Determination of thermodynamic properties from the speed of sound

Abstract

We describe methods by which all of the observable thermodynamic properties of a compressed gas. including the compressibility factor and the isochoric heat capacity, ,nay be determined from sound speed data by numerical integration of a pair of partial differenti~,l equations. The technique ,nay be employed over a wide range of conditions. Initial values are required, but we demonstrate that values specified on an isotherm close to the critical temperature are sufficient for application of the method to the entire homogeneous fluid region at subcritical densities. The method may also be extended to higher densities at temperatures above the critical. The effects of errors in both the initial values and the speed of sound are examined in detail by means of ~,nalytic and numerical results. The rest, Its indicate that all of the observable thermodynamic properties may be obtained with an uncertainty equal to or less than that achievable by the best available alternative techniques.KEY WORDS: equation of state: speed of sound: thermodynamic properties.

The speed of sound and derived thermodynamic properties of ethane at temperatures between 220 K and 450 K and pressures up to 10.5 MPa

“…(16) Transport properties were obtained from two sources: the viscosity was calculated from the correlation due to Younglove and Ely, (17) while the thermal conductivity was obtained from the correlation reported by Vesovic et al (18) The zero-pressure radius of the resonator was taken from our recent calibration measurements. (5) The possibility of dispersion arising from vibrational relaxation in the gas was also investigated. Mean vibrational relaxation times t vib for ethane (assuming series excitation of all internal modes) were estimated from the observed resonance line widths by the method described elsewhere.…”

“…The speed of sound u was determined from the frequencies f 0n of the radial modes by analysis in terms of the standard acoustic model in which (u/a 0 ) is given by: (1,2,5,15) (u/a 0 ) = (2pa/a 0 )…”

“…The pressure was corrected for the hydrostatic head between the equatorial plane of the resonator and the mid-point of the pressure transducer as described previously. (5) At most, this correction amounted to 1.9 kPa.…”

“…(2,5) Speeds of sound were determined from each of the lowest five radial resonances of the gas-filled spherical resonator. The mean temperature of the gas was inferred from the readings of a pair of capsule-type platinum-resistance thermometers attached to the outer surface of the spherical resonator.…”

“…(1)(2)(3)(4)(5) The results may be used to determine other thermodynamic properties through a process of numerical integration (2,(6)(7)(8) or to determine parameters in semi-realistic models of the two-and three-body intermolecular potential-energy functions. (9)(10)(11)(12)(13) In the present paper we report new measurements of the speed of sound u in gaseous ethane at temperatures between 220 K and 450 K and with pressures up to 10.5 MPa.…”