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On the thermodynamics of mixtures

I. Mixtures of rigid heat conductors

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References

  • [1871] Stefan, J., Über das Gleichgewicht und die Bewegung, insbesondere die Diffusion von Gasmengen. Akad. Wiss. Wien 63, 63–124.

    Google Scholar 

  • [1876] Massieu, V. J., Mémoire sur les fonctions caractéristiques des divers fluides et sur la théorie des vapeurs. Mém. présentés par divers savants à l'Acad. Sci. 22, 92pp.

  • [1892] Duhem, P. M. M., Commentaire aux principes de la thermodynamique. J. Math. Pures Appl. (4) 8, 269–330.

    Google Scholar 

  • [1893] Duhem, P. M. M., Dissolutions et mélanges. Trav. Mém. Fac. de Lille 3, 1–136.

    Google Scholar 

  • [1894] Duhem, P. M. M., Commentaire aux principes de la thermodynamique; 3me Partie. J. Math. Pures Appl. (4) 10, 207–285.

    Google Scholar 

  • [1911] Jaumann, G., Geschlossenes System physikalischer und chemischer Differentialgesetze. Akad. Wiss. Wien 120, 385–530.

    Google Scholar 

  • [1917] Lohr, E., Entropieprinzip und geschlossenes Gleichungssystem. Denkschriften Akad. Wiss. Wien 93, 339–421.

    Google Scholar 

  • [1931] Onsager, L., Reciprocal relations in irreversible processes I. Phys. Rev. 37, 405–426.

    Google Scholar 

  • [1938] Meissner, W., Thermodynamische Behandlung stationärer Vorgänge in Mehrphasensystemen. Ann. der Physik 32(5), 115–127.

    Google Scholar 

  • [1939] Bateman, H., The aerodynamics of reacting substances. Proc. Nat. Acad. Sci. USA 25, 388–391.

    Google Scholar 

  • [1940] Eckart, C., The thermodynamics of irreversible processes. II. Fluid mixtures. Phys. Rev. 58(2), 269–275.

    Google Scholar 

  • [1941] Meixner, J., Zur Thermodynamik der Thermodiffusion. Ann. der Physik 39(5), 333–356.

    Google Scholar 

  • [1954] Prigogine, I., & R. Defay, Chemical Thermodynamics. London-New York-Toronto: Longmans Green.

    Google Scholar 

  • [1954] Hirschfelder, J. O., C. F. Curtiss, & R. B. Bird, Molecular Theory of Gases and Liquids. New York: Wiley.

    Google Scholar 

  • [1957] Truesdell, C, Sulle basi della termomeccanica. Rend. Accad. Lincei (8) 22, 33–88, 158–166. English transl, in Rational Mechanics of Materials. Intl. Sci. Rev. Ser. 292–305. New York: Gordon & Breach 1965.

    Google Scholar 

  • [1959] Meixner, J., & H. G. Reik, Thermodynamik der irreversiblen Prozesse. In: The Encyclopedia of Physics, Vol. III/2, edited by S. Flügge. Berlin-Göttingen-Heidelberg: Springer.

    Google Scholar 

  • [1959] Nachbar, W., F. Williams, & S. S. Penner, The conservation equations for independent coexistent continua and for multicomponent reacting gas mixtures. QuartAppl. Math. 17, 43–54.

    Google Scholar 

  • [1960] Truesdell, C., & R. A. Toupin, The Classical Field Theories. In: The Encyclopedia of Physics, Vol. III/1, edited by S. Flügge. Berlin-Göttingen-Heidelberg: Springer.

    Google Scholar 

  • [1961] Truesdell, C., Una teoria meccanica della diffusione. Celebraz. Archimedee Sec. XX

  • (1960) III Simposio di mecc. e mat. applic. 161–168.

  • [1962] de Groot, S. R., & P. Mazur, Non-Equilibrium Thermodynamics. Amsterdam: North-Holland.

    Google Scholar 

  • [1962] Truesdell, C., Mechanical basis of diffusion. J. Chem. Phys. 37, 2336–2344.

    Google Scholar 

  • [1963] Coleman, B.D., & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13, 167–178.

    Google Scholar 

  • [1964] Adkins, J.E., Diffusion of fluids through aeolotropic highly elastic solids. Arch. Rational Mech. Anal. 15, 222–234.

    Google Scholar 

  • [1964] Coleman, B.D., & V.J. Mizel, Thermodynamics and departures from Fourier's law of heat conduction. Arch. Rational Mech. Anal. 13, 245–261.

    Google Scholar 

  • [1964] Green, A.E., & J.E. Adkins, A contribution to the theory of non-linear diffusion. Arch. Rational Mech. Anal. 15, 235–246.

    Google Scholar 

  • [1964] Kelly, P.D., A reacting continuum. Intern. J. Engng. Sci. 2, 129–153.

    Google Scholar 

  • [1964] Sikorski, R., Boolean Algebras (2nd ed.). Berlin-Göttingen-Heidelberg-New York: Springer.

    Google Scholar 

  • [1965] Eringen, A.C., & J.D. Ingram, A continuum theory of chemically reacting media I. Intern. J. Engng. Sci. 3, 197–212.

    Google Scholar 

  • [1965] Green, A. E., & P.M. Naghdi, A dynamical theory of interacting continua. Intern. J. Engng. Sci. 3, 231–241.

    Google Scholar 

  • [1965] Noll, W., The foundations of mechanics. Res. Rept. 66-2, Dept. of Mathematics, CMU= Non-Linear Continuum Theories (1966) 159–200, Roma: Edizioni Cremonese.

    Google Scholar 

  • [1965] Truesdell, C., & W. Noll, The Non-Linear Field Theories of Mechanics. In: The Encyclopedia of Physics, Vol. III/3, edited by S. Flügge. Berlin-Heidelberg-New York: Springer.

    Google Scholar 

  • [1966] Crochet, M.J., & P.M. Naghdi, Constitutive equations for flow of fluid through an elastic solid. Intern. J. Engng. Sci. 4, 383–401.

    Google Scholar 

  • [1965] Green, A.E., & T.R. Steel, Constitutive equations for interacting continua. Intern. J. Engng. Sci. 4, 483–500.

    Google Scholar 

  • [1965] Mills, N., Incompressible mixture of Newtonian fluids. Intern. J. Engng. Sci. 4, 97–112.

    Google Scholar 

  • [1967] Bowen, R.M., Toward a thermodynamics and mechanics of mixtures. Arch. Rational Mech. Anal. 24, 370–403.

    Google Scholar 

  • [1967] Green, A.E., & P.M. Naghdi, A theory of mixtures. Arch. Rational Mech. Anal. 24, 243–263.

    Google Scholar 

  • [1967] Gurtin, M.E., & W.O. Williams, An axiomatic foundation for continuum thermodynamics. Arch. Rational Mech. Anal. 26, 83–117.

    Google Scholar 

  • [1967] Ingram, J.D., & A. C. Eringen, A continuum theory of chemically reacting continua — II constitutive equations of reacting fluid mixtures. Intern. J. Engng. Sci. 5, 289–322.

    Google Scholar 

  • [1968] Dunwoody, N.T., & I. Müller, A thermodynamic theory of two chemically reacting ideal gases with different temperatures. Arch. Rational Mech. Anal. 29, 344–369.

    Google Scholar 

  • [1968] Green, A.E., & P.M. Naghdi, A note on mixtures. Intern. J. Engng. Sci. 6, 631–635.

    Google Scholar 

  • [1968] Gurtin, M.E., W. Noll, & W.O. Williams, On the foundations of thermodynamics. Res. Rept. 68–42, Dept. of Mathematics, CMU.

  • [1968] Müller, I., A thermodynamic theory of mixture of fluids. Arch. Rational Mech. Anal. 28, 1–39.

    Google Scholar 

  • [1968] Steel, T.R., Determination of the constitutive coefficients for a mixture of two solids. ONR Report No. AM-68-4.

  • [1969] Bowen, R.M., & J.C. Wiese, Diffusion in mixtures of elastic materials. Intern. J. Engng. Sci., in press.

  • [1969] Bowen, R.M., & D.J. Garcia, Multiple temperature effects in a mixture of rigid heat conductors. To be published.

  • [1969] Doria, M.L., Some general results for non-reacting binary mixtures of fluids. Arch. Rational Mech. Anal. 32, 343–368.

    Google Scholar 

  • [1969] Green, A.E., & P.M. Naghdi, On basic equations for mixtures. Rept. No. AM-69-4, Univ. of California, Berkeley.

    Google Scholar 

  • [1969] Truesdell, C., Rational Thermodynamics: A Course of Lectures on Selected Topics. New York: McGraw-Hill.

    Google Scholar 

  • [1969] Williams, W.O., On internal interactions and the concept of thermal isolation. Arch. Rational Mech. Anal. 34, 245–258.

    Google Scholar 

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  1. Department of Mathematics, Carnegie-Mellon University, Pittsburgh

    Morton E. Gurtin & Guilherme M. de La Penha

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  1. Morton E. Gurtin
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  2. Guilherme M. de La Penha
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Gurtin, M.E., de La Penha, G.M. On the thermodynamics of mixtures. Arch. Rational Mech. Anal. 36, 390–410 (1970). https://doi.org/10.1007/BF00282275

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