Third sound and the onset of superfluidity in unsaturated helium films

A simple model, commonly used for describing the behavior of the superfluid film is examined, and it is found to become spontaneously unstable when the partial molar entropy falls below a certain finite value for each temperature and film thickness. The instability is proposed as the cause of the onset curve for superfluidity in unsaturated films, and comparisons with experiment are made. In addition, the use of thermodynamic identities in the model leads to a new and more accurate expression for the velocity of third sound in terms of other measurable quantities.