An approach to get thermodynamic properties from speed of sound

An approach for estimating thermodynamic properties of gases from the speed of sound u, is proposed. The square u², the compression factor Z and the molar heat capacity at constant volume C_V are connected by two coupled nonlinear partial differential equations. Previous approaches to solving this system differ in the conditions used on the range of temperature values [T_min,T_max]. In this work we propose the use of Dirichlet boundary conditions at T_min, T_max. The virial series of the compression factor Z = 1+Bρ+Cρ²+... and other properties leads the problem to the solution of a recursive set of linear ordinary differential equations for the B, C. Analytic solutions of the B equation for Argon are used to study the stability of our approach and previous ones under perturbation errors of the input data. The results show that the approach yields B with a relative error bounded basically by that of the boundary values and the error of other approaches can be some orders of magnitude lager.