Thermodynamic properties of CO 2 are derived from speed of sound in the temperature range 300 to 360 K (from 0 to 6 MPa), and 300 to 220 K (from 0 to 90% of the saturation pressure). The density, the specific heat capacity at constant pressure, and the specific heat capacity at constant volume are obtained by numerical integration of differential equations connecting the speed of sound with other thermodynamic properties. The set of differential equations is solved as the initial value problem, with the initial values specified along the isotherm at 300 K in terms of several accurate values of the density and the specific heat capacity at constant pressure. The density, the specific heat capacity at constant pressure and the specific heat capacity at constant volume are derived with the absolute average deviations of 0.018%, 0.19%, and 0.18%, respectively. The results of numerical integration are extrapolated to the saturation line for , c p , and c v with the absolute average deviations of 0.056%, 2.31%, and 1.32%, respectively.

A procedure for deriving thermodynamic properties of gases from speed of sound is presented. It is based on numerical integration of ordinary differential equations (ODEs) (rather than partial differential equations-PDEs) connecting speed of sound with other thermodynamic properties in the T -p domain. The procedure enables more powerful methods of higher-order approximation to ODEs to be used (e.g., Runge-Kutta) and requires only Dirichlet initial conditions. It was tested on gaseous argon in the temperature range from 250 to 450 K and in the pressure range from 0.2 to 12 MPa, and also on gaseous methane in the temperature range from 275 to 375 K and in the pressure range from 0.4 to 10 MPa. The density and isobaric heat capacity of argon were derived with absolute average deviations of 0.007% and 0.03%, respectively. The density and isobaric heat capacity of methane were derived with absolute average deviations of 0.006% and 0.09%, respectively.

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