Application to helium- 4 103STTTTFig. 9. 6 The variation ofentropy withtemperatureforliquid^4 He, showing a verticaltangent atTTλ.
Allthisbears some relation to the BE gas, althoughthe actualtransitionin^4 He
is more sudden than that oftheidealgas. Itisbelievedthat thedifference canbe
attributed to the strong interactions between^4 He atoms in the liquid (see Chapter 14,
section 14.3,for afullerdiscussion). Furthermore, the transition takes place at a
temperature ofthe correct order ofmagnitude, thevalue ofTTTBfor an idealgas of
bosons with the bare^4 He mass and the density of liquid^4 He being about 3.1 K.
Even more reminiscent oftheBEgasisthe nature ofthe superfluidHeII. Its
properties are well described bya ‘two-fluid model’, in which the liquid is thought
of as a mixture of two interpenetrating fluids. One of these, the normal fluid, has the
properties ofa conventionalfluid, very likethethermalN(th)fraction oftheBEgas,
(9. 6 ). Whereas the other fluid, the superfluid, behaves like the condensate fraction
n 0 , in that it carries no entropy and displays no friction.
An excellent exampleofthe two-fluidproperties arises when theviscosityofliq-
uid HeII is measured. The answer is found to depend dramatically on the type of
experimentalmethod.
If viscosity is measured by the drag on a rotating disc or a vibrating wire, thena
reasonablevalueisfound,similar to thatfor HeI, althoughreducingsomewhat as
Tis lowered well belowTTλ.
If,however, the measurementismadebyallowing thehelium toflow through
tubes, onefindsthe astonishinganswer zerofor theviscosity.Thefluidcanflow
with alarming ease (up to some critical velocity) through the thinnest channels;
hence the term ‘superfluid’. It can even syphonitselfover theedge ofa container
throughsuperflowinthe surfacefilm.
The explanationin terms ofthe twofluidsisclear. Thedragmethodswillpickout
the most viscous fluid, and that is the normal fluid. The gradual reduction belowTTλ
arisesfrom the gradualreduction ofthe normalfluidconcentration (cf.N(th)) asTis
lowered.Ontheotherhandtheflow experiments pickout the smallest viscosity.Only
the superfluid flows through a fine tube, and this has zero viscosity since it carries
no entropy. Ademonstration thatitisthe(effectivelyT=0) superfluidonlywhich
flows is to observe that the flowproduces a temperature difference between the ends