This work presents measurements of the speed-of-sound in the vapor phase of 1,1,1,2,3,3,3-heptafl... more This work presents measurements of the speed-of-sound in the vapor phase of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea). The measurements were obtained in a stainless-steel spherical resonator with a volume of t900 cm 3 at temperatures between 260 and 380 K and at pressures up to 500 kPa. Ideal-gas heat capacities and acoustic virial coefficients are directly produced from the data. A Helmholtz equation of state of high accuracy is proposed, whose parameters are directly obtained from speed-of-sound data fitting. The ideal-gas heat capacity data are fit by a functions and used when fitting the Helmholtz equation for the vapor phase. From this equation of state other thermodynamic state function are derived. Due to the high accuracy of the equation, only very precise experimental data are suitable for the model validation and only density measurements have these requirements. A very high accuracy is reached in density prediction, showing the obtained Helmholtz equation to be very reliable. The deduced vapor densities are furthermore compared with those obtained from acoustic virial coefficients with the temperature dependences calculated from hard-core square-well potentials.
Using a quasispherical, microwave cavity resonator, we measured the refractive index of helium to... more Using a quasispherical, microwave cavity resonator, we measured the refractive index of helium to deduce its molar polarizability A(epsilon) in the limit of zero density. We obtained (A(epsilon,meas) - A(epsilon,theory))/A(epsilon) = (-1.8 +/- 9.1) x 10(-6), where the standard uncertainty (9.1 ppm) is a factor of 3.3 smaller than that of the best previous measurement. If the theoretical value of A(epsilon) is accepted, these data determine a value for the Boltzmann constant that is only 1.8 +/- 9.1 ppm larger than the accepted value. Our techniques will enable a helium-based pressure standard and measurements of thermodynamic temperatures.
Acoustic thermometry using a gas-filled quasi-spherical resonator (QSR) is one of the most promis... more Acoustic thermometry using a gas-filled quasi-spherical resonator (QSR) is one of the most promising techniques for measuring the Boltzmann constant kB with low uncertainty. Dimensional metrology with coordinate measurement machines (CMMs) can be used to determine the resonator's volume, either directly or in combination with measurements of the resonator's microwave spectra. We assessed the uncertainty achievable when using a CMM to characterize the shape and volume of three QSRs. The resonators differed significantly in their design and construction: their inner volumes ranged between 524 cm3 and 2225 cm3, while the QSR geometries ranged from a diamond-turned triaxial ellipsoid to the variable misalignment of spheroidal hemispheres. Comparative coordinate measurements of two solid spherical density standards were used to identify and estimate type B uncertainties. We tested the regression of the CMM data to spherical harmonic expansions and determined the volume of a QSR directly with a relative uncertainty uR < 30 parts in 106. Additionally, spherical harmonic regression of the CMM data can place uncertainty bounds on the eccentricity parameters, epsilo1 and epsilo2, typically with a relative uncertainty uR &ap; 0.02. This is sufficient to determine corrections to both the acoustic and the microwave resonance frequencies of the QSR with a relative uncertainty uR < 1 part in 106 for all resonances. These figures assume that the enclosed volume of an assembled QSR is equal to the sum of the volumes of its two component 'hemispheres'. In practice this cannot be strictly true and the additional uncertainties in the volume of the assembled QSR are discussed.
A newly designed experimental apparatus has been used to measure the speed of sound u in high-pur... more A newly designed experimental apparatus has been used to measure the speed of sound u in high-purity water on nine isotherms between 274 and 394 K and at pressures up to 90 MPa. The measurement technique is based on a traditional double-reflector pulse-echo method with a single piezoceramic transducer placed at unequal distances from two stainless steel reflectors. The transit times of an acoustic pulse are measured at a high sampling rate by a digital oscilloscope. The distances between the transducer and the reflectors were obtained at ambient temperature and pressure by direct measurements with a coordinate measuring machine. The speeds of sound are subject to an overall estimated uncertainty of 0.05 %. The acoustic data were combined with available values of density ρ and isobaric heat capacity c p along one isobar at atmospheric pressure to calculate the same quantities over the whole temperature and pressure range by means of a numerical integration technique. These results were compared with those calculated from the IAPWS-95 formulation with corresponding relative deviations which are within 0.1%.
Current progress in the INRiM experiment for the determination of the Boltzmann constant k B by m... more 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
Photoacoustic Spectroscopy (PAS) has been performed on Porous Silicon Layers (PSL) obtained by ch... more Photoacoustic Spectroscopy (PAS) has been performed on Porous Silicon Layers (PSL) obtained by chemical and electrochemical etching of crystalline Silicon. In the investigated energy range (2.0eV-4.7eV) the samples behave as optically opaque and show strong light scattering properties so to prevent the application of standard reflectivityftrasmission techniques. PAS proves suitable in studying porous media, providing evidence that PSLs retain the original cristallinity. The presence of native oxides on PSLs has been revealed by PAS.
Condenser microphones are more commonly used and have been extensively modeled and characterized ... more Condenser microphones are more commonly used and have been extensively modeled and characterized in air at ambient temperature and static pressure. However, several applications of interest for metrology and physical acoustics require to use these transducers in significantly different environmental conditions. Particularly, the extremely accurate determination of the speed of sound in monoatomic gases, which is pursued for a determination of the Boltzmann constant k by an acoustic method, entails the use of condenser microphones mounted within a spherical cavity, over a wide range of static pressures, at the temperature of the triple point of water (273.16 K). To further increase the accuracy achievable in this application, the microphone frequency response and its acoustic input impedance need to be precisely determined over the same static pressure and temperature range. Few previous works examined the influence of static pressure, temperature, and gas composition on the microphone's sensitivity. In this work, the results of relative calibrations of 1/4 in. condenser microphones obtained using an electrostatic actuator technique are presented. The calibrations are performed in pure helium and argon gas at temperatures near 273 K and in the pressure range between 10 and 600 kPa. These experimental results are compared with the predictions of a realistic model available in the literature, finding a remarkable good agreement. The model provides an estimate of the acoustic impedance of 1/4 in. condenser microphones as a function of frequency and static pressure and is used to calculate the corresponding frequency perturbations induced on the normal modes of a spherical cavity when this is filled with helium or argon gas.
This work presents measurements of the speed-of-sound in the vapor phase of 1,1,1,2,3,3,3-heptafl... more This work presents measurements of the speed-of-sound in the vapor phase of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea). The measurements were obtained in a stainless-steel spherical resonator with a volume of t900 cm 3 at temperatures between 260 and 380 K and at pressures up to 500 kPa. Ideal-gas heat capacities and acoustic virial coefficients are directly produced from the data. A Helmholtz equation of state of high accuracy is proposed, whose parameters are directly obtained from speed-of-sound data fitting. The ideal-gas heat capacity data are fit by a functions and used when fitting the Helmholtz equation for the vapor phase. From this equation of state other thermodynamic state function are derived. Due to the high accuracy of the equation, only very precise experimental data are suitable for the model validation and only density measurements have these requirements. A very high accuracy is reached in density prediction, showing the obtained Helmholtz equation to be very reliable. The deduced vapor densities are furthermore compared with those obtained from acoustic virial coefficients with the temperature dependences calculated from hard-core square-well potentials.
Using a quasispherical, microwave cavity resonator, we measured the refractive index of helium to... more Using a quasispherical, microwave cavity resonator, we measured the refractive index of helium to deduce its molar polarizability A(epsilon) in the limit of zero density. We obtained (A(epsilon,meas) - A(epsilon,theory))/A(epsilon) = (-1.8 +/- 9.1) x 10(-6), where the standard uncertainty (9.1 ppm) is a factor of 3.3 smaller than that of the best previous measurement. If the theoretical value of A(epsilon) is accepted, these data determine a value for the Boltzmann constant that is only 1.8 +/- 9.1 ppm larger than the accepted value. Our techniques will enable a helium-based pressure standard and measurements of thermodynamic temperatures.
Acoustic thermometry using a gas-filled quasi-spherical resonator (QSR) is one of the most promis... more Acoustic thermometry using a gas-filled quasi-spherical resonator (QSR) is one of the most promising techniques for measuring the Boltzmann constant kB with low uncertainty. Dimensional metrology with coordinate measurement machines (CMMs) can be used to determine the resonator's volume, either directly or in combination with measurements of the resonator's microwave spectra. We assessed the uncertainty achievable when using a CMM to characterize the shape and volume of three QSRs. The resonators differed significantly in their design and construction: their inner volumes ranged between 524 cm3 and 2225 cm3, while the QSR geometries ranged from a diamond-turned triaxial ellipsoid to the variable misalignment of spheroidal hemispheres. Comparative coordinate measurements of two solid spherical density standards were used to identify and estimate type B uncertainties. We tested the regression of the CMM data to spherical harmonic expansions and determined the volume of a QSR directly with a relative uncertainty uR < 30 parts in 106. Additionally, spherical harmonic regression of the CMM data can place uncertainty bounds on the eccentricity parameters, epsilo1 and epsilo2, typically with a relative uncertainty uR &ap; 0.02. This is sufficient to determine corrections to both the acoustic and the microwave resonance frequencies of the QSR with a relative uncertainty uR < 1 part in 106 for all resonances. These figures assume that the enclosed volume of an assembled QSR is equal to the sum of the volumes of its two component 'hemispheres'. In practice this cannot be strictly true and the additional uncertainties in the volume of the assembled QSR are discussed.
A newly designed experimental apparatus has been used to measure the speed of sound u in high-pur... more A newly designed experimental apparatus has been used to measure the speed of sound u in high-purity water on nine isotherms between 274 and 394 K and at pressures up to 90 MPa. The measurement technique is based on a traditional double-reflector pulse-echo method with a single piezoceramic transducer placed at unequal distances from two stainless steel reflectors. The transit times of an acoustic pulse are measured at a high sampling rate by a digital oscilloscope. The distances between the transducer and the reflectors were obtained at ambient temperature and pressure by direct measurements with a coordinate measuring machine. The speeds of sound are subject to an overall estimated uncertainty of 0.05 %. The acoustic data were combined with available values of density ρ and isobaric heat capacity c p along one isobar at atmospheric pressure to calculate the same quantities over the whole temperature and pressure range by means of a numerical integration technique. These results were compared with those calculated from the IAPWS-95 formulation with corresponding relative deviations which are within 0.1%.
Current progress in the INRiM experiment for the determination of the Boltzmann constant k B by m... more 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
Photoacoustic Spectroscopy (PAS) has been performed on Porous Silicon Layers (PSL) obtained by ch... more Photoacoustic Spectroscopy (PAS) has been performed on Porous Silicon Layers (PSL) obtained by chemical and electrochemical etching of crystalline Silicon. In the investigated energy range (2.0eV-4.7eV) the samples behave as optically opaque and show strong light scattering properties so to prevent the application of standard reflectivityftrasmission techniques. PAS proves suitable in studying porous media, providing evidence that PSLs retain the original cristallinity. The presence of native oxides on PSLs has been revealed by PAS.
Condenser microphones are more commonly used and have been extensively modeled and characterized ... more Condenser microphones are more commonly used and have been extensively modeled and characterized in air at ambient temperature and static pressure. However, several applications of interest for metrology and physical acoustics require to use these transducers in significantly different environmental conditions. Particularly, the extremely accurate determination of the speed of sound in monoatomic gases, which is pursued for a determination of the Boltzmann constant k by an acoustic method, entails the use of condenser microphones mounted within a spherical cavity, over a wide range of static pressures, at the temperature of the triple point of water (273.16 K). To further increase the accuracy achievable in this application, the microphone frequency response and its acoustic input impedance need to be precisely determined over the same static pressure and temperature range. Few previous works examined the influence of static pressure, temperature, and gas composition on the microphone's sensitivity. In this work, the results of relative calibrations of 1/4 in. condenser microphones obtained using an electrostatic actuator technique are presented. The calibrations are performed in pure helium and argon gas at temperatures near 273 K and in the pressure range between 10 and 600 kPa. These experimental results are compared with the predictions of a realistic model available in the literature, finding a remarkable good agreement. The model provides an estimate of the acoustic impedance of 1/4 in. condenser microphones as a function of frequency and static pressure and is used to calculate the corresponding frequency perturbations induced on the normal modes of a spherical cavity when this is filled with helium or argon gas.
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Papers by R. Gavioso