A numerical procedure for deriving the thermodynamic properties , , and of the vapor phase in the subcritical temperature range from the speed of sound is presented. The set of differential equations connecting these properties with the speed of sound is solved as the initial-value problem in domain . The initial values of and are specified along the isotherm with the highest temperature, at a several values of [0.1,？1.0]. The values of are generated by the reference equation of state, while the values of are derived from the speed of sound, by solving another set of differential equations in domain in the transcritical temperature range. This set of equations is solved as the initial-boundary-value problem. The initial values of and are specified along the isochore in the limit of the ideal gas, at several isotherms distributed according to the Chebyshev points of the second kind. The boundary values of are specified along the same isotherm and along another isotherm with a higher temperature, at several values of . The procedure is tested on Ar, N2, CH4, and CO2, with the mean AADs for , , and at 0.0003%, 0.0046%, and 0.0061%, respectively (0.0007%, 0.0130%, and 0.0189% along the saturation line). 1. Introduction The speed of sound is the property of a fluid which is measured with an exceptional accuracy (Ewing and Goodwin [1], Estrada-Alexanders and Trusler [2], Costa Gomes and Trusler [3], Trusler and Zarari [4], and Estrada-Alexanders and Trusler [5]). While the speed of sound itself is a piece of useful information about a fluid, other thermodynamic properties like the density and the heat capacity, which may be derived from it, make the speed of sound even more useful. However, the speed of sound in a fluid is connected to these properties through the set of nonlinear partial differential equations of the second order. The general solution to this set of equations has not been found yet, except for the gaseous phase under low pressures (Trusler et al. [6] and Estela-Uribe and Trusler [7]). At moderate and higher pressures a procedure based on the numerical integration may be used for obtaining the particular solution (Estrada-Alexanders et al. [8] and Bijedi？ and Neimarlija [9–11]). The main disadvantage of this approach is the need for the initial and/or the boundary values of the quantities being calculated (the Dirichlet conditions) and their derivatives with respect to an independent variable (the Neumann conditions). In the previous paper (Bijedi？ and Neimarlija [11]) it was shown that the compressibility factor and the heat capacity of a
References
[1]
M. B. Ewing and A. R. H. Goodwin, “An apparatus based on a spherical resonator for measuring the speed of sound in gases at high pressures. Results for argon at temperatures between 255 K and 300 K and at pressures up to 7 MPa,” The Journal of Chemical Thermodynamics, vol. 24, no. 5, pp. 531–547, 1992.
[2]
A. F. Estrada-Alexanders and J. P. M. Trusler, “The speed of sound in gaseous argon at temperatures between 110？K and 450？K and at pressures up to 19？MPa,” The Journal of Chemical Thermodynamics, vol. 27, no. 10, pp. 1075–1089, 1995.
[3]
M. F. Costa Gomes and J. P. M. Trusler, “The speed of sound in nitrogen at temperatures between ？K and ？K and at pressures up to 30 MPa,” Journal of Chemical Thermodynamics, vol. 30, no. 5, pp. 527–534, 1998.
[4]
J. P. M. Trusler and M. Zarari, “The speed of sound and derived thermodynamic properties of methane at temperatures between 275 K and 375 K and pressures up to 10 MPa,” The Journal of Chemical Thermodynamics, vol. 24, no. 9, pp. 973–991, 1992.
[5]
A. F. Estrada-Alexanders and J. P. M. Trusler, “Speed of sound in carbon dioxide at temperatures between (220 and 450) K and pressures up to 14 MPa,” Journal of Chemical Thermodynamics, vol. 30, no. 12, pp. 1589–1601, 1998.
[6]
J. P. M. Trusler, W. A. Wakeham, and M. P. Zarari, “Model intermolecular potentials and virial coefficients determined from the speed of sound,” Molecular Physics, vol. 90, no. 5, pp. 695–703, 1997.
[7]
J. F. Estela-Uribe and J. P. M. Trusler, “Acoustic and volumetric virial coefficients of nitrogen,” International Journal of Thermophysics, vol. 21, no. 5, pp. 1033–1044, 2000.
[8]
A. F. Estrada-Alexanders, J. P. M. Trusler, and M. P. Zarari, “Determination of thermodynamic properties from the speed of sound,” International Journal of Thermophysics, vol. 16, no. 3, pp. 663–673, 1995.
[9]
M. Bijedi？ and N. Neimarlija, “Thermodynamic properties of gases from speed-of-sound measurements,” International Journal of Thermophysics, vol. 28, no. 1, pp. 268–278, 2007.
[10]
M. Bijedi？ and N. Neimarlija, “Thermodynamic properties of carbon dioxide derived from the speed of sound,” Journal of the Iranian Chemical Society, vol. 5, no. 2, pp. 286–295, 2008.
[11]
M. Bijedi？ and N. Neimarlija, “Speed of sound as a source of accurate thermodynamic properties of gases,” Latin American Applied Research, vol. 43, no. 4, pp. 393–398, 2013.
[12]
J. P. M. Trusler, Physical Acoustics and Metrology of Fluids, Adam Hilger, Bristol, UK, 1991.
[13]
M. J. Moran and H. N. Shapiro, Fundamentals of Engineering Thermodynamics, John Wiley & Sons, Chichester, UK, 5th edition, 2006.
[14]
D. Y. Peng and D. B. Robinson, “A new two-constant equation of state,” Industrial and Engineering Chemistry Fundamentals, vol. 15, no. 1, pp. 59–64, 1976.
[15]
T. E. Hull, W. H. Enright, and K. R. Jackson, “User's guide for DVERK—a subroutine for solving non-stiff ODEs,” Tech. Rep., University of Toronto, Toronto, Canada, 1976.
[16]
C. Tegeler, R. Span, and W. Wagner, “A new equation of state for argon covering the fluid region for temperatures from the melting line to 700 K at pressures up to 1000 MPa,” Journal of Physical and Chemical Reference Data, vol. 28, no. 3, pp. 779–850, 1999.
[17]
R. Span, E. W. Lemmon, R. T. Jacobsen, W. Wagner, and A. Yokozeki, “A reference equation of state for the thermodynamic properties of nitrogen for temperatures from 63.151 to 1000 K and pressures to 2200 MPa,” Journal of Physical and Chemical Reference Data, vol. 29, no. 6, pp. 1361–1433, 2000.
[18]
U. Setzmann and W. Wagner, “A new equation of state and tables of thermodynamic properties for methane covering the range from the melting line to 625？K at pressures up to 1000？MPa,” Journal of Physical and Chemical Reference Data, vol. 20, no. 6, pp. 1061–1155, 1991.
[19]
R. Span and W. Wagner, “A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100？K at pressures up to 800？MPa,” Journal of Physical and Chemical Reference Data, vol. 25, no. 6, pp. 1509–1596, 1996.
