1Characteristics of a cryogenic fluid1. Critical, normal boiling, and triple point temperatures of cryogenic fluids2. Vapor pressure of liquids3. Liquid Helium4. SuperfluidsCritical, normal boiling, and triple point temperatures of cryogenic fluidsNote log temperature scaleFigure adapted from Cryogenic Engineering by Thomas M. Flynn, Dekker:NY (1997), p. 80Vapor pressure of liquidsFigure adapted from Cryogenic Engineering by Thomas M. Flynn, Dekker:NY (1997), p. 81Helium• Spherical shape• Two isotropic forms: 3He and 4He•Low mass• Van der Waals forces Æ low critical and boiling points• Remains a liquid even at absolute zero (unless external pressure is applied)How do you spell the word for making a gas into a liquid?A. liquifyB. liquefyC. liquafyD. liquifiE. liquiphySpelling BeeIn whose laboratory was helium first liquefied?A. Sir James DewarB. CailletetC. WroblewskiD. OnnesE. Van der WaalsName that man21882-Helium liquefied at Leiden UniversityH. Kamerlingh Onnes was one of the first professors in experimental physics atLeiden University. His lab first to liquefy helium (1908), for which he was awarded the Nobel prize in 1913, and he discovered superconductivity in 1911. He liquefied hydrogen to pre-cool the helium gas in his liquefier.• In 1882, Onnes was appointed Professor of Experimental Physics at Leiden University. In 1895, he established Leiden Laboratory• His researches were mainly based on the theories of J.D. van der Waals and H.A. Lorentz• Was able to bring the temperature of helium down to 0.9 °K, justifying the saying that the coldest spot on earth was situated at Leiden.Heike Kamerlingh Onnes (left)and Van der Waals in Leidenat the helium 'liquefactor' (1908)Who would have ever thought…Heike Kamerlingh Onnes, his stamp, and (right) showing his helium liquefactor to passers-by: Niels Bohr (visiting fromKopenhagen), Hendrik Lorentz, and Paul Ehrenfest (far left). Why Not A Solid?• Zero-Point Energy• E = (3h^2)/(8mV^(2/3)) energy of a free particle in a small box• E decreases as V increases Æ the effect of the Zero-Point to raise molar volume• Kinetic energy exceeds the interaction potential energy Heike Kamerlingh Onnes discovered superconductivity, the almost total lack of electrical resistance in certain materials when cooled to a temperature near absolute zero.Superconductivity-1911Phase Diagrams4He3HeRegular substance3Superfluidity occurs in 4He at about 4.2 K but only below about 0.002 K in 3He. Why?A. 3He is rarer than 4He in natureB. 3He is always in smaller containers than is 4HeC. 3He has different chemical properties than 4HeD. 4He superfluidity is an electronic process while 3He superfluidity is a nuclear processE. 3He superfluidity is an electronic process while 4He superfluidity is a nuclear processWhy so low?Helium-4 Phase Diagram• At 2.17K 4He undergoes a transition to the superfluid state• The lambda line separates He I and He II•3He does not become a superfluid until below 2mK There are two isotopes of helium--under what circumstances do their liquid states mix?A. They do not mix-it would violate thermodynamics to have a mixture at absolute zero.B. They only mix when at absolute zeroC. 3He can mix in 4He but not the other way around at absolute zeroDo superfluids mix?Helium Mixtures1931: Keesom discovered lambda-specific heats in helium at LeidenHeat CapacityTemperatureDensity[Frank Pobell, 1992]4He(Boson)Allen and Misener and Kapitza (1939)Tλ=2.17KHe IHe IISuperfluidity in Helium 4 in 1938• Superfluidity is a dramatic visible manifestation of quantum mechanics, being the result of Bose–Einstein condensation in which a macroscopic number of 4He atoms occupy the same, single-particle quantum state. It was discovered simultaneously byKapitza, Allen and Misenerworking separately, though only Kapitza received the Nobel prize. It is also amusing to note that Allen was a “classical physicist” at heart, who didn’t much care for the subatomic world. He discovered superfluidity with a pen light.Fig. 2. (A through C) Microscope images showing an edge-on view ofsuperfluid drops on a horizontal Cs substrate. Thedark bar in the upper half of the image is the capillary tube.The pictures show the outline of the drop as well as its mirrorimage in the reflective substrate. As the volume of the drop increasedfrom (A) to (B), the contact angle remained constant. When fluidwas withdraw as in (C), the contact angle decreased but . the diameterremained constantScience 24 October 1997:Vol. 278. no. 5338, pp. 664 -666 Figure 3. Microscope image of a superfluid drop on a Cs substrate inclined at 10° to the horizontal. A drop hanging off of the capillaryis also seen in the upper right. The drop on the inclined substrateis stationary. The downhill edge of the drop has the same contact angle as shown in Fig. 2B, whereas the uphill edge has a vanishingcontact angle.4Superfluidity of the Quantum Fluid, 4He8.9Å≈=mkThT3λThermal de Broglie wavelength of 4He at 2K:≥ mean interparticle distance of 4He ≈ 3.6 Å[Frank Pobell, 1992]Breaker experiment:The Fountain Effect-1938• In february 1938 J.F. Allen and H. Jones had found that when they heated superfluid helium on one side of a porous medium or a thin capillary, the pressure increased sufficiently to produce a fountain effect at the end of the tube which contained the liquid. The “fountain effect” was a spectacular phenomenon that was impossible to understand within classical thermodynamics.SuperfluidsThe viscosity of liquidhelium 4 vanishes below2.17 KThe thermal conductivitybecomes very largeA spectacular thermo-mechanical effect: the"fountain effect"Two Fluid Model– Landau in 194156 % ρFluid density0 2.0 TλT (K)ρρnρsρ=ρn+ρs≈ 0.14g/cm3Sn=SHe η= ηnρnnormal fluidSs =0ηs =0ρsSuper-fluidTwo fluidsentropyviscositydensityTwo Fluid modelon)conservati (momentum 0)(on)conservati(entropy 0on)conservati (mass 0=∂∂+∂∂∇−=∇⋅+∂∂≡=⋅∇+∂∂=⋅∇+∂∂ααµυυυυυρρυρρrPtJtDtDststiisssssnGGGGGGGGGGTwo-fluid equations for He II:total mass flowssnnJυρυρυρGGGG+=≡jsissjninnijijpP,,,,υυρυυρδ++=stress tensor[S.J. Putterman, 1974]Viscosity (µP)4He(oscillating disc viscometer)[W.H. Keesom, 1938]Quantization of Superfluid CirculationQuantization of superfluid circulation:scmnmnhds/ 1097.924−×≈=⋅=∫AGGυκ(postulated separately in 1955 by Onsager and Feynman)The angular