Properties of Superfluid Helium (He II)

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SUPERFLUID HELIUM (He II, Superfluidity)

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Superfluid or Helium II technology has been developed quite successfully in the past decades in both aerospace and magnet cooling systems. Unlike most fluids, liquid helium below the Lambda temperature (T

= 2.172 K) behaves as a Non-Newtonian fluid. It can flow through narrow gaps or capillaries without any viscous dissipation. It also has unusually high thermal conductivity. Other strange properties of superfluid include the Rollin film, mechanocaloric effect and fountain effect. The two fluid model postulated by Landau and Tisza is the most accepted theory for predicting superfluid behavior. It is the purpose of this web page to present the special properties of He II. Empirical equations are given wherever possible for the easy of integrating these property functions.

The vapor pressure (in torr) of Superfluid (He II) can be approximated by the following equation,

Log P = -3.018 (1/T) + 2.484 Log T - 0.00297 T⁴ + 2.197

The two fluid model postulates that the density of liquid helium is composed of the density of the superfluid and that of the normal fluid.

_s +

_n

The density of the normal fluid is given by the following equation.

r_n = r (T/T_l)^5.6

The entropy of the superfluid can be represented by

S = 1.5838 (T/T_l)^5.6

The specific heat of He II is

C_v = (dQ/dT)_v = T(dS/dT)_v= 5.6 (T/T_l)^5.6

Knowing the vapor pressure, one can calculate the latent heat of vaporization of Superfluid

l = RT²(dP/dT)/P

The viscosity of He II is represented by

h_n = 8.7 x 10^-3 (e^D/KT) T^-1/2 + 11 + (2(2.2-T))^-1

The first term on the right hand side of the above equation is based on Landaus collision theory with D being the energy gap between the phonon and the roton state. Landau suggested that D/K has a value between 8 and 9 K. In the present equation, a value of D/K = 8.0802 K is assumed.

The surface tension of liquid helium can be written as

s = 0.37 - 0.0079 T^7/3

Material on this page is taken from an extension course the author taught at UCLA.

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About the author- Dr. Sidney Yuan is a consultant in the field of Low Temperature Physics and Cryogenics, and has written a Book on Cryogenics and published extensively in the field. E-Mail.

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