  In this paper we propose a thermodynamically consistent model for
superfluid-normal phase transition in liquid helium, accounting for variations
of temperature and density. The phase transition is described by means of an
order parameter, according to the Ginzburg-Landau theory, emphasizing the
analogies between superfluidity and superconductivity. The normal component of
the velocity is assumed to be compressible and the usual phase diagram of
liquid helium is recovered. Moreover, the continuity equation leads to a
dependence between density and temperature in agreement with the experimental
data.
