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International Journal of Thermophysics, 2014, Volume 35, Issue 11, pp 2115-2123.
E.B. Postnikov1, A.L. Goncharov1, V.V. Melent’ev2.
1. Department of Theoretical Physics, Kursk State University, Radishcheva st., 33, 305000, Kursk, Russia.
2. Laboratory of Molecular Acoustics, Kursk State University, Radishcheva st., 33, 305000, Kursk, Russia.
Abstract
We consider the possibilities for prediction of liquids’ density under pressure basing on the inverse reduced fluctuations parameter, which is directly connected with the isothermal compressibility. This quantity can be determined basing on the thermodynamical properties of saturated liquid and it consists of only two constant parameters within a relatively wide region close to the melting points. It is confirmed by the comparison with the experimental data on n-alkanes that the derived expression is a quite reasonable estimator without a necessity to fit data along some parts of isotherms for different temperatures. At the same time the obtained formula: i) can be reduced to the form of the Tait equation and ii) the resulting Tait’s parameters in this representation have a clear physical meaning as functions of the excess entropy, which determines the mentioned reduced fluctuations.
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Significance statement
The Tait equation is an isothermal equation of state, which describes the density of liquid as a function of the applied pressure. It is de facto reference standard representing the corresponding data for engineering applications. However, its conventional usage as an approximant requires the knowledge of referent points measured under an elevated pressure and results in the pairs of Tait constants determined for each isotherm separately. Our approach is based on the fact of exponential character of the inverse reduced density fluctuations, which does not depend on the temperature along the liquid-vapour coexistence line in a wide range of state parameters and can be extended into the single phase region. As a result, one obtains only two constant parameters using much more simple measurements under the saturation (or even normal pressure) conditions. These parameters can be used for the practical calculations of normal liquid’s density up to hundreds MPa with a high accuracy.
Figure Legend
The comparison of hexane’s densities calculated via the proposed two-parametrical fluctuation-based equation of state (curves) and the experimental data [Daridon et al. Int. J. Thermophys. 19 (1998) 145] for the isotherms from 293.15 K to 343 K with the step 5 K.
