Editing Superfluid helium-4 (section)

=== Thermodynamics ===
[[File:Phase diagram of 4He 01.svg|thumb|Fig. 1. Phase diagram of <sup>4</sup>He. In this diagram is also given the λ-line.]]
[[File:He liquid tbotevadobis damokidebuleba TemperaTurastan 350-en.svg|thumb|Fig. 2. Heat capacity of liquid <sup>4</sup>He at saturated vapor pressure as function of the temperature. The peak at T=2.17 K marks a (second-order) phase transition.]]
[[File:Normal and superfluid density 01.jpg|thumb|Fig. 3. Temperature dependence of the relative superfluid and normal components ρ<sub>n</sub>/ρ and ρ<sub>s</sub>/ρ as functions of ''T''.]]

Figure 1 is the [[phase diagram]] of <sup>4</sup>He.<ref>{{cite journal|last1=Swenson|first1=C.|year=1950|title=The Liquid-Solid Transformation in Helium near Absolute Zero|journal=Physical Review|volume=79|issue=4|page=626|bibcode=1950PhRv...79..626S|doi=10.1103/PhysRev.79.626}}</ref> It is a 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 (thermodynamics)|critical point]] where the difference between gas and liquid disappears. The diagram shows the remarkable property that <sup>4</sup>He is liquid even at [[absolute zero]]. <sup>4</sup>He is only solid at pressures above 25 [[bar (unit)|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.<ref>{{cite journal|last1=Keesom|first1=W.H.|last2=Keesom|first2=A.P.|year=1935|title=New measurements on the specific heat of liquid helium|journal=Physica|volume=2|issue=1|page=557|bibcode=1935Phy.....2..557K|doi=10.1016/S0031-8914(35)90128-8}}</ref><ref>{{cite book|last1=Buckingham|first1=M.J.|title=The nature of the λ-transition in liquid helium|last2=Fairbank|first2=W.M.|date=1961|isbn=978-0-444-53309-8|series=Progress in Low Temperature Physics|volume=3|page=80|chapter=Chapter III The Nature of the λ-Transition in Liquid Helium|doi=10.1016/S0079-6417(08)60134-1}}</ref> See figure 2, which shows a peak at 2.172 K, the so-called λ-point of <sup>4</sup>He.

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 ρ<sub>n</sub>/ρ and ρ<sub>s</sub>/ρ, with ρ<sub>n</sub> (ρ<sub>s</sub>) the density of the normal (superfluid) component, and ρ (the total density), depends on temperature and is represented in figure 3.<ref>E.L. Andronikashvili Zh. Éksp. Teor. Fiz, Vol.16 p.780 (1946), Vol.18 p. 424 (1948)</ref> By lowering the temperature, the fraction of the superfluid density increases from zero at ''T''<sub>λ</sub> to one at zero kelvins.  Below 1&nbsp;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 ρ<sub>n</sub> + ρ<sub>s</sub> = constant) which are similar to ordinary sound waves. This effect is called [[second sound]]. Due to the temperature dependence of ρ<sub>n</sub> (figure 3) these waves in ρ<sub>n</sub> are also temperature waves.

[[File:helium-II-creep.svg|thumb|right|Fig. 4. Helium II will "creep" along surfaces in order to find its own level – after a short while, the levels in the two containers will equalize. The [[Rollin film]] also covers the interior of the larger container; if it were not sealed, the helium II would creep out and escape.]]

[[File:Liquid helium Rollin film.jpg|thumb|right|Fig. 5. The liquid helium is in the superfluid phase. As long as it remains superfluid, it creeps up the wall of the cup as a thin film. It comes down on the outside, forming a drop which will fall into the liquid below. Another drop will form – and so on – until the cup is empty.]]