The two-fluid model of Hell

Hel is a fairly normal liquid, remarkable only for its low temperature and density. The transition to Hell that occurs at the lambda temperature is not an ordinary, first order, phase change since there is no abrupt change in specific volume and specific entropy. Nor is it a formation of molecules or loosely bound complexes (no Raman effect). Further, X-ray studies show no kind of pseudo-crystallisation. 

If the translational energies of the helium atoms are represented on an energy-level diagram, to account for the phenomena shown by Hell there must be a gap in the energy-level spectrum between the lowest level and the next, above which the spectrum of levels 

the ordinary density of Hell is given by the sum of and p. Both Pjj and Pg are functions of temperature, but the density of Hell p varies only slightly with temperature, and this variation can often be ignored. Since the superfluid has zero entropy, the normal fluid has a specific entropy equal to that of Hell. 

When Hell flows through very narrow tubes the motion of the normal fluid is restricted by its viscosity, but the superfluid moves readily with zero viscosity and flow without friction is observed. The damping of a disc oscillating in a liquid depends on the product of the density and viscosity. For Hell the appropriate density is p and so the viscosity is not zero at finite temperatures, but decreases rapidly with temperature. 

In the experiment on the helium film, the exposed surfaces of the beaker are in equilibrium with the saturated vapour of the liquid of the bath and will, therefore, be covered by an adsorbed layer of helium. At temperatures below the superfluid is able to flow in the adsorbed layer or film which, therefore, acts as a sort of syphon. The driving force for the motion is the difference in gravitational potential energy of the liquid in the beaker and in the bath, which leads to a difference in the specific Helmholtz functions. 

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