Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the local form of the second law of thermodynamics in continuum mechanics

Author: L. C. Woods
Journal: Quart. Appl. Math. 39 (1981), 119-126
MSC: Primary 80A05; Secondary 00A69, 73B30
DOI: https://doi.org/10.1090/qam/613955
MathSciNet review: 613955
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Abstract: The Clausius-Duhem inequality $ \sigma \left( {r,t} \right) \ge 0$, a widely adopted axiom in continuum mechanics, leads to the conclusion that for many materials the entropy $ s$ cannot depend on gradients like the temperature gradient g and the velocity gradient e. But this is at variance with the received view (since Gibbs) that entropy is a function of thermodynamic state, however detailed that state description may be. Gradients, and even higher derivatives of macroscopic variables, may be included as state variables (although only on macroscopic time scales shorter than or comparable with their natural relaxation times), and the fundamental property of entropy is its convexity--the more detailed the specification of state, the smaller is the corresponding value of entropy.

References [Enhancements On Off] (What's this?)

  • [1] B. D. Coleman, Arch. Rat. Mech. Anal. 17, 1-46, 230-254 (1964) MR 0171419
  • [2] S. R. de Groot and P. Mazur, Non-equilibrium thermodynamics, North Holland Pub. Co. (1962) MR 0140332
  • [3] A. C. Eringen (ed.), Continuum physics, Vol. II, Academic Press, 115-126 (1975) MR 0468444
  • [4] R. L. Fosdick and K. R. Rajagopal, Proc. Roy. Soc. A369, 351-377 (1980)
  • [5] H. Grad, Comm. Pure Applied Math. 2, 331 (1949) MR 0033674
  • [6] R. Haase, Thermodynamics of irreversible processes, Addison-Wesley (1968)
  • [7] W. Jaunzemis, Continuum mechanics, Macmillan (1967)
  • [8] D. C. Leigh, Non-linear continuum mechanics, McGraw-Hill (1967)
  • [9] A. Shavit and Y. Zvarin, Technion Report TME-110, Haifa (1970)
  • [10] C. Truesdell and W. Noll, The non-linear field theories of mechanics, in Handbuch der Physik (ed. Flugge) III/3, Springer, Berlin (1965) MR 0193816
  • [11] L. C. Woods, The thermodynamics of fluid systems, Oxford (1975)
  • [12] L. C. Woods, J. Fluid Mech. 101, 225-241 (1980) MR 605384

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DOI: https://doi.org/10.1090/qam/613955
Article copyright: © Copyright 1981 American Mathematical Society

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