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Emphasized that limiting values are different when approaching transition from above and below
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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 language|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&nbsp;nK below the transition in an experiment included in a [[Space Shuttle]] payload in 1992.<ref name=JPL>{{cite journal| title=Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point | first1=J.A.| last1=Lipa| first2=D. R.| last2=Swanson| first3=J. A.| last3=Nissen| first4=T. C. P.| last4=Chui| first5=U. E.| last5=Israelsson| journal=[[Physical Review Letters]]| year=1996| volume=76| issue=6| pages=944–7| doi=10.1103/PhysRevLett.76.944|bibcode = 1996PhRvL..76..944L| pmid=10061591| hdl=2060/19950007794}}</ref>
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 language|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&nbsp;nK below the transition in an experiment included in a [[Space Shuttle]] payload in 1992.<ref name=JPL>{{cite journal| title=Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point | first1=J.A.| last1=Lipa| first2=D. R.| last2=Swanson| first3=J. A.| last3=Nissen| first4=T. C. P.| last4=Chui| first5=U. E.| last5=Israelsson| journal=[[Physical Review Letters]]| year=1996| volume=76| issue=6| pages=944–7| doi=10.1103/PhysRevLett.76.944|bibcode = 1996PhRvL..76..944L| pmid=10061591| hdl=2060/19950007794}}</ref>
Although the heat capacity has a peak, it does not tend towards [[infinity]] (contrary to what the graph may suggest) but to a finite large value of about 100 J/(mol K).<ref name=JPL /> The behavior of the heat capacity near the peak is described by the formula <math>C\approx A t^{-\alpha}+B</math> where <math>t=|1-T/T_c|</math> is the reduced temperature, <math>T_c</math> is the Lambda point temperature, <math>A,B</math> are constants, and <math>\alpha\approx-0.01</math> is the [[Critical_exponent|critical exponent]].<ref name=JPL /> Since this exponent is negative for the superfluid transition, the limiting specific heat value is finite.<ref>For other phase transitions <math>\alpha</math> may be negative (e.g. <math>\alpha\approx+0.1</math> for [[Critical point (thermodynamics)|the liquid-vapor critical point]] which has [[Ising critical exponents]]). For those phase transitions specific heat does tend to infinity. </ref>
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.<ref name=JPL /> The behavior of the heat capacity near the peak is described by the formula <math>C\approx A_\pm t^{-\alpha}+B_\pm</math> where <math>t=|1-T/T_c|</math> is the reduced temperature, <math>T_c</math> is the Lambda point temperature, <math>A_\pm,B_\pm</math> are constants (different above and below the transition temperature), and <math>\alpha\approx-0.01</math> is the [[Critical_exponent|critical exponent]].<ref name=JPL /> Since this exponent is negative for the superfluid transition, specific heat remains finite.<ref>For other phase transitions <math>\alpha</math> may be negative (e.g. <math>\alpha\approx+0.1</math> for [[Critical point (thermodynamics)|the liquid-vapor critical point]] which has [[Ising critical exponents]]). For those phase transitions specific heat does tend to infinity. </ref>
== See also ==
== See also ==

Revision as of 17:39, 3 January 2020

The plot of the specific heat capacity versus temperature.

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]

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 where is the reduced temperature, is the Lambda point temperature, are constants (different above and below the transition temperature), and is the critical exponent.[3] Since this exponent is negative for the superfluid transition, specific heat remains finite.[4]

See also

References

  1. ^ 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.
  2. ^ 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.
  3. ^ a b c 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.
  4. ^ For other phase transitions may be negative (e.g. for the liquid-vapor critical point which has Ising critical exponents). For those phase transitions specific heat does tend to infinity.
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