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One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
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The Gibbs Paradox: Early History and Solutions.

Olivier Darrigol1

  • 1UMR SPHere, CNRS, Université Denis Diderot, 75013 Paris, France.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

This article traces the history of the Gibbs paradox, offering philosophical insights and critiquing its solutions. It uses statistical mechanics to clarify foundational concepts and address misunderstandings in physical theory.

Area of Science:

  • Thermodynamics and Statistical Mechanics
  • History and Philosophy of Science

Background:

  • The Gibbs paradox, a long-standing puzzle in thermodynamics, arises from the apparent discontinuity in entropy when identical particles are mixed.
  • Understanding this paradox is crucial for the foundations of statistical mechanics and the interpretation of physical theories.

Purpose of the Study:

  • To provide a comprehensive historical account of the Gibbs paradox.
  • To critically analyze various proposed solutions from historical and contemporary perspectives.
  • To leverage the history of statistical mechanics for conceptual clarity and to address fundamental misunderstandings in physics.

Main Methods:

  • Historical analysis of scientific literature on the Gibbs paradox.
  • Philosophical examination of proposed solutions and their underlying assumptions.
Keywords:
Gibbs paradoxentropyirreversibilitymixingthermochemistry

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  • Conceptual clarification through the lens of statistical mechanics.

    • Main Results:

    • The study elucidates the origins and evolution of the Gibbs paradox.
    • It critically evaluates the strengths and weaknesses of different approaches to resolving the paradox.
    • Connections are drawn between the paradox and broader issues in the interpretation of physical theories.

    Conclusions:

    • The Gibbs paradox highlights fundamental conceptual challenges in statistical mechanics.
    • Resolving the paradox requires careful consideration of the nature of physical theory and its foundations.
    • A historical perspective enriches our understanding of ongoing debates in the philosophy of physics.