The Lambda point is the temperature at which normal fluid helium (helium I) makes the transition to superfluid helium II (approximately 2.17 K at 1 atmosphere). The lowest pressure at which He-I and He-II can coexist is the vapor−He-I−He-II triple point at 2.1768 K (−270.9732 °C) and 5.048 kPa (0.04982 atm), which is the "saturated vapor pressure" at that temperature (pure helium gas in thermal equilibrium over the liquid surface, in a hermetic container).[1] The highest pressure at which He-I and He-II can coexist is the bcc−He-I−He-II triple point with a helium solid at 1.762 K (−271.388 °C), 29.725 atm (3,011.9 kPa).[2]
The point's name derives from the graph (pictured) that results from plotting the specific heat capacity as a function of temperature (for a given pressure in the above range, in the example shown, at 1 atmosphere), which resembles the Greek letter lambda. The specific heat capacity has a sharp peak as the temperature approaches the lambda point. The tip of the peak is so sharp that a critical exponent characterizing the divergence of the heat capacity can be measured precisely only in zero gravity, to provide a uniform density over a substantial volume of fluid. Hence the heat capacity was measured within 2 nK below the transition in an experiment included in a Space Shuttle payload in 1992.[3]
Unsolved problem in physics:
Explain the discrepancy between the experimental and theoretical determinations of the heat capacity critical exponent α for the superfuid transition in helium-4.[4]
(more unsolved problems in physics)
Although the heat capacity has a peak, it does not tend towards infinity (contrary to what the graph may suggest), but has finite limiting values when approaching the transition from above and below.[3] The behavior of the heat capacity near the peak is described by the formula \( {\displaystyle C\approx A_{\pm }t^{-\alpha }+B_{\pm }} \) where \( {\displaystyle t=|1-T/T_{c}|} \) is the reduced temperature, \( T_{c} \) is the Lambda point temperature, \( {\displaystyle A_{\pm },B_{\pm }} \) are constants (different above and below the transition temperature), and α is the critical exponent: \( {\displaystyle \alpha =-0.0127(3)} \) .[3][5] Since this exponent is negative for the superfluid transition, specific heat remains finite.[6]
The quoted experimental value of α is in a significant disagreement[7][4] with the most precise theoretical determinations[8][9][10] coming from high temperature expansion techniques, Monte Carlo methods and the conformal bootstrap.
See also
Lambda point refrigerator
References
Donnelly, Russell J.; Barenghi, Carlo F. (1998). "The Observed Properties of Liquid Helium at the Saturated Vapor Pressure". Journal of Physical and Chemical Reference Data. 27 (6): 1217–1274. Bibcode:1998JPCRD..27.1217D. doi:10.1063/1.556028.
Hoffer, J. K.; Gardner, W. R.; Waterfield, C. G.; Phillips, N. E. (April 1976). "Thermodynamic properties of 4He. II. The bcc phase and the P-T and VT phase diagrams below 2 K". Journal of Low Temperature Physics. 23 (1): 63–102. Bibcode:1976JLTP...23...63H. doi:10.1007/BF00117245.
Lipa, J.A.; Swanson, D. R.; Nissen, J. A.; Chui, T. C. P.; Israelsson, U. E. (1996). "Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point". Physical Review Letters. 76 (6): 944–7. Bibcode:1996PhRvL..76..944L. doi:10.1103/PhysRevLett.76.944. hdl:2060/19950007794. PMID 10061591.
Rychkov, Slava (2020-01-31). "Conformal bootstrap and the λ-point specific heat experimental anomaly". Journal Club for Condensed Matter Physics. doi:10.36471/JCCM_January_2020_02.
Lipa, J. A.; Nissen, J. A.; Stricker, D. A.; Swanson, D. R.; Chui, T. C. P. (2003-11-14). "Specific heat of liquid helium in zero gravity very near the lambda point". Physical Review B. 68 (17): 174518. arXiv:cond-mat/0310163. Bibcode:2003PhRvB..68q4518L. doi:10.1103/PhysRevB.68.174518.
For other phase transitions \( \alpha \) may be negative (e.g. \( {\displaystyle \alpha \approx +0.1} \) for the liquid-vapor critical point which has Ising critical exponents). For those phase transitions specific heat does tend to infinity.
Vicari, Ettore (2008-03-21). "Critical phenomena and renormalization-group flow of multi-parameter Phi4 theories". Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007). Regensburg, Germany: Sissa Medialab. 42: 023. doi:10.22323/1.042.0023.
Campostrini, Massimo; Hasenbusch, Martin; Pelissetto, Andrea; Vicari, Ettore (2006-10-06). "Theoretical estimates of the critical exponents of the superfluid transition in \( ^{4}\mathrm{He} \) by lattice methods". Physical Review B. 74 (14): 144506. arXiv:cond-mat/0605083. doi:10.1103/PhysRevB.74.144506.
Hasenbusch, Martin (2019-12-26). "Monte Carlo study of an improved clock model in three dimensions". Physical Review B. 100 (22): 224517. arXiv:1910.05916. Bibcode:2019PhRvB.100v4517H. doi:10.1103/PhysRevB.100.224517. ISSN 2469-9950.
Chester, Shai M.; Landry, Walter; Liu, Junyu; Poland, David; Simmons-Duffin, David; Su, Ning; Vichi, Alessandro (2019-12-06). "Carving out OPE space and precise $O(2)$ model critical exponents". arXiv:1912.03324 [hep-th].
External links
What is superfluidity?
Hellenica World - Scientific Library
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