Foundations of Physics

, Volume 44, Issue 3, pp 235–247 | Cite as

Experimental Test of a Thermodynamic Paradox

  • D. P. SheehanEmail author
  • D. J. Mallin
  • J. T. Garamella
  • W. F. Sheehan


In 2000, a simple, foundational thermodynamic paradox was proposed: a sealed blackbody cavity contains a diatomic gas and a radiometer whose apposing vane surfaces dissociate and recombine the gas to different degrees (A\(_{2} \rightleftharpoons \) 2A). As a result of differing desorption rates for A and A\(_{2}\), there arise between the vane faces permanent pressure and temperature differences, either of which can be harnessed to perform work, in apparent conflict with the second law of thermodynamics. Here we report on the first experimental realization of this paradox, involving the dissociation of low-pressure hydrogen gas on high-temperature refractory metals (tungsten and rhenium) under blackbody cavity conditions. The results, corroborated by other laboratory studies and supported by theory, confirm the paradoxical temperature difference and point to physics beyond the traditional understanding of the second law.


Second law of thermodynamics Nonequilibrium Catalysis Paradox 



The authors acknowledge T. Herrinton, S.L. Miller, J. Opdycke and P.C. Sheehan for discussions. T.M. Welsh and B. Cragin ( are thanked for the article’s figures, and D. Parsons for apparatus engineering and machining. This research was financially supported by Paradigm Energy Research Corporation. This article is dedicated to the memory of V. Čápek. Each author made significant contributions to the research presented in this article.


  1. 1.
    Loschmidt, J. Über den Zustand des Wärmegleichgewichtes eines Systeme von Körpern mit Rucksicht auf die Schwerkraft. Sitzungsber. Kais. Akad. Wiss. Wien, Math. Naturwiss. Classe 73, 128–142 (1876)Google Scholar
  2. 2.
    Zermelo, E.: Über einen Satz der Dynamik und die mechanische Wärmetheorie. Ann. Phys. 57, 485–494 (1896)CrossRefGoogle Scholar
  3. 3.
    Gibbs, J.W.: On the equilibrium of heterogeneous substances. Trans. Conn. Acad. 3(108–248), 343–524 (1873)Google Scholar
  4. 4.
    Leff, H.S., Rex, A.F. (eds.): Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing. Institute of Physics, Bristol (2003)Google Scholar
  5. 5.
    Čápek, V., Sheehan, D.P.: Challenges to the Second Law of Thermodynamics: Theory and Experiment, Fundamental Theories of Physics, vol. 146. Springer, Dordrecht (2005)Google Scholar
  6. 6.
    Duncan, T.L.: Comment on ‘Dynamically maintained steady-state pressure gradients’. Phys. Rev. E 61, 4661 (2000)ADSCrossRefGoogle Scholar
  7. 7.
    Sheehan, D.P.: Dynamically maintained steady-state pressure gradients. Phys. Rev. E 57, 6660–6666 (1998)ADSCrossRefGoogle Scholar
  8. 8.
    Motley, R.W.: Q-Machines. Academic Press, New York (1975)Google Scholar
  9. 9.
    Jansen, F., Chen, I., Machonkin, M.A.: On the thermal dissociation of hydrogen. J. Appl. Phys. 66, 5749–5755 (1989)ADSCrossRefGoogle Scholar
  10. 10.
    Schäfer, L., Klages, C.-P., Meier, U., Kohse-Höinghaus, K.: Atomic hydrogen concentration profiles at filaments used for chemical vapor deposition of diamond. Appl. Phys. Lett. 58, 571–573 (1991)ADSCrossRefGoogle Scholar
  11. 11.
    Otsuka, T., Ihara, M., Komiyama, H.: Hydrogen dissociation on hot tantalum and tungsten filaments under diamond deposition conditions. J. Appl. Phys. 77, 893–898 (1995)ADSCrossRefGoogle Scholar
  12. 12.
    Sheehan, D.P.: The second law and chemically-induced, steady-state pressure gradients: controversy, corroboration and caveats. Phys. Lett. A 280, 185–190 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    Qi, X., Chen, Z., Wang, G.: Formation and transport of atomic hydrogen in hot filament chemical vapor deposition reactors. J. Mater. Sci. Technol. 19, 235–239 (2003)CrossRefGoogle Scholar
  14. 14.
    Sheehan, D.P., Garamella, J.T., Mallin, D.J., Sheehan, W.F.: Experimental challenge to the second law of thermodynamics in high-temperature, gas-surface reactions. Phys. Scr. T151, 014030 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    Sheehan, D.P.: Heterogeneous catalysis in the long mean free path regime. Phys. Rev. E 88, 032125 (2013)ADSCrossRefGoogle Scholar
  16. 16.
    Langmuir, I.: The dissociation of hydrogen into atoms. J. Am. Chem. Soc. 34, 860–877 (1912)CrossRefGoogle Scholar
  17. 17.
    Langmuir, I.: The dissociation of hydrogen into atoms. II. Calculation of the degree of dissociation and the heat of formation. J. Am. Chem. Soc. 37, 417–458 (1915)CrossRefGoogle Scholar
  18. 18.
    Zheng, W., Gallagher, A.: Hydrogen dissociation on high-temperature tungsten. Surf. Sci. 600, 2207–2213 (2006)ADSCrossRefGoogle Scholar
  19. 19.
    Livshits, A.I., El Balghiti, F., Bacal, M.: Dissociation of hydrogen molecules on metal filaments in H\(^{-}\) sources. Plasma Sour. Sci. Technol. 3, 465–472 (1994)ADSCrossRefGoogle Scholar
  20. 20.
    Manufacturers of commercial H-atom sources include Veeco (, e-Science! ( and Tectra (

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • D. P. Sheehan
    • 1
    Email author
  • D. J. Mallin
    • 2
  • J. T. Garamella
    • 3
  • W. F. Sheehan
    • 4
  1. 1.Department of PhysicsUniversity of San DiegoSan DiegoUSA
  2. 2.Department of Physics and AstronomyUniversity of California, IrvineIrvineUSA
  3. 3.Department of Physics and AstronomyUniversity of MinnesotaMinneapolisUSA
  4. 4.Department of ChemistrySanta Clara UniversitySanta ClaraUSA

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