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Related Experiment Videos

On the Relation Between lambda Lines and Phase Separations.

O K Rice1

  • 1Department of Chemistry, University of North Carolina, Chapel Hill, N.C. 27514.

Proceedings of the National Academy of Sciences of the United States of America
|April 1, 1973
PubMed
Summary
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This study challenges the assumption that specific heat is maximal on lambda lines in (3)He-(4)He solutions. It reveals that chemical potentials likely do not vanish, and specific heat may not reach its maximum, except at tricritical points.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Traditional assumption: slope of isotherm vanishes on lambda line, leading to maximal specific heat (e.g., C(V)) and adherence to Buckingham-Fairbank relation.
  • This assumption is prevalent in understanding phase transitions and thermodynamic properties.

Purpose of the Study:

  • To investigate the behavior of chemical potentials and specific heat in (3)He-(4)He solutions along the lambda line.
  • To re-evaluate the conditions under which specific heat reaches its maximum value.
  • To provide a statistical thermodynamic description of tricritical points and compare with experimental data.

Main Methods:

  • Heuristic theoretical arguments applied to (3)He-(4)He solutions.
  • Analysis of chemical potentials (μ(4), μ(3)) and mole fraction (x(3)).

Related Experiment Videos

  • Statistical thermodynamic modeling of tricritical points.
  • Examination of experimental data for solid NH(4)Cl and (3)He-(4)He solutions.

    • Main Results:

    • In (3)He-(4)He solutions, chemical potentials ([unk]μ(4)/[unk]x(3) and [unk]μ(3)/[unk]x(3)) likely do not vanish along the lambda line.
    • Specific heat C(x3) may not attain its maximum possible value, though it can approach infinity as x(3) approaches 0.
    • Only at the tricritical point does [unk]μ(4)/[unk]x(3) vanish, and C(x3) reaches a maximum before instability.
    • Experimental data for solid NH(4)Cl suggests [unk]P/[unk]V(T) does not vanish along the transition line at higher temperatures.
    • Singular behavior observed at the tricritical point in (3)He-(4)He solutions appears to be present along the lambda line as well.
    • Analysis of binary liquid solutions indicates that a tendency for C(V) to exceed its maximum can lead to a flattened coexistence curve.

    Conclusions:

    • The assumption of vanishing isotherm slopes and maximal specific heat on lambda lines is challenged for (3)He-(4)He solutions.
    • Tricritical points represent unique states where specific thermodynamic conditions are met, unlike general lambda lines.
    • The findings offer a more nuanced understanding of phase transitions and critical phenomena in multi-component systems.