Acoustic Resonator Experiments at the Triple Point of Water: First Results for the Boltzmann Constant and Remaining Challenges

We report on two sets of isothermal acoustic measurements made with argon close to the triple point of water using a 50 mm radius, thin-walled, diamond-turned quasisphere. Our two isotherms yielded values for the Boltzmann constant, k _B, which differ by 0.9 parts in 10⁶, and have an average value of k _B = (1.380 649 6 ± 0.000 004 3) × 10⁻²³J · K⁻¹. The relative uncertainty is 3.1 parts in 10⁶, and the average value is 0.58 parts in 10⁶ below the 2006 CODATA value (Mohr et al. Rev Mod Phys 80:633, 2008), and so the values are consistent within their combined (k = 1) uncertainties.     

Measurement of the Boltzmann Constant <Emphasis Type="Italic">k</Emphasis><Subscript>B</Subscript> Using a Quasi-Spherical Acoustic Resonator

There is currently great interest in the international metrological community for new accurate determinations of the Boltzmann constant k _B, with the prospect of a new definition of the unit of thermodynamic temperature, the kelvin. In fact, k _B relates the unit of energy (the joule) to the unit of the thermodynamic temperature (the kelvin). One of the most accurate ways to access the value of the Boltzmann constant is from measurements of the velocity of the sound in a noble gas. In the method described here, the experimental determination has been performed in a closed quasi-spherical cavity. To improve the accuracy, all the parameters in the experiment (purity of the gas, static pressure, temperature, exact shape of the cavity monitored by EM microwaves, etc.) have to be carefully controlled. Correction terms have been computed using carefully validated theoretical models, and applied to the acoustic and microwave signals. We report on two sets of isothermal acoustic measurements yielding the value k _B = 1.380 647 74(171) × 10⁻²³ J · K⁻¹ with a relative standard uncertainty of 1.24 parts in 10⁶. This value lies 1.9 parts in 10⁶ below the 2006 CODATA value (Mohr et al., Rev. Mod. Phys. 80, 633 (2008)), but, according to the uncertainties, remains consistent with it.     

Measurements of Specific Heat Capacity of Gaseous R-143a Using a Flow Calorimeter

The isobaric specific heat capacity (c _p ) was measured for R-143a (1,1,1-trifluoroethane) in the gas phase. Ten measurements for R-143a were obtained at temperatures from 311 to 343 K and at pressures from 1.6 to 2.4 MPa. Some of them are close to the saturation curve. The expanded uncertainty (k = 2) of the temperature measurements is estimated to be less 25 mK, and that of the pressure measurements is less 8 kPa. The expanded uncertainty for c _p is estimated to range from 9 to 32 J·kg⁻¹·K⁻¹. Also, the experimental data were evaluated with available equations of state.     

Dynamic Measurements of the Temperature Coefficient of Resistance in the Transient Plane Source Sensor

The extended dynamic plane source (EDPS) method is one of the transient methods for measurements of the thermal conductivity and thermal diffusivity in solids. This technique uses a transient plane source (TPS) sensor, which serves as the heat source and thermometer. Its calibration consists of measuring the temperature dependence of the TPS sensor resistance and computing the temperature coefficient of resistance (TCR) using least-squares (LS) estimation. The goal of this study is to calibrate the TPS sensor directly in the apparatus for the EDPS method. The article presents an uncertainty assessment of the TCR measurement. The main sources of uncertainty stem from resistance measurements of the constant resistor and platinum thermometer calibration. The LS estimate of the TCR in a nickel TPS sensor is 4.83 × 10⁻³ K⁻¹ at 20 °C and 4.57 × 10⁻³ K⁻¹ at 45 °C with a combined standard uncertainty better than 0.04 × 10⁻³ K⁻¹, which is 0.7 %.     

A Study of Specific Heat Capacity Functions of Polyvinyl Alcohol–<Emphasis Type="Italic">Cassava</Emphasis> Starch Blends

The specific heat capacity (C _sp) of polyvinyl alcohol (PVOH) blends with cassava starch (CSS) was studied by the differential scanning calorimetry method. Specimens of PVOH–CSS blends: PPV37 (70 mass% CSS) and PPV46 (60 mass% CSS) were prepared by a melt blending method with glycerol added as a plasticizer. The results showed that the specific heat capacity of PPV37 and PPV46 at temperatures from 330 K to 530 K increased from (2.963 to 14.995)  J· g⁻¹ · K⁻¹ and (2.517 to 14.727)  J · g⁻¹· K⁻¹, respectively. The specific heat capacity of PVOH–CSS depends on the amount of starch. The specific heat capacity of the specimens can be approximated by polynomial equations with a curve fitting regression > 0.992. For instance, the specific heat capacity (in J · g⁻¹ · K⁻¹) of PPV37 can be expressed by C _sp = −17.824 + 0.063T and PPV46 by C _sp = −18.047 + 0.061T, where T is the temperature (in K).     

Thermal-Conductivity Characterization of Gas Diffusion Layer in Proton Exchange Membrane Fuel Cells and Electrolyzers Under Mechanical Loading

Accurate information on the temperature field and associated heat transfer rates is particularly important for proton exchange membrane fuel cells (PEMFC) and PEM electrolyzers. An important parameter in fuel cell and electrolyzer performance analysis is the effective thermal conductivity of the gas diffusion layer (GDL) which is a solid porous medium. Usually, this parameter is introduced in modeling and performance analysis without taking into account the dependence of the GDL thermal conductivity λ (in W · m⁻¹ · K⁻¹) on mechanical compression. Nevertheless, mechanical stresses arising in an operating system can change significantly the thermal conductivity and heat exchange. Metrology allowing the characterization of the GDL thermal conductivity as a function of the applied mechanical compression has been developed in this study using the transient hot-wire technique (THW). This method is the best for obtaining standard reference data in fluids, but it is rarely used for thermal-conductivity measurements in solids. The experiments provided with Quintech carbon cloth indicate a strong dependence (up to 300%) of the thermal conductivity λ on the applied mechanical load. The experiments have been provided in the pressure range 0 < p < 8 MPa which corresponds to stresses arising in fuel cells. All obtained experimental results have been fitted by the equation λ = 0.9log(12p + 17)(1 − 0.4e^−50p ) with 9% uncertainty. The obtained experimental dependence can be used for correct modeling of coupled thermo/electro-mechanical phenomena in fuel cells and electrolyzers. Special attention has been devoted to justification of the main hypotheses of the THW method and for estimation of the possible influence of the contact resistances. For this purpose, measurements with a different number of carbon cloth layers have been provided. The conducted experiments indicate the independence of the measured thermal conductivity on the number of GDL layers and, thus, justify the robustness of the developed method and apparatus for this type of application.     

Trilobal Polyimide Fiber Insulation for Cryogenic Applications

Recent measurements have shown a record-breaking low thermal conductivity λ_total of less than 0.25 × 10⁻³ W·m⁻¹·K⁻¹ at temperatures of 120 K for an evacuated sample consisting of polyimide fibers with a trilobal fiber cross section. Existing models for the heat transport in fiber insulations cannot sufficiently describe fiber insulations consisting of fibers with non-cylindrical cross sections. In this article, a modification for the model for cylindrical fibers will be presented. The modifications for the trilobal cross section of the fiber will be explained and compared to the original cylindrical model. The results of the theoretical calculations will be discussed in comparison to experimental results of measurements performed with a guarded hot-plate apparatus at temperatures in the range from 120 K to 420 K.     

Thermophysical Property Measurements of Liquid Gadolinium by Containerless Methods

Thermophysical properties of liquid gadolinium were measured using non-contact diagnostic techniques with an electrostatic levitator. Over the 1585 K to 1920 K temperature range, the density can be expressed as ρ(T) = 7.41 × 10³ − 0.46 (T − T _m) (kg · m⁻³) where T _m = 1585 K, yielding a volume expansion coefficient of 6.2 × 10⁻⁵ K⁻¹. In addition, the surface tension data can be fitted as γ(T) = 8.22 × 10² − 0.097(T − T _m)(10⁻³ N · m⁻¹) over the 1613 K to 1803 K span and the viscosity as η(T) = 1.7exp[1.4 × 10⁴/(RT)](10⁻³ Pa · s) over the same temperature range.     

Influence of Spacer Systems on Heat Transfer in Evacuated Glazing

One attractive possibility to essentially improve the insulation properties of glazing is to evacuate the space between the glass panes. This eliminates heat transport due to convection between the glass panes and suppresses the thermal conductivity of the remaining low pressure filling gas atmosphere. The glass panes can be prevented from collapsing by using a matrix of spacers. These spacers, however, increase heat transfer between the glass panes. To quantify this effect, heat transfer through samples of evacuated glazing was experimentally determined. The samples were prepared with different kinds of spacer materials and spacer distances. The measurements were performed with a guarded hot-plate apparatus under steady-state conditions and at room temperature. The measuring chamber of the guarded hot plate was evacuated to < 10⁻² Pa. An external pressure load of 0.1 MPa was applied on the samples to ensure realistic system conditions. Radiative heat transfer was significantly reduced by preparing the samples with a low-ε coating on one of the glass panes. In a first step, measurements without any spacers allowed quantification of the amount of radiative heat transfer. With these data, the measurements with spacers could be corrected to separate the effect of the spacers on thermal heat transfer. The influence of the thermal conductivity of the spacer material, as well as the distance between the spacers and the spacer geometry, was experimentally investigated and showed good agreement with simulation results. For mechanically stable matrices with cylindrical spacers, experimental thermal conductance values ≤0.44W·m⁻² ·K⁻¹ were found. This shows that U _g -values of about 0.5W · m⁻² · K⁻¹ are achievable in evacuated glazing, if highly efficient low-emissivity coatings are used.     

Measurement of the Specific Heat of Plastic Waste/Fly Ash Composite Material Using Differential Scanning Calorimetry

Plastic waste/fly ash composite, which is made mostly from plastic waste and fly ash, is one of the materials developed for the purpose of recycling. Currently, the composite is used for cable troughs shielding underground lines. However, there exists little information concerning the thermophysical properties of the composite. Thermophysical properties and the structure of the composite must be determined to estimate the heat transfer in the composite and create the different proportions of the composite material. This article deals with measurements of the specific heat of the plastic waste/fly ash composite and its components using a differential scanning calorimeter. The composite sample, which ranged from 10 mg to 19 mg in mass, was cut from a cable trough. The standard reference material is synthetic sapphire disks of 19.6 mg and 29.6 mg in mass. The specific heat of the plastic waste/fly ash composite increases from 1.25 kJ · kg⁻¹ · K⁻¹ to 1.59 kJ · kg⁻¹ · K⁻¹ at temperatures from 305 K to 360 K. The uncertainty for the specific heat data of the composite is estimated to be about 4 %. In addition, the specific heat value depends heavily on the content of the plastic waste.     

Thermal Diffusivity and Heat of Formation of Harzburgite and Its Major Constituent Minerals

The thermal diffusivity, D, and its temperature dependence of Oman harzburgite rock and its major mineral olivine have been evaluated from the basic properties such as seismic velocities, density, and Debye temperature. The Arrhenius-type temperature dependence of the diffusivity was utilized to evaluate the heat of formation, ΔH _D. The diffusivity values, 1.80mm² · s⁻¹ and 2.1mm² · s⁻¹ obtained at room temperature for harzburgite and olivine, respectively, are consistent with available data. The diffusivity values for Oman harzburgite are overestimated by an amount of 0.27mm² · s⁻¹ relative to those of PNG harzburgite. The ΔH _D value (−2.40 kJ · mol⁻¹) for harzburgite rock of the Oman ophiolite suite is comparable with that (−2.90 kJ · mol⁻¹) of the harzburgite rock of Papua New Guinea. The disagreements in the thermal diffusivity and heat of formation values may be partly due to ignoring the effect of pyroxene in Oman harzburgite.     

Cylindrical Acoustic Resonator for the Re-determination of the Boltzmann Constant

The progress towards re-determining the Boltzmann constant k _B using two fixed-path, gas-filled, cylindrical, acoustic cavity resonators is described. The difference in the lengths of the cavities is measured using optical interferometry. Thus, a literature value for the density of mercury is not used, in contrast with the presently accepted determination of k _B. The longitudinal acoustic resonance modes of a cylindrical cavity have lower quality factors Q than the radial modes of gas-filled, spherical cavities, of equal volume. The lower Qs result in lower signal-to-noise ratios and wider, asymmetric resonances. To improve signal-to-noise ratios, conventional capacitance microphones were replaced with 6.3 mm diameter piezoelectric transducers (PZTs) installed on the outer surfaces of each resonator and coupled to the cavity by diaphragms. This arrangement preserved the shape of the cylindrical cavity, prevented contamination of the gas inside the cavity, and enabled us to measure the longitudinal resonance frequencies with a relative standard uncertainty of 0.2 × 10⁻⁶. The lengths of the cavities and the modes studied will be chosen to reduce the acoustic perturbations due to non-zero boundary admittances at the endplates, e.g., from endplate bending and ducts and/or transducers installed in the endplates. Alternatively, the acoustic perturbations generated by the viscous and thermal boundary layers at the gas–solid boundary can be reduced. Using the techniques outlined here, k _B can be re-determined with an estimated relative standard uncertainty of 1.5 × 10⁻⁶.     

The Viscosity of Aqueous Alkali-Chloride Solutions up to 623 K, 1,000 bar,and High Ionic Strength

An accurate viscosity (dynamic viscosity) model is developed for aqueous alkali-chloride solutions of the binary systems, LiCl–H₂O, NaCl–H₂O, and KCl–H₂O, from 273 K to 623 K, and from 1 bar to 1,000 bar and up to high ionic strength. The valid ionic strengths for the LiCl–H₂O, NaCl–H₂O, and KCl–H₂O systems are 0 to 16.7 mol · kg⁻¹, 0 to 6 mol · kg⁻¹, and 0 to 4.5 mol · kg⁻¹, respectively. Comparison of the model with about 4,150 experimental data points concludes that the average absolute viscosity deviation from experimental data in the above range is within or about 1 % for the LiCl–H₂O, NaCl–H₂O, and KCl–H₂O mixtures, indicating the model is of experimental accuracy. With a simple mixing rule, this model can be extrapolated to predict the viscosity of ternary aqueous alkali-chloride solutions, making it useful in reservoir fluid flow simulation. A computer code is developed for this model and can be obtained from the author: (maoshide@cugb.edu.cn).     

Distillation Separation of Hydrofluoric Acid and Nitric Acid from Acid Waste Using the Salt Effect on Vapor–Liquid Equilibrium

This study presents the distillation separation of hydrofluoric acid with use of the salt effect on the vapor–liquid equilibrium for acid aqueous solutions and acid mixtures. The vapor–liquid equilibrium of hydrofluoric acid + salt systems (fluorite, potassium nitrate, cesium nitrate) was measured using an apparatus made of perfluoro alkylvinylether. Cesium nitrate showed a salting-out effect on the vapor–liquid equilibrium of the hydrofluoric acid–water system. Fluorite and potassium nitrate showed a salting-in effect on the hydrofluoric acid–water system. Separation of hydrofluoric acid from an acid mixture containing nitric acid and hydrofluoric acid was tested by the simple distillation treatment using the salt effect of cesium nitrate (45 mass%). An acid mixture of nitric acid (5.0 mol · dm⁻³) and hydrofluoric acid (5.0 mol · dm⁻³) was prepared as a sample solution for distillation tests. The concentration of nitric acid in the first distillate decreased from 5.0 mol · dm⁻³ to 1.13 mol · dm⁻³, and the concentration of hydrofluoric acid increased to 5.41 mol · dm⁻³. This first distillate was further distilled without the addition of salt. The concentrations of hydrofluoric acid and nitric acid in the second distillate were 7.21 mol · dm⁻³ and 0.46 mol · dm⁻³, respectively. It was thus found that the salt effect on vapor–liquid equilibrium of acid mixtures was effective for the recycling of acids from acid mixture wastes.     

Adiabatic Calorimetry as Support to the Certification of High-Purity Liquid Reference Materials

The certification of high-purity liquid reference materials is supported by several analytical techniques (e.g., gas chromatography, liquid chromatography, Karl Fischer coulometry, inductively coupled plasma mass spectrometry, differential scanning calorimetry, adiabatic calorimetry). Most of them provide information on a limited set of specific impurities present in the sample (indirect methods). Adiabatic calorimetry [1] complementarily provides the overall molar fraction of impurities with sensitivity down to few μmol · mol⁻¹ without giving any information about the nature of the impurities present in the sample (direct method). As the combination of adiabatic calorimetry with one (or more than one) indirect chemical techniques was regarded as an optimal methodology, NMi VSL developed an adiabatic calorimetry facility for the purity determination of high-purity liquid reference materials [2]. Within the framework of collaboration with NMIJ, a benzene-certified reference material (NMIJ CRM 4002) from NMIJ was analyzed by adiabatic calorimetry at NMi VSL. The results of this measurement are reported in this paper. Good agreement with the NMIJ-certified purity value (99.992 ± 0.003) cmol · mol⁻¹ was found. The influence of different data analysis approaches (e.g., extrapolation functions, melting ranges) on the measurement results is reported. The uncertainty of the measured purity was estimated.     

Thermal Transport Properties of Functionally Graded Carbon Aerogels

Novel graded carbon aerogels were synthesized to study the impact of different synthesis parameters on the material properties on a single sample and to test a new, locally resolved thermal-conductivity measurement technique. Two identical cylindrical aerogels with a graded structure along the main cylindrical axis were synthesized. Along the gradient with an extension of about 20 mm the densities range from 240 kg·m⁻³ to 370 kg·m⁻³ and the effective pore diameter determined via small angle X-ray scattering and SEM increase systematically from 70 nm up to 11,000 nm. One specimen was cut perpendicular to the cylinder axis into disc-shaped samples; their thermal conductivities in an argon atmosphere, as determined via a standard laser-flash technique, range from 0.06W·m⁻¹·K⁻¹ to 0.12W·m⁻¹·K⁻¹ at 600 °C. The second specimen, cut to obtain a sample with the gradient in-plane, was investigated with a spatially resolved laser-flash technique at ambient conditions. The results of the two different techniques are compared and discussed in detail.     

Thermodynamic Properties of Matrine in Ethanol

In this paper, the enthalpies of dissolution of matrine in ethanol (EtOH) were measured using a RD496-2000 Calvet microcalorimeter at 309.65 K under atmospheric pressure. The differential enthalpy (Δ_dif H _m) and molar enthalpy (Δ_sol H _m) of dissolution of matrine in ethanol were determined. And the relationship between heat and the amount of solute was also established. Based on the thermodynamic and kinetic knowledge, the corresponding kinetic equation that described the dissolution process was determined to be \fracdadt=2.36×10^-4(1-a)^1.09{\frac{{\rm d}\alpha}{{\rm d}t}=2.36\times 10^{-4}(1-\alpha )^{1.09}} . Moreover, the half-life, t _1/2 = 48.89 min, Δ_sol H _m = −12.40 kJ · mol⁻¹, Δ_sol S _m = −354.7 J · mol⁻¹ · K⁻¹, and Δ _sol G _m =  97.43  kJ · mol⁻¹ of the dissolution process were also obtained. The results show that this work not only provides a simple method for the determination of the half-life for a drug but also offers a theoretical reference for the clinical application of matrine.     

Spectrophotometric determination of Ce(IV) usingo-phenylenediamine in steels

A simple and sensitive spectrophotometric method for the determination of cerium(IV) was developed. Witho-phenylenediamine cerium(IV) gives an orange-red colour with an absorption maximum at 470 nm. The system obeys Beer’s law in the range 7 ppm to 500 ppm with a molar absorptivity of 2·4 × 10³l mol⁻¹ cm⁻¹ and Sandell sensitivity of 0·5 ppm. Interference by various ions was studied. This method was used for the determination of cerium in low-alloy steels and the results are in good agreement with the certified values.     

Improvements in the Dynamic Plane Source Method

Three sources of errors in the extended dynamic plane source (EDPS) method caused by the discrepancy between experiment and model are analyzed. The source effect is eliminated by introducing the nuisance parameter R ₀ and the surface effect by a surrounding vacuum. The original model assumes a constant heating power but a constant current is used in the experiment. Suppression of this effect leads to a new solution of the heat equation designated as the constant-current model. The measurements on polymethylmetacrylate (PMMA) in vacuum, evaluated by the constant-current model, provided results of λ = 0.191 W.m⁻¹.K⁻¹ and a = 0.118 ×10⁻⁶ m ².s ^{− 1}, which are in good agreement with published values. The total standard uncertainty was estimated as 1.5 % for both thermophysical properties.     

Measurement of the In-plane Thermal Diffusivity and Temperature-Dependent Convection Coefficient Using a Transient Fin Model and Infrared Thermography

The transient fin model introduced recently for determination of the in-plane thermal diffusivity of planar samples with the help of infrared thermography was modified so as to be applicable to poor heat conductors. The new model now includes a temperature-dependent heat loss by convective heat transfer, suitable for an experimental setup in which the sample is aligned parallel to a weak, forced air flow stabilizing otherwise the convective heat transfer. The temperature field in the sample was measured with an infrared camera while the sample was heated at one edge. The symmetric temperature field created was averaged over the central fifth of the sample to obtain one-dimensional temperature profiles, both transient and stationary, which were fitted by a numerical solution of the fin model. One of the fitting parameters was the thermal diffusivity, and with a known density and specific heat capacity, the thermal conductivity was thus determined. The test measurements with tantalum samples gave the result (57.5 ± 0.2) W · m⁻¹ · K⁻¹ in excellent agreement with the known value. The other fitting parameter was a temperature-dependent heat loss coefficient from which the lower limit for the temperature-dependent convection coefficient was determined. For the stationary state the result was (1.0 ± 0.2) W · m⁻² · K⁻¹ at the temperature of the flowing air, and its temperature dependence was found to be (0.22 ± 0.01) W ·m⁻² · K⁻².