Abstract:
The simple Laplace formula for the speed of sound in gases is corrected to account for three real-gas effects: molecular degrees of freedom which in equilibrium are not fully excited, deviations from the ideal-gas law, and dispersion due to relaxation processes. These are called the specific-heat, virial, and relaxation corrections, respectively. The specific-heat correction is based on a power-series expansion of C[inf p0] (specific heat at zero pressure) with respect to temperature. The virial correction is based on a three-parameter formula by Kaye and Laby for the second virial coefficient and a new five-parameter empirical formula for the third virial coefficient. Both are used to derive the corresponding acoustic virial coefficients. The relaxation correction is based on both Landau--Teller and Arrhenius temperature dependencies and inverse-pressure scaling. Using independent handbook data to obtain values for the above three corrections, the theory is capable of yielding sound-speed estimates to high accuracy over a wide range of temperatures and pressures. The theoretical uncertainty is due to the uncertainty in the original data, smoothing process, and truncation error; these are discussed in detail.