Density and Heat Capacity of Liquids from Speed of Sound

Two different methods for deriving the density and isobaric heat capacity of liquids in the subcritical pressure range, from the speed of sound, are recommended. In each method, corresponding set of differential equations relating these properties is solved as the initial boundary value problem (IBVP). The initial values are specified at the lowest pressure of the range and the boundary values along the saturation line. In the first method, numerical integration is performed along the paths connecting the Chebyshev points of the second kind between the minimum and maximum temperature at each pressure. In the second method, numerical integration is performed along the isotherms distributed in the same way, with the temperature range being extended to the saturation line after each integration step. The methods are tested with the following substances: Ar, N2, CO2, and CH4. The results obtained for the density and isobaric heat capacity have the average absolute deviation from the reference data of 0.0005% and 0.0219%, respectively. These results served as the initial values for deriving the same properties in the transcritical pressure range up to the pressure approximately twice as large as the critical pressure. The results obtained in this pressure range have respective deviations of 0.0019% and 0.1303%.