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Critical fluctuations and the equation of state of Van der Waals

Author

Listed:
  • Wyczalkowska, A.Kostrowicka
  • Sengers, J.V
  • Anisimov, M.A

Abstract

It is well known that classical equations of state, like the Van der Waals equation, fail in the region near the critical point of a fluid, where the behavior of the thermodynamic properties is strongly affected by density fluctuations. In this paper, we present a theoretical approach to correct classical cubic equations of state for the effects of critical fluctuations. The approach utilizes a transformation deduced from the renormalization-group theory of critical phenomena that was developed earlier for a classical Landau expansion of the Helmholtz-free-energy density. Using the Van der Waals equation as an example, we explain how critical fluctuations lower the critical temperature, flatten the coexistence curve, induce a singularity in the isochoric heat capacity, and lead to apparent critical exponents that depend on the temperature distance from the critical point.

Suggested Citation

  • Wyczalkowska, A.Kostrowicka & Sengers, J.V & Anisimov, M.A, 2004. "Critical fluctuations and the equation of state of Van der Waals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(3), pages 482-512.
    • Handle: RePEc:eee:phsmap:v:334:y:2004:i:3:p:482-512
    DOI: 10.1016/j.physa.2003.11.021
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