Determination of the thermodynamic properties of water from the speed of sound

Abstract

Thermodynamic properties of compressed liquids may be obtained from measurements of the speed of sound by means of thermodynamic integration subject to initial values of density and isobaric specific heat capacity along a single low-pressure isobar. In this paper, we present an analysis of the errors in the derived properties arising from perturbations in both the speedof-sound surface and the initial values. These errors are described in first order by a pair of partial differential equations that we integrate for the example case of water with various scenarios for the errors in the sound speed and the initial values. The analysis shows that errors in either the speed of sound or the initial values of density that are rapidly oscillating functions of temperature have a disproportionately large influence on the derived properties, especially at low temperatures. In view of this, we have obtained a more accurate empirical representation of the recent experimental speed-of-sound data for water [Lin and Trusler, J. Chem. Phys. 136, (2012) 094511] and use this in a new thermodynamic integration to obtain derived properties including density, isobaric heat capacity and isobaric thermal expansivity at temperatures between (253.15 and 473.15) K at pressures up to 400 MPa. The densities obtained in this way are in very close agreement with those reported by Lin and Trusler, but the isobaric specific heat capacity and the isobaric expansivity both differ significantly in the extremes of low temperatures and high pressures.

Density, sound speed and derived thermophysical properties of n-nonane at temperatures between (283.15 and 473.15) K and at pressures up to 390 MPa

“…The method was first used by Davis and Gordon [45] for mercury and improved by Sun et al [46]. The algorithm used [47] and the uncertainty of the method have also been studied in detail in a recent paper [48].…”

Computation of Liquid Isothermal Compressibility from Density Measurements: An Application to Toluene

“…This potentiality, specific to speed of sound, has been used for obtaining isentropic and isothermal compressibility coefficients of a large number of pure liquids and liquid mixtures. In particular, Kell and Whalley and, recently, Trusler and Lemmon calculated the thermodynamic properties of water from the speed of sound, whereas Davis and Gordon used this method for estimating the compressibility of liquid mercury at ultrahigh pressure (GPa). Muringer et al followed by several other groups − investigated the compressibility of hydrocarbons from ultrasonic speed measurements.…”

Speed-of-Sound Measurements and Derived Thermodynamic Properties of Liquid Isobutane

“…This method is called thermodynamic integration and was originally devised by Davis and Gordon in 1967. Ever since, it has been applied by many authors, and various algorithms have been suggested to integrate the system of partial differential equations, e.g., refs − . Because all thermodynamic properties can be calculated in the domain of the speed-of-sound measurements, the thermodynamic integration provides a means for generating comprehensive data sets that can be used as part of the database for developing wide-ranging Helmholtz energy formulations for pure fluids and mixtures.…”

“…For the density, accurate values at low pressures are available for many fluids, but data for the isobaric heat capacity are often not available or are associated with large uncertainties. Only for fluids such as water, for which the properties at ambient pressure are known very accurately, can this method be adopted. , Another possibility is to derive initial values for the specific isobaric heat capacity c p from very accurate speed-of-sound and density data sets at low pressure by the thermodynamic relation in which T is the thermodynamic temperature, ρ is density, p is pressure, and c denotes the speed of sound. When the density data are correlated accurately as a function of temperature and pressure, the partial derivatives along the initial isobar of the integration can easily be calculated, and precise values of the specific isobaric heat capacity can be derived by eq .…”

“…Only for fluids such as water, for which the properties at ambient pressure are known very accurately, can this method be adopted. 17,18 Another possibility is to derive initial values for the specific isobaric heat capacity c p from very accurate speed-of-sound and density data sets at low pressure by the thermodynamic relation ρ…”