On a Connection between the Fountain Effect, Second Sound, and Thermal Conductivity in Liquid Helium II

1947 ◽  
Vol 71 (11) ◽  
pp. 828-828 ◽  
Author(s):  
Lothar Meyer ◽  
William Band
Keyword(s):  
Thermal Conductivity ◽  
Liquid Helium ◽  
Second Sound ◽  
Helium Ii

THE ATTENUATION OF SECOND SOUND IN LIQUID HELIUM II ABOVE 1°K.

1954 ◽  
Vol 32 (6) ◽  
pp. 381-392 ◽  
Author(s):  
K. R. Atkins ◽  
K. H. Hart
Keyword(s):  
Thermal Conductivity ◽  
Continuous Wave ◽  
Pulse Length ◽  
Boundary Effects ◽  
Second Sound ◽  
Sound Beam ◽  
Helium Ii ◽  
Viscosity Effects ◽  
Order Of Magnitude ◽  
Good Agreement

The second sound was in the form of a pulsed continuous wave with a pulse length of 1 to 2 msec, and a carrier frequency of 10 or 20 kc./s. The change in amplitude of the pulse was measured as the distance between the transmitter and the receiver was varied. To avoid boundary effects, no propagation tube was used and allowance had to be made for the spreading of the second sound beam. The attenuation was found to increase with increasing second sound amplitude. The attenuation extrapolated to zero amplitude had a finite value which increased rapidly as the temperature was lowered towards 1°K. Its order of magnitude was too large to be explained by viscosity effects, but was in good agreement with a thermal conductivity effect predicted by Khalatnikov.

The thermal conductivity of solid helium

1952 ◽  
Vol 214 (1119) ◽  
pp. 546-563 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Single Crystals ◽  
Liquid Helium ◽  
Solid Helium ◽  
Boundary Scattering ◽  
Conductivity Measurements ◽  
Helium Ii ◽  
Characteristic Temperatures ◽  
Thermal Conductivities

The thermal conductivities of crystals of solid helium at densities between 0⋅194 and 0⋅218 g/cm 3 have been measured at liquid-helium temperatures. In order to interpret the results, the specific heat of solid helium at these densities has been measured from 0⋅6 to 1⋅4° K. The range of densities employed is sufficient to allow the observation of Debye characteristic temperatures varying by 40 %, and of thermal conductivities varying by factors of over 10. It is shown that the conductivity measurements are in accord with the ‘umklapp’ type of thermal resistance derived by Peierls (1929, 1935). Further work was restricted by the difficulty of obtaining good single crystals in narrow tubes, but measurements of the conductivity at one density were obtained down to 0⋅3° K. In this region the conductivity is limited by boundary scattering and is higher than that observed by other authors for liquid helium II at similar temperatures.

Momentum transfer and heat flow in liquid helium II

1939 ◽  
Vol 35 (1) ◽  
pp. 114-122 ◽  
Author(s):  
J. F. Allen ◽  
J. Reekie
Keyword(s):  
Thermal Conductivity ◽  
Hydrostatic Pressure ◽  
Heat Flow ◽  
Momentum Transfer ◽  
Liquid Helium ◽  
Liquid Flow ◽  
Glass Capillary ◽  
Considerable Part ◽  
Helium Ii ◽  
Steady Heat

It has been found by one of the authors (1) in collaboration with Dr H. Jones that a flow of heat in liquid He ii is accompanied by what seems to be a transfer of momentum. The effect can be seen when the channel through which the heat and liquid flow consists of a smooth-walled glass capillary, such as shown in Fig. 1a. Due to the high thermal conductivity of He ii, a considerable part of the heat put into the reservoir is carried down through the capillary to the bath. When a steady heat flow exists, a flow of liquid takes place in the opposite direction, and the level of the liquid in the reservoir is seen to be higher than that in the bath. Smooth capillaries, however, produce a rise in level of only 1 or 2 cm. at most, since the viscosity of the liquid is small and hydrostatic pressure pulls the accumulated liquid in the reservoir back through the capillary. When the heat flow is large, violent surging is observed in the reservoir, but there is no further rise in level.

Quantum hydrodynamics and the theory of liquid helium

1953 ◽  
Vol 219 (1137) ◽  
pp. 257-270 ◽  
Keyword(s):  
Energy Spectrum ◽  
Liquid Helium ◽  
Fluid Velocity ◽  
Second Sound ◽  
Quantum Hydrodynamics ◽  
Dynamical Equations ◽  
Helium Ii ◽  
Apparent Variation ◽  
Theory Of Fields ◽  
Good Agreement

The Clebsch formula, u = –∇ ϕ – χ ∇ ψ , for the fluid velocity allows the classical hydro-dynamical equations, including vorticity, to be derived from a variational principle, and put into canonical form. The standard quantization procedure of the theory of fields then gives a set of field operators satisfying the commutation relations obtained (starting from different premises) by Landau (1941). The Hamiltonian contains terms corresponding to the excitation of the ‘roton’ states of Landau’s theory, with an energy spectrum (allowing for the atomicity of real liquids by a ‘cut off’ in the Fourier analysis of the field variables) of the form E = ∆ + p 2 /2 μ . The observed variations of specific heat and second-sound velocity in liquid helium II may be interpreted to give values of ∆ in good agreement with the theory, with an apparent variation of μ with p , perhaps attributable to roton-roton and phonon-roton interactions.

Second Sound Attenuation in Liquid Helium II

1954 ◽  
Vol 95 (2) ◽  
pp. 321-327 ◽  
Author(s):  
W. B. Hanson ◽  
J. R. Pellam
Keyword(s):  
Liquid Helium ◽  
Sound Attenuation ◽  
Second Sound ◽  
Helium Ii

Pulsed Second Sound in Liquid Helium II

1948 ◽  
Vol 74 (7) ◽  
pp. 841-841 ◽  
Author(s):  
J. R. Pellam
Keyword(s):  
Liquid Helium ◽  
Second Sound ◽  
Helium Ii

Second Sound Velocity in Paramagnetically Cooled Liquid Helium II

1949 ◽  
Vol 76 (6) ◽  
pp. 869-870 ◽  
Author(s):  
John R. Pellam ◽  
Russell B. Scott
Keyword(s):  
Sound Velocity ◽  
Liquid Helium ◽  
Second Sound ◽  
Helium Ii
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