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Sufficient progress towards redefining the International System of Units (SI) in terms of exact values of fundamental constants has been achieved. Exact values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant N A from the CODATA 2017 Special Adjustment of the Fundamental Constants are presented here. These...
Citations
... Since 1885, the fixed number of entities in one mole has been measured (with uncertainty) through various experiments, materials, and methods in which the mole is quantified by mass, Becker (2001), Mohr et al (2018), Newell et al (2018). The mass of one atom of carbon-12 is fixed. ...
... The SI (1970) Avogadro number is the measurand (quantity intended to be measured) for all measurements of the fixed number of entities in one mole from 1970 to 2019. The CODATA 2017 value of this measurand is 6.022 140 758 × 10 23 with relative standard uncertainty 1 × 10 −8 , Newell et al (2018). The SI (2019) The SI established the numerical values of the defining constants such that (the magnitudes of) the current SI units are consistent with the previous SI units. ...
The SI (2019) claims that the Avogadro constant NA has the same character as the other six defining constants ΔνCs, c, h, e, k, and Kcd, and that the same approach that is used to redefine the other base units may also be used to redefine the mole based on NA. The SI (2019) states that the expression NA = 6.022 140 76 × 10²³ × mol⁻¹ is a defining relation whose inversion provides the algebraic definition of the mole. This Letter shows that NA is not the defining constant of the mole. The unit mole is defined by the SI description of the Avogadro number {NA}.
... As a convention, the value of the Planck constant is defined to be an exact value, see e. g. Newell et al. (2018) or Workman et al. (2022). ...
... In this section, we show that volume in nature is measurable and observable. Thereby, we use the SI units, see e. g. Newell et al. (2018), whereby other units are alternatively applicable, such as 2) or such as Gaussian units, see e. g. Jackson (1975). ...
Volume in nature is a foundation of present-day physics.
The volume dynamics, VD, is implied by evident properties:
invariance of the speed of light and zero rest mass of volume
The VD includes:
the existence and reality of volume portions, VPs,
change tensors of VPs, including electromagnetic waves,
the differential equation describing change tensors, form of wave packets,
formation and propagation of VPs,
real quantities are identified via the Hacking criterion.
The VD implies and explains present-day physics, e. g.
gravity and transmission of gravitational interaction,
curvature of spacetime,
general relativity as a semiclassical and averaging approximation,
universal formation of quanta, a generalized Schrödinger equation, the postulates of quantum physics,
the Schrödinger equation as a nonrelativistic approximation,
an improved and generalized version of quantum field theory, including nonlocality & causality, without infinity – as expected, as real volume inside the light horizon cannot cause a real infinity.
The VD implies, explains and clarifies properties of space, e. g.
VD implies density of volume in our heterogeneous universe,
VD provides the time evolution of the Hubble constant (front cover), this solves the Hubble tension,
real VPs represent the wave function and its generalization,
VD clarifies real zero-point-oscillations, real Casimir force and real VPs and solves the cosmological constant problem,
causality with nonlocality is clarified,
formation of matter has been derived,
the era of cosmic ‘inflation’ has been derived and clarified,
the elementary charge, the electroweak couplings and many elementary particles have been derived and explained,
the cosmological parameters have been derived fundamentally.
Thus, the VD clarifies, generalizes and unifies present-day physics.
All results are in precise accordance with observation. Thereby, no fit has been executed, and no hypothesis has been introduced.
We derive all findings in a systematic, clear & smooth manner. We summarize our results by definitions, propositions & theorems. We are classes from grade 10 or higher, courses, research clubs, enthusiasts, observers, experimentalists, mathematicians, scientists, researchers . . .
... where M = 114.0416 × 10 -3 kg mol -1 is the molar mass of R1234ze(Z) and R = 8.3144626 J mol -1 K -1 is the molar gas constant (Newell et al., 2018). At all temperatures, the relative fitting precision of our determinations of 0 (T) resulted less than 0.03%, while the corresponding accuracy is limited by the imperfect knowledge of the composition of the sample under test, as commented below. ...
Measurements of the speed of sound in gaseous cis-1,3,3,3-tetrafluoroprop-1-ene, (R1234ze(Z)), are presented. The measurements were performed using a quasi-spherical acoustic resonator at temperatures between 307 K and 420 K and pressures up to 1.8 MPa. Ideal-gas heat capacities and acoustic virial coefficients over the same temperature range were directly calculated from the results. The relative accuracy of our determinations of the speed of sound w(p,T) of R1234ze(Z) was approximately 0.02%. The accuracy of the determination of the ideal gas heat capacity ratio (T) was approximately 0.25%. These data were found to be mostly consistent with the predictions of a fundamental equation of state of R1234ze(Z).
... where R = kN A is the molar gas constant, and the values of the Boltzmann constant k and the Avogadro constant N A are defined exactly [28] by the international system of units (SI) [29]. By setting γ 0 to its exact value of 5/3 in equation (1), i.e. by assuming that the composition of Ne ref is entirely monatomic, M ref can be obtained and compared to the reference value of the neon molar mass M IUPAC based on the updated compilation of standard atomic weights by the International Union of Pure and Applied Chemistry (IUPAC) [30]. ...
We report comprehensive and accurate measurements of the speed of sound in neon. These measurements were carried out by a double-path-length pulse-echo technique and cover the temperature range between 200 K and 420 K with pressures up to 100 MPa. The standard uncertainties are 1.9 mK in temperature, 22 parts in 10⁶ in pressure and 35 parts in 10⁶ in speed of sound. The third and fourth acoustic virial coefficients of neon were derived from the speed of sound data in the temperature range of the measurements by fitting a fourth-order acoustic virial expansion in pressure with the second acoustic virial coefficient constrained from first-principles calculations. To support our claimed uncertainty, we determined the ratio M/γ0 between the molar mass M and the ideal-gas heat capacity ratio γ0 of the neon sample with a relative standard uncertainty of 7.7 parts in 10⁶ by additional speed of sound measurements using a spherical resonator at 273.16 K.
... It shows the results of the measurements carried out from 2011 to 2017 by both the Kibble balance and XRCD experiments. The black dot is the value recommended by the CODATA in 2017 [42,43] and was adopted by the 26th CGPM to redefine the kilogram. ment). ...
... The values measured by Kibble balances and the XRCD method submitted to CODATA for the 2017 special adjustment were not in perfect agreement. To achieve consistency, a multiplicative expansion factor of 1.7 was applied to the uncertainties of the data shown in Figure 2 [42]. This correction to the uncertainties of the data led to the implementation of a procedure for a smooth and reliable transition between the international prototype and the new SI realizations of the kilogram. ...
The International System of Units (SI), the current form of the metric system and the world’s most used system of units, has been continuously updated and refined since the Metre Convention of 1875 to ensure that it remains up to date with the latest scientific and technological advances. The General Conference on Weights and Measures, at its 26th meeting in 2018, decided to adopt stipulated values of seven physical constants linked to seven measurement units (the second, meter, kilogram, ampere, kelvin, mole, and candela). This paper reviews the technologies developed, in intense and long-standing work, to determine the Avogadro and Planck constants, which are now integral to realising the kilogram.
... The molar gas constant used in this work is R = 8.314462618 J K −1 mol −1 [5], and all temperatures are based on the temperature scale ITS-90. ...
In this work, a state-of-the-art static apparatus for vapor pressure measurements in a temperature range of 363−463 K and a wide pressure range of 1−13,330 Pa is introduced and described. The performance of the apparatus was evaluated by a meticulous procedure of measuring the vapor pressure of five reference materials of different volatility, anthracene, benzophenone, ferrocene, naphthalene, and dibenzothiophene. The last two compounds were studied in the blind test regime, i.e., the results were compared to literature only after finishing the experiments. During benchmarking the performance of the apparatus, it was found appropriate to develop new vapor pressure equations for ferrocene and anthracene that included high-temperature data from the STAT9 apparatus. By combining the new data with previously selected vapor pressures, sublimation enthalpies, and ideal-gas and condensed phase heat capacities, we have obtained a consistent sublimation pressure equation for anthracene and ferrocene. For anthracene, the correlation procedure covered melting properties and liquid-phase vapor pressure data to support the description of the high-temperature region. The revised vapor pressure equations and sublimation enthalpies may serve as solid foundation for future research in this field.
... The derivative of the product implies the DEQ (45). The DEQs (46,47) are derived as described in part (3c). ...
... That portion exhibits essential properties of quanta. Moreover, quanta have the essential advantage that they can form enormously stable states in an extremely precise manner, see [33], [45], [46]. In order to show that the portions in Eq. (177) have the same property, we analyze the stability of minimal portions next. ...
Present-day physics has two different essential theories, quantum physics, and general relativity. But we live in one world. Thus, unification is essential for further progress in science. In this paper, a fundamental exact unification is presented. It is based on volume in nature. Such volume consists of volume-portions with two evident properties in principle: Firstly, each volume-portion has a volumetric property, that property can be described by metric tensors used in general relativity. Secondly, volume has no rest mass, and as a consequence, each volume-portion propagates in space or spacetime. That property is essential and beyond the metric space concept of general relativity. Volume-portions in nature occur in a very pure and observable form in the intergalactic space. In this paper, the volume-dynamics of the volume-portions are derived. With it, the unification of quantum physics and general relativity is derived, and many fundamental problems of physics have been solved. Moreover, the deep reason is clarified for the following fact: Present-day general relativity does not provide that unification, whereas the volume dynamics does provide that unification.
... For JNT, the synthesiser is operated as a broadband quantum-based voltage-noise source (QVNS), enabling a significant increase in bandwidth of the noise thermometer with a corresponding reduction in the uncertainty. The development of the QVNS culminated in the 2017 Boltzmann constant determination at National Institute of Metrology (NIM China), which achieved a relative uncertainty of 2.7 × 10 −6 [22] and contributed to the special adjustment of the fundamental constants [23] by the Committee on Data of the International Science Council (CODATA) prior to the redefinition of the kelvin. Similar state-of-the-art JNT measurements of k were completed at NIST and the National Metrology Institute of Japan (NMIJ Japan) and achieved, respectively, relative uncertainties of 5.0 × 10 −6 [20,21] and 1.0 × 10 −5 [24]. ...
... Equation (4) for the correlator error includes an error term for the noise-current-noise-voltage correlation. As implied by (23) and (24), the noise current and noise voltage share a physical cause, so a high correlation might be expected. However, the 90 • phase shift between the noise voltage and the noise-current due to the passage of the current through a capacitance, means that the correlation is imaginary and, on average, zero. ...
Johnson noise thermometry (JNT) is a purely electronic method of thermodynamic thermometry. In primary JNT, the temperature is inferred from a comparison of the Johnson noise voltage of a resistor at the unknown temperature with a pseudo-random noise synthesized by a quantum-based voltage-noise source (QVNS). The advantages of the method are that it relies entirely on electronic measurements, and it can be used over a wide range of temperatures due to the ability of the QVNS to generate programmable, scalable, and accurate reference signals. The disadvantages are the requirement of cryogenic operation of the QVNS, the need to match the frequency responses of the leads of the sense resistor and the QVNS, and long measurement times. This review collates advice on current best practice for a primary Johnson noise thermometer based on the switched correlator and QVNS. The method achieves an uncertainty of about 1 mK near 300 K and is suited to operation between 4 K and 1000 K.
... Molar masses of the compounds were calculated based on IUPAC recommendations [80]. For the calculations, the molar gas constant R = 8.314462618 J K −1 mol −1 was used [81]. ...
An extensive thermodynamic study of N-methylformamide (CAS RN: 123-39-7) and N,N-dimethylformamide (CAS RN: 68-12-2), is presented in this work. The liquid heat capacities of N-methylformamide were measured by Tian–Calvet calorimetry in the temperature interval (250 – 300) K. The vapor pressures for N-methylformamide and N,N-dimethylformamide were measured using static method in the temperature range 238 K to 308 K. The ideal-gas thermo-dynamic properties were calculated using a combination of the density functional theory (DFT) and statistical thermodynamics. A consistent thermodynamic description was developed using the method of simultaneous correlation, where the experimental and selected titerature data for vapor pressures, vaporization enthalpies, and liquid phase heat capacities and calculated ide-al-gas heat capacities are treated together to ensure overall thermodynamic consistency of the results. Resulting vapor pressure equation is valid from the triple point to the normal boiling point temperature.
... According to the International Vocabulary of Metrology-Basic and general concepts and associated terms (VIM), a primary reference measurement procedure-short primary method-is a "reference measurement procedure used to obtain a measurement result without relation to a measurement standard for a quantity of the same kind…" [7]. The numerical values of h and N A were released after a least squares adjustment by the CODATA (Committee on Data for Science and Technology) Task Group on Fundamental Constants in 2017 [8]. The data used for this release originated from two experimental approaches: One method for the realization of h and N A is provided by the Kibble balance experiment [9] and a special variant, the joule balance experiment [10], while the second experimental route is called the x-ray crystal density (XRCD) method (also known as the Avogadro-Project or the silicon route) [11,12]. ...
The molar mass and isotopic composition of a new silicon single crystal material (Si28-31Pr11) highly enriched in ²⁸ Si has been determined in the context of the X-ray crystal density (XRCD) method used for the realization and dissemination of the SI base units ‒ the mole and the kilogram. Isotope ratio measurements have been performed using a high-resolution multicollector-inductively coupled plasma mass spectrometer (MC-ICP-MS) with improved technical performance. By applying the Virtual-Element Isotope Dilution Mass Spectrometry (VE-IDMS) method, different crystal areas enclosing the locations of two silicon spheres have been investigated with respect to the magnitude of tentative variations in the molar mass and isotopic composition of the respective samples as a function of their original location in the crystal ingot. In total, 18 subsamples from four different axial and several related radial posi-tions have been characterized. An average molar mass M (Si28-31Pr11) = 27.976 941 464(41) g mol ⁻¹ corresponding to a relative combined uncertainty u c,rel ( M (Si28-31Pr11)) = 1.4 × 10 ⁻⁹ was yielded. The average enrichment in ²⁸ Si of the crystal is expressed by the mean amount-of-substance fraction x ( ²⁸ Si) = 0.999 985 350(37) mol/mol. Two spheres were cut from the crystal ingot. The average molar masses of the spheres Si28kg_03_a and Si28kg_03_b are: M (Si28kg_03_a) = 27.976 941 467(43) g mol ⁻¹ and M (Si28kg_03_b) = 27.976 941 461(44) g mol ⁻¹ , respectively. The results are discussed using uncertainty budgets according to the Guide to the expression of uncertainty in measurement (GUM). A homogeneous distribution of the molar mass throughout the crystal is suggested, qualifying it as a material for a primary stand-ard – a silicon sphere – for the realization and dissemination of the mole and the kilogram. A comparison with enriched silicon crystals that are already available is given.
