoustic array (N = 4) featuring CSAC-equipped elements show that optimal disciplining is important for continued array coherence. Clock drift equivalent to a 10% wavelength error at 0.3, 1, and 10 kHz was reached at approximately 25, 10, and 3 days, respectively. Within application-specific limits, this technology brings enhanced capabilities to acoustic thermometry, geoacoustic, biological, and under-ice acoustic oceanography.

Research on Temperature Field Reconstruction Based on RBF Approximation with Polynomial Reproduction Considering the Refraction Effect of Sound Wave Paths

The temperature field distribution directly reflects the combustion condition in a furnace．In this paper, acoustic thermometry to reconstruct temperature distribution is investigated. A method based on radial basis function... | Find, read and cite all the research you need on Tech Science Press

Thermometry system development for thermoradiotherapy of deep-seated tumours

Therapeutic hyperthermia (including RF hyperthermia) in combination with radiotherapy (called thermoradiotherapy) is one of widely used contemporary cancer treatment methods. The independent electron linac and RF system or their combinations are necessary for effective therapy. Whole-body hyperthermia is used for treatment of metastatic cancer that was spread throughout the body, regional one is used for treatment of part of the body (for instance leg or abdominal cavity). Local hyperthermia with characteristic size of heating volume of 20-100 mm permits to heat tumour without overheating of healthy tissues. The thermometry of deep suited tissues during the hyperthermia process is an important and complex task. Invasive methods as thermistors, optical sensors or thermo-couples can not be widely used because all of them are able to transport tumor cells to the healthy region of the patient body. Distant methods of the temperature measurement such, as radiothermometry and acoustic thermometry can not be used for tissues seated deeper than 5-7 cm. One of possible ways to solve the problem of temperature measurement of the deep suited tissues is discussed in this article: it was proposed to use the same electrodes for RF hyperthermia and thermometry. As known electrodynamics characteristics of tissues are sufficiently depends on temperature. It was proposed to use this effect for active radiothermometry in local hyperthermia. Two opposite RF dipoles can be used as generator and receiver of pick-up signal.

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.

New measurement of the Boltzmann constant k by acoustic thermometry of helium-4 gas

The SI unit of temperature will soon be redefined in terms of a fixed value of the Boltzmann constant k derived from an ensemble of measurements worldwide. We report on a new determination of k using acoustic thermometry of helium-4 gas in a 3 l volume quasi-spherical resonator. The method is based on the accurate determination of acoustic and microwave resonances to measure the speed of sound at different pressures. We find for the universal gas constant R = 8.314 4614(50) J·mol−1·K−1. Using the current best available value of the Avogadro constant, we obtain k = 1.380 648 78(83) × 10−23 J·K−1 with u(k)/k = 0.60 × 10−6, where the uncertainty u is one standard uncertainty corresponding to a 68% confidence level. This value is consistent with our previous determinations and with that of the 2014 CODATA adjustment of the fundamental constants (Mohr et al 2016 Rev. Mod. Phys. 88 035009), within the standard uncertainties. We combined the present values of k and u(k) with earlier values that were measured at LNE. Assuming the maximum possible correlations between the measurements, (kpresent/〈k〉 − 1) = 0.07 × 10−6 and the combined ur(k) is reduced to 0.56 × 10−6. Assuming minimum correlations, (kpresent/〈k〉 − 1) = 0.10 × 10−6 and the combined ur(k) is reduced to 0.48 × 10−6.

Physical and computer-based modeling in internal temperature reconstruction by the method of passive acoustic thermometry

The purpose of this work was to investigate experimentally the capacity of passive acoustic thermometry (PAT) for the reconstruction of 1D, time-variable distributions of the internal temperature. Because in the PAT a noise signal is measured, a considerable integration time (about one minute) is required to attain an acceptable error level (0.5–1K). To optimize the time, an algorithm was proposed to take account of the fact that the temperature satisfied the heat equation. The problem was reduced to that of determining two parameters (initial temperature and thermal diffusivity) of the object under study. The desired parameters were considered constant and were not determined anew after each measurement; instead, their values were refined using all the previous measurements. The proposed algorithm was tested experimentally (where the temperature was reconstructed in a model object, a slab of polytetrafluoroethylene) and investigated by means of computer modeling. The duration of one measurement was about 5.5s. As a result, an error of the temperature reconstruction of about 0.5K, acceptable for medical applications, was attained after 30–60s (depending on the depth) from the beginning of the measurements. After that, temperature distributions can be reconstructed after each measurement without loss of the reconstruction accuracy. The proposed method can be used to control the temperature under a local hyperthermia, lasting 1 min and more, of the human body.

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.

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.

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.

Ira Dyer and MIT Arctic acoustics research

Ira Dyer and his colleague Art Baggeroer began MIT’s Arctic Acoustics research efforts in the latter half of the 1970s. In this pre-GPS and newly digital era, Ira helped define an ambitious program for the Office of Naval Research that brought large-aperture high-quality acoustic array data acquisition to bear on the problems of Arctic acoustic science. Supporting a generation of graduate students, this work explored ambient noise generation mechanisms in the ice, Arctic basin reverberation, seismic reflection and refraction studies to understand the underlying crustal structure, and long-range propagation that is now exploited for acoustic thermometry to study global climate change. Advanced signal processing, combined with fundamental physical understanding and modeling of the ice, water column, and underlying crust vastly increased our understanding of these phenomena in the Arctic. I will show some of the results of this work, and how it has been extended for use in active sonars and measurements of sea-ice dynamics over large areas of the Arctic.

Primary thermometry from 2.5 K to 140 K applying dielectric-constant gas thermometry

Recent thermodynamic temperature measurements at PTB with dielectric-constant gas thermometry were performed up to 140 K. Particular care was taken to check for possible systematic sources of errors by repeating experiments applying two new measuring capacitors and both helium and neon as working gases. The development of a new method for determining the effective compressibility of the new capacitors as a function of temperature has decreased the uncertainty significantly. The combination of the recently obtained results with former values of thermodynamic temperature, corrected using new thermodynamic input data, has yielded a consistent dataset in the range from 2.5 K to 38 K as well as at 84 K, 120 K, 130 K, and 140 K. This dataset is in good agreement with the newest results of acoustic gas thermometry, which has quite different sources of uncertainty compared with dielectric-constant gas thermometry.

Further Estimates of $$(T-T_{90})$$ ( T - T 90 ) Close to the Triple Point of Water

Recent advances in primary acoustic gas thermometry (AGT) have revealed significant differences between temperature measurements using the International Temperature Scale of 1990, \(T_{90}\), and thermodynamic temperature, T. In 2015, we published estimates of the differences \((T-T_{90})\) from 118 K to 303 K, which showed interesting behavior in the region around the triple point of water, \(T_\mathrm{TPW}=273.16\) K. In that work, the \(T_{90}\) measurements below \(T_\mathrm{TPW}\) used a different ensemble of capsule standard platinum resistance thermometers (SPRTs) than the \(T_{90}\) measurements above \(T_\mathrm{TPW}\). In this work, we extend our earlier measurements using the same ensemble of SPRTs above and below \(T_\mathrm{TPW}\), enabling a deeper analysis of the slope \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) around \(T_\mathrm{TPW}\). In this article, we present the results of seven AGT isotherms in the temperature range 258 K to 323 K. The derived values of \((T-T_{90})\) have exceptionally low uncertainties and are in good agreement with our previous data and other AGT results. We present the values \((T-T_{90})\) alongside our previous estimates, with the resistance ratios W(T) from two SPRTs which have been used across the full range 118 K to 323 K. Additionally, our measurements show discontinuities in \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) at \(T_\mathrm{TPW}\) which are consistent with the slope discontinuity in the SPRT deviation functions. Since this discontinuity is by definition non-unique, and can take a range of values including zero, we suggest that mathematical representations of \((T-T_{90})\), such as those in the mise en pratique for the kelvin (Fellmuth et al. in Philos Trans R Soc A 374:20150037, 2016. doi: 10.1098/rsta.2015.0037), should have continuity of \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) at \(T_\mathrm{TPW}\).

Acoustic thermometry for detecting quenches in superconducting coils and conductor stacks

Quench detection capability is essential for reliable operation and protection of superconducting magnets, coils, cables, and machinery. We propose a quench detection technique based on sensing local temperature variations in the bulk of a superconducting winding by monitoring its transient acoustic response. Our approach is primarily aimed at coils and devices built with high-temperature superconductor materials where quench detection using standard voltage-based techniques may be inefficient due to the slow velocity of quench propagation. The acoustic sensing technique is non-invasive, fast, and capable of detecting temperature variations of less than 1 K in the interior of the superconductor cable stack in a 77 K cryogenic environment. We show results of finite element modeling and experiments conducted on a model superconductor stack demonstrating viability of the technique for practical quench detection, discuss sensitivity limits of the technique, and its various applications.

Microwave measurements of the length and thermal expansion of a cylindrical resonator for primary acoustic gas thermometry

In the application of acoustic gas thermometry to determine the Boltzmann constant and thermodynamic temperatures using resonant cavities, the internal dimensions or the thermal expansion of the cavity have to be known accurately. For this purpose, measurement of the microwave resonances has proved to be an accurate and convenient experimental technique for dimensional measurement of acoustic resonators. We report measurements of the length and longitudinal thermal expansion of a prototype cylindrical cavity made of oxygen-free copper. We studied four non-degenerate transverse magnetic modes for three isotherms at 243, 258 and 273 K. Two procedures were investigated for calculating the length and longitudinal thermal expansion of the cavity at the temperatures examined. The results from both methods agree well. The relative standard uncertainties for the measurements of length and longitudinal thermal expansion are less than 0.47 × 10−6 and 0.04 × 10−6, respectively, from 243 to 273 K. The low uncertainty achieved here provides confidence to pursue a determination of the Boltzmann constant and thermodynamic temperature with a cylindrical cavity and microwave techniques.