A determination of the molar gas constant R by acoustic thermometry in helium

We have determined the acoustic and microwave frequencies of a misaligned spherical resonator maintained near the temperature of the triple point of water and filled with helium with carefully characterized molar mass M = (4.002 6032 ± 0.000 0015) g mol-1, with a relative standard uncertainty ur(M) = 0.37×10-6. From these data and traceable thermometry we estimate the speed of sound in our sample of helium at TTPW = 273.16 K and zero pressure to be u0 2 = (945 710.45 ± 0.85) m2 s-2 and correspondingly deduce the value R = (8.314 4743 ± 0.000 0088) J mol-1 K-1 for the molar gas constant. We estimate the value k = R/NA = (1.380 6508 ± 0.000 0015) × 10-23 J K-1 for the Boltzmann constant using the currently accepted value of the Avogadro constant NA. These estimates of R and k, with a relative standard uncertainty of 1.06 × 10-6, are 1.47 parts in 106 above the values recommended by CODATA in 2010

Velocità del suono nei fluidi Speed of sound in fluids

La velocità del suono è una grandezza fisica determinata dalle proprietà – temperatura, pressione, composizione – e dallo stato di aggregazione del mezzo in cui la perturbazione acustica si propaga. La sua misura sperimentale permette quindi di ottenere una stima delle proprietà che caratterizzano tali stati in una varietà di condizioni e di scale dimensionali, da microscopiche a planetarie. Limitandosi al caso di mezzi fluidi omogenei, si descrivono una serie di applicazioni della misura della velocità del suono che hanno un interesse scientifico o pratico attuale. Per ognuna di esse la descrizione è accompagnata da una illustrazione essenziale dei principi teorici che ne costituiscono il fondamento.The speed of sound is a physical quantity determined by the properties – temperature, pressure, composition – and by the state of matter of the acoustic propagation medium. As a consequence, the experimental determination of the speed of sound may provide an estimate of these properties in a variety of physical conditions over a range of dimensional scales spanning from microscopic to planetary. Limiting the discussion to consider the case of homogenous fluids, a number of current applications of such measurements which have a scientific or practical interest is reviewed. The description of each application is supplemented by a succinct illustration of the underlying theoretical basis

A Low-Cost Instrument for the Accurate Measurement of Resonances in Microwave Cavities

Since vector network analysis became available, it demonstrated its accuracy and versatility in a variety of applications, including the accurate measurement of resonances in microwave cavities. Unfortunately, the high cost and bulkiness of vector network analyzers (VNAs) set a limit to their applicability. This paper presents and discusses the design and the initial performance tests of a simplified instrument which may represent a valid alternative to VNAs in those applications where the high quality factors of a microwave resonator have to be determined with comparable accuracy but at low cost, allowing field portability and the embedment in a more complex measurement system. Triggered by the recent development of quasi-spherical microwave resonators and their successful utilization in gas metrology, we choose the extremely precise measurement of their eigenfrequencies as a suitable test bench to validate the specifications and assess the performance of the proposed instrument