pressure-temperature (p-T) diagram indicating the solid and liquid regions separated by the melting curve (between the liquid and solid state) and the liquid and gas region, separated by the vapor-pressure line. This latter ends in the critical point where the difference between gas and liquid disappears. The diagram shows the remarkable property that 4He is liquid even at absolute zero. 4He is only solid at pressures above 25 bar. Figure 1 also shows the λ-line. This is the line that separates two fluid regions in the phase diagram indicated by He-I and He-II. In the He-I region the helium behaves like a normal fluid; in the He-II region the helium is superfluid. The name lambda-line comes from the specific heat – temperature plot which has the shape of the Greek letter λ. See figure 2, which shows a peak at 2.172 K, the so-called λ-point of 4He. Below the lambda line the liquid can be described by the so-called two-fluid model. It behaves as if it consists of two components: a normal component, which behaves like a normal fluid, and a superfluid component with zero viscosity and zero entropy. The ratios of the respective densities ρn/ρ and ρs/ρ, with ρn (ρs) the density of the normal (superfluid) component, and ρ (the total density), depends on temperature and is represented in figure 3. By lowering the temperature, the fraction of the superfluid density increases from zero at Tλ to one at zero kelvins. Below 1 K the helium is almost completely superfluid. It is possible to create density waves of the normal component (and hence of the superfluid component since ρn + ρs = constant) which are similar to ordinary sound waves. This effect is called second sound. Due to the temperature dependence of ρn (figure 3) these waves in ρn are also temperature waves. Superfluid hydrodynamics The equation of motion for the superfluid component, in a somewhat simplified form, is given by Newton's law The mass M4 is the molar mass of 4He, and is the velocity of the superfluid component. The time derivative is the so-called hydrodynamic derivative, i.e. the rate of increase of the velocity when moving with the fluid. In the case of superfluid 4He in the gravitational field the force is given by In this expression μ is the molar chemical potential, g the gravitational acceleration, and z the vertical coordinate. Thus we get the equation