Measurements of the Sound Velocity in the Critical Region of Argon

  • W. van Dael
  • A. van Itterbeek
  • J. Thoen
Conference paper
Part of the Advances in Cryogenic Engineering book series (ACRE, volume 12)


The equilibrium sound velocity in an homogeneous phase fluid is given by
$$ {W^2} = \frac{1}{{\rho {\beta _s}}} = \frac{{{C_p}}} {{{C_v}}}\frac{1} {{\rho {\beta _T}}} $$
At the critical point C p → ∞ and according to experimental evidence obtained by Voronel’ f1,2] and Moldover [3] C v also approaches infinity. This means that in (1) the sound velocity becomes indeterminate at the critical point. Using the thermodynamic relation between C p and C v , (1) can be transformed into
$$ {W^2} = \frac{{{V^2}}}{M}\left[ { - {{\left( {\frac{{\partial p}}{{\partial V}}} \right)}_T} + \frac{T}{{{C_v}}}\left( {\frac{{\partial p}}{{{\partial _T}}}} \right)_v^2} \right] $$
At the critical point the first term vanishes while the second one tends to a finite value if C v remains finite, and it goes to zero if C v ∞.


Critical Region Sound Velocity Logarithmic Singularity Resonator Length Narrow Capillary Tube 
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Copyright information

© Springer Science+Business Media New York 1967

Authors and Affiliations

  • W. van Dael
    • 1
  • A. van Itterbeek
    • 1
  • J. Thoen
    • 1
  1. 1.Instituut voor Lage Temperaturen en Technische FysikaLeuvenBelgium

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