Skip to main content
SpringerLink
Log in

Thermodynamics based on a work inequality

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. J. Serrin (ed.), New Perspectives in Thermodynamics, Springer-Verlag, Berlin etc., 1986.

    Google Scholar 

  2. C. Truesdell, “A third line of argument in thermodynamics”, in [1], pp. 79–83.

  3. C. Truesdell, “The efficiency of a homogeneous heat engine”, Journal of Mathematical and Physical Sciences (Madras), 7 (1973), 349–371, and 9 (1975), 193–194.

    Google Scholar 

  4. C. Truesdell, “Improved estimates of the efficiencies of irreversible heat engines”, Annali di Mat. Pura ed Applic. (4), 108 (1976), 305–323.

    Google Scholar 

  5. C. Truesdell, “Proof that my work estimate implies the Clausius-Planck inequality”, Accad. Naz. dei Lincei, Rend. Cl. Sci. fiz. mat. e nat. (8), 68 (1980), 191–199.

    Google Scholar 

  6. C. Truesdell, “The mathematical foundations of elasticity and fluid dynamics”, J. Rational Mech. Anal., 1 (1952), 125–300, 2 (1953), 595–616, and 3 (1954), 801.

    Google Scholar 

  7. C. Truesdell & R. Toupin, “The classical field theories”, in Encyclopedia of Physics ed. by S. Flügge, Vol. 3, Part l (Springer-Verlag, Berlin etc., 1960), pp. 226–793.

    Google Scholar 

  8. B. D. Coleman & W. Noll, “The thermodynamics of elastic materials with heat conduction and viscosity”, Arch. Rational Mech. Anal. 13 (1963), 167–178.

    Google Scholar 

  9. C. Truesdell, Rational Thermodynamics, Second Edition, Springer-Verlag, New York etc., 1984.

    Google Scholar 

  10. J. Serrin, “Conceptual analysis of the classical second laws of thermodynamics”, Arch. Rational Mech. Anal. 70 (1979), 355–371.

    Google Scholar 

  11. A. E. Green & P. M. Naghdi, “The second law of thermodynamics and cyclic processes”, J. Appl. Mech. 45 (1978), 487–492.

    Google Scholar 

  12. R. L. Fosdick & J. Serrin, “Global properties of continuum thermodynamic processes”, Arch. Rational Mech. Anal. 59 (1975), 97–109.

    Google Scholar 

  13. B. D. Coleman, “Thermodynamics of materials with memory”, Arch. Rational Mech. Anal. 17 (1964), 1–46.

    Google Scholar 

  14. B. D. Coleman & J. M. Greenberg, “Thermodynamics and the stability of fluid motion”, Arch. Rational Mech. Anal. 25 (1967), 321–341.

    Google Scholar 

  15. B. D. Coleman, “On the stability of equilibrium states of general fluids”, Arch. Rational Mech. Anal. 36 (1970), 1–32.

    Google Scholar 

  16. C. Truesdell & S. Bharatha, The Concepts and Logic of Classical Thermodynamics as a Theory of Heat Engines, Rigorously Constructed upon the Foundation laid by S. Carnot and F. Reech, Springer-Verlag, New York etc., 1977.

    Google Scholar 

  17. J. W. Gibbs, Scientific Papers, Vol. 1, Dover Publications, New York, 1961.

    Google Scholar 

  18. J. Serrin, “The concepts of thermodynamics”, in Contemporary Developments in Continuum Mechanics and Partial Differential Equations ed. by G. M. de la Penha and L. A. Medeiros (North-Holland, Amsterdam etc., 1978), pp. 411–451.

    Google Scholar 

  19. J. Serrin, Lectures on thermodynamics, University of Naples, 1979.

  20. J. Serrin, “An outline of thermodynamic structure”, in [1], pp. 3–32.

  21. M. Šilhavý, “On the Clausius inequality”, in Euromech 111 Symposium. Constitutive Modelling in Inelasticity. Abstracts (Mariánské Lázně, September 26–28, 1978, Czechoslovak Academy of Sciences and Škoda, National Corporation, Plzěn), p. 68.

    Google Scholar 

  22. M. Šilhavý, “On the Clausius inequality”, manuscript, 1979; published in revised form, “On the Clausius inequality”, Arch. Rational Mech. Anal. 81 (1983), 221–243.

    Google Scholar 

  23. M. Šilhavý, “On measures, convex cones, and foundations of thermodynamics. I. Systems with vector-valued actions. II. Thermodynamic systems”, Czech. J. Phys., B 30 (1980), 841–861, 961–991.

    Google Scholar 

  24. M. Šilhavý, “On the second law of thermodynamics. I. General framework. II. Inequalities for cyclic processes”, Czech. J. Phys., B 32 (1982), 987–1010, 1073–1099.

    Google Scholar 

  25. M. Šilhavý, “Thermodynamics of cyclic processes”, Appendix G7 in [9], pp. 545–555.

  26. M. Šilhavý, “Foundations of continuum thermodynamics”, in [1], pp. 33–48.

  27. H. Lebesgue, Leçons sur l'Intégration et la Recherche des Fonctions Primitives, Chelsea Publishing Company, New York, 1973.

    Google Scholar 

  28. G. E. Shilov & B. L. Gurevich, Integral, Measure and Derivative: A Unified Approach, translated by R. A. Silverman, Dover Publications, New York, 1977.

    Google Scholar 

  29. J. Serrin, Lectures given at the NSF-CBMS Regional Conference on the Mathematical Foundations of Thermodynamics (July 16–21, 1978), Ball State University, Muncie, Indiana. All references to these lectures are based on the notes I took at Muncie.

    Google Scholar 

  30. C.-S. Man, “Proof that the Clausius-Serrin inequality is equivalent to a strengthened ‘Kelvin's law’”, Accad. Naz. dei Lincei, Rend. Cl. Sci. fiz. mat. e nat. (8), 69 (1980), 399–409.

    Google Scholar 

  31. R. Clausius, “On a modified form of the second fundamental theorem in the mechanical theory of heat”, Philosophical Magazine (4), 12 (1856), 81–98.

    Google Scholar 

  32. W. Thomson (later Lord Kelvin), “On the dynamical theory of heat, with numerical results deduced from Mr. Joule's equivalent of a thermal unit, and Mr. Regnault's observations on steam, Parts I–III”, Transactions of the Royal Society of Edinburgh 20 (1850/1853), Part 2, 261–268, 289–298.

  33. R. Clausius, “On the application of the theorem of the equivalence of transformations to the internal work of a mass of matter”, Philosophical Magazine (4), 24 (1862), 81–97, 201–213.

    Google Scholar 

  34. R. Clausius, Die Mechanische Wärmetheorie, Bd. 1, Friedrich Vieweg und Sohn, Braunschweig, 1876.

    Google Scholar 

  35. M. Planck, Treatise on Thermodynamics, translated by A. Ogg, Third Edition, Dover Publications, New York, 1945.

    Google Scholar 

  36. C. Truesdell, “Irreversible heat engines and the second law of thermodynamics”, Letters in Heat and Mass Transfer 3 (1976), 267–290.

    Google Scholar 

  37. A. E. Green & N. Laws, “On a global entropy production inequality”, Quart. Journ. Mech. and Applied Math. 25 (1972), 1–11.

    Google Scholar 

  38. M. Ricou, “The laws of thermodynamics for non-cyclic processes”, in [1], pp. 85–97.

  39. P. E. Sobolevsii, “Equation of parabolic type in a Banach space”, Trudy Moskov. Mat. Obšč. 10 (1961), 297–350; English translation, American Mathematical Society Translations, Series 2, 49 (1961), 1–62.

    Google Scholar 

  40. P. E. Sobolevskii, “Local and nonlocal existence theorems for nonlinear second-order parabolic equations”, Soviet Mathematics 2 (1961), 63–66.

    Google Scholar 

  41. O. A. Ladyženskaja, V. A. Solonnikov, & N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, translated by S. Smith, American Mathematical Society, Providence, 1968.

    Google Scholar 

  42. B. D. Coleman & V. L. Mizel, “Existence of caloric equations of state in thermodynamics”, J. Chem. Phys. 40 (1964), 1116–1125.

    Google Scholar 

  43. W. A. Day, The Thermodynamics of Simple Materials with Fading Memory, Springer-Verlag, Berlin etc., 1972.

    Google Scholar 

  44. A. C. Pipkin & R. S. Rivlin, “The formulation of constitutive equations in continuum physics”, Technical Report DA 4531/4 to the Department of Army, Ordnance Corps, 1958.

  45. J. L. Ericksen, “A thermo-kinetic view of elastic stability theory”, Int. J. Solids Structures 2 (1966), 573–580.

    Google Scholar 

  46. J. L. Ericksen, “Thermoelastic stability”, in Proceedings of the Fifth U.S. National Congress of Applied Mechanics, 1966, pp. 187–193.

  47. P. M. M. Duhem, Traité d'Énergétique ou de Thermodynamique Générale, t. 2, Gauthier-Villars, Paris, 1911.

    Google Scholar 

  48. B. D. Coleman & E. H. Dill, “On thermodynamics and the stability of motion of materials with memory”, Arch. Rational Mech. Anal. 51 (1973), 1–53.

    Google Scholar 

  49. B. D. Coleman, “The energy criterion for stability in continuum thermodynamics”, Rendiconti del Seminario Matematico e Fisico di Milano 43 (1973), 85–99.

    Google Scholar 

  50. K. Hutter, “The foundations of thermodynamics, its basic postulates and implications. A review of modern thermodynamics”, Acta Mechanica 27 (1977), 1–54.

    Google Scholar 

  51. B. D. Coleman & D. R. Owen, “A mathematical foundation for thermodynamics”, Arch. Rational Mech. Anal. 54 (1974), 1–104.

    Google Scholar 

  52. B. D. Coleman, D. R. Owen, & J. Serrin, “The second law of thermodynamics for systems with approximate cycles”, Arch. Rational Mech. Anal. 77 (1981), 103–142.

    Google Scholar 

  53. D. R. Owen, “The second law of thermodynamics for semi-systems with few approximate cycles”, Arch. Rational Mech. Anal. 80 (1982), 39–55.

    Google Scholar 

  54. M. Feinberg & R. Lavine, “Thermodynamics based on the Hahn-Banach theorem: the Clausius inequality”, Arch. Rational Mech. Anal. 82 (1983), 203–293.

    Google Scholar 

  55. M. Ricou, “A general first law for thermodynamics”, Arch. Rational Mech. Anal. 101 (1988), 365–385.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington

    Chi-Sing Man

Authors
  1. Chi-Sing Man
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by D. R. Owen

To Clifford Truesdell, my mentor, in deep gratitude

Rights and permissions

Reprints and permissions

About this article

Cite this article

Man, CS. Thermodynamics based on a work inequality. Arch. Rational Mech. Anal. 106, 1–61 (1989). https://doi.org/10.1007/BF00275914

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00275914

Keywords

Search

Navigation