A new and reliable calibration method for vibrating tube densimeters over wide ranges of temperature and pressure Isabel M.S. Lampreia ⇑ , Carlos A. Nieto de Castro Departamento de Química e Bioquímica, Centro de Ciências Moleculares e Materiais, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal article info Article history: Received 25 May 2010 Received in revised form 18 October 2010 Accepted 8 November 2010 Available online 20 November 2010 Keywords: Vibrating tube densimeter Calibration High pressure Reference density values abstract A new method for accurately converting vibrating tube periods of oscillation in density values is pre- sented. This method is based on the fundamental requirement of the non-dependence on pressure of the vibration period of the cell under vacuum. An analytical method permits to correctly evaluate the evacuated vibrating tube periods of the Anton Paar cells namely the high pressure cells, 512 and 512P, as a function of temperature. It is further shown that the previously experimental method for the deter- mination of this parameter is not suitable for obtaining reliable density values. A new simple calibration procedure is described and tested over wide ranges of temperature, T = (283.15 to 323.15) K and pressure, P = (0.1 to 60) MPa. New recommended density values for n-alkanes (C 6 ,C 7 ,C 8 , and C 10 ) and tetrachloro- methane, calculated by the proposed method, are given and compared with literature values in terms of mutual uncertainties. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Density is by far the most important property in chemical industry. Accurate experimental density data for pure fluids and their mixtures, as a function of pressure and temperature, are re- quired for a huge number of physical and chemical applications. The direct evaluation of its derived mechanical coefficients, iso- thermal compressibility and isobaric expansibility, the establish- ment of reliable equations of state (EOS) and the calculation of other important properties such as the molar isobaric heat capacity or dynamic viscosity are some of the intermediate steps leading to important scientific and technological applications, namely in heat and mass transfer in moving fluids. Different absolute and relative methods for the experimental determination of density under pressure, based on diverse physical principles, have been used by various authors aiming to improve the accuracy of the data [1–6]. Among relative methods the vibrat- ing tube densimetry [1] has been most used both in research and industry due to its precision and easiness of operation. Its accuracy is, however, very much dependent on the calibration procedure employed. Since their first appearance as density meters the mechanical oscillator densimeter has proven to be one of the most versatile and accurate instruments for relative measurements. Its main limitation relies on the fact that it has not been feasible so far to transform it in an absolute instrument, due to the lack of a correct modelling of its working equation. It is therefore necessary to ana- lyze the theoretical basis of the mechanical oscillator densimeter, trying to understand the physical meaning of the calibration con- stants and improve their determination. This has been made by various authors [7–13]. A typical mechanical oscillator densimeter measures the frequency of vibration of an excited oscillator and its dependence on the mass of the oscillator. The oscillator consists usually of a U-shaped tube, made from glass or stainless steel, fused into a dual-wall cylinder, which is also made of glass or stainless steel, according to the cell type. The space between the U-shaped tube and the inner wall of the dual-wall cylinder is filled with a gas of high thermal conductivity, to aid a rapid temperature equilibration of the sample inside the oscillator, and of low density, to avoid additional damping in the vibrating move. Through the dual-wall cylinder a thermostatic liquid flows. This assemblage is designated by densimeter cell. The U-shaped tube is forced to oscillate by two magnetic dy- namic converters in connection with an electronic control and amplifier circuit which guarantees constant amplitude of the oscil- lator tube. The direction of the oscillation is normal to the plane of the U-shaped tube. Under this type of geometry the system exe- cutes a simple harmonic oscillation, if the time duration of an oscil- lation can be made short, in order to minimize the small damping introduced by the restriction of the U-shaped connection to the support and by the gas in the inner wall of the dual-wall cylinder. This is the case when the time of response is of the order of ls. There is in fact a microscopic flow of fluid inside and outside during the vibration that might induce secondary flows, making the measurements dependent on the viscosity of the fluid. 0021-9614/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2010.11.002 ⇑ Corresponding author. Tel.: +351 217500995; fax: +351 217500088. E-mail address: milampreia@fc.ul.pt (I.M.S. Lampreia). J. Chem. Thermodynamics 43 (2011) 537–545 Contents lists available at ScienceDirect J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct