Virial treatment of the speed of sound in cold, dense atmospheres and application to Titan

The speed of sound in a gas can be used to identify its composition, as has been done on the Earth. We show that, unlike in terrestrial applications, the third virial coefficient cannot be neglected in cold and dense atmospheres. We derive a model for the speed of sound of pure gases and gas mixtures at low temperatures and high pressures, based on the virial equation. After comparing the results of our model to measured data, we apply our model to the atmosphere of Titan. The difference between our third-order virial expansion and the commonly used second-order expansion is significant, showing that the third virial coefficient needs to be taken into account when accurate speed-of-sound measurements are used to derive atmospheric properties under Titan conditions.