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Part of the book series: Handbuch der Physik / Encyclopedia of Physics ((PHYSIK 3,volume 3 / 12))

Abstract

For the purposes of this article, the subject of the kinetic theory of gases is considered to be coextensive with the theory of the Boltzmann equation. We consider only the original equation of Maxwell and of Boltzmann for classical point molecules and short range forces, putting aside the equally interesting but distinct questions which arise from the inclusion of internal degrees of freedom, quantum interactions, inverse square forces, and imperfect gases. The special case of a Knudsen gas of freely streaming particles is only touched on, mainly for purposes of comparison.

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References

  1. Becker, R.: Z. Physik 8, 321 (1922).

    Article  ADS  Google Scholar 

  2. Bhatnager, P. L., E. P. Gross and M. Krook: Phys. Rev. 94, 511 (1954).

    Article  ADS  Google Scholar 

  3. Bogolubov, N.: J. Phys. USSR. 10, 265 (1946).

    MathSciNet  Google Scholar 

  4. Born, M., and H. S. Green: Proc. Roy. Soc. Lond., Ser. A 188, 10 (1946).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Born, M., and H. S. Green: A General Kinetic Theory of Liquids. Cambridge 1949.

    Google Scholar 

  6. Brout, R.: Physica, Haag 22, 509 (1956).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Brout, R., and I. Prigogine: Physica, Haag 22, 621 (1956).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Burnett, D.: Proc. Lond. Math. Soc. 40, 382 (1935).

    Article  Google Scholar 

  9. Carleman, T.: Acta math., Stockh. 60, 91 (1933).

    MathSciNet  Google Scholar 

  10. Chapman, S.: Phil. Trans. Roy. Soc. Lond. A 217, 115 (1917).

    Article  ADS  Google Scholar 

  11. Chapman, S., and T. G. Cowling: The Mathematical Theory of Non-Uniform Gases, Cambridge University Press 1952.

    Google Scholar 

  12. Cotter, J. R.: Proc. Roy. Irish Acad. A 55, 1 (1952).

    MathSciNet  Google Scholar 

  13. Degroot, S. R.: Thermodynamics of Irreversible Processes. New York: Interscience 1951.

    Google Scholar 

  14. Demarcus, W. C.: The Problem of Knudsen Flow. U.S. Atomic Energy Commission, Report K-1302, ORGDP.

    Google Scholar 

  15. Ehrenfest, P., U. T. Ehrenfest: Encykl. math. Wiss. 4, 2 (1911).

    Google Scholar 

  16. Enskog, D.: Kinetische Theorie der Vorgänge in mäßig verdünnten Gasen. Uppsala 1917.

    Google Scholar 

  17. Enskog, D.: Ark. Mat., Astronom. Phys., Ser. A 21, 1 (1928).

    Google Scholar 

  18. Frisch, H. L.: J. Chem. Phys. 22, 1713 (1954).

    Article  MathSciNet  ADS  Google Scholar 

  19. Goldberg, R.: Slow Flow of a Rarefied Gas Past a Spherical Obstacle. Thesis, New York University, 1954.

    Google Scholar 

  20. Grad, H.: Kinetic Theory and Statistical Mechanics, mimeographed notes. Institute of Mathematical Sciences, New York University, 1949.

    Google Scholar 

  21. Grad, H.: Comm. Pure Appl. Math. 2, 325 (1949).

    Article  MathSciNet  MATH  Google Scholar 

  22. Grad, H.: Comm Pure Appl. Math. 2, 331 (1949).

    Article  MathSciNet  MATH  Google Scholar 

  23. Grad, H.: Comm. Pure Appl. Math. 5, 257 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  24. Grad, H.: Comm. Pure Appl. Math. 5, 455 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  25. Grad, H.: J. Phys. Chem. 56, 1039 (1952).

    Article  MathSciNet  Google Scholar 

  26. Green, M. S.: J. Chem. Phys. 25, 836 (1956).

    Article  MathSciNet  ADS  Google Scholar 

  27. Gross, E. P., and M. Krook: Phys. Rev. 102, 593 (1956).

    Article  ADS  MATH  Google Scholar 

  28. Gross, E. P., E. A. Jackson and S. Ziering: Ann. of Physics 1, 141 (1957).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. Hecke, E.: Math. Z. 12, 274 (1922).

    Article  MathSciNet  Google Scholar 

  30. Hilbert, D.: Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen. Wien: J. B. Teubner 1924.

    Google Scholar 

  31. Hopf, E.: Ergodentheorie. New York: Chelsea Publ. Co. 1948.

    Google Scholar 

  32. Ikenberry, E., and C. Truesdell: J. Rat. Mech. Analysis 5, 1 (1956).

    MathSciNet  MATH  Google Scholar 

  33. Illingworth, C. R.: Proc. Cambridge Phil. Soc. 46, 469 (1950).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. Irving, J. H., and J. G. Kirkwood: J. Chem. Phys. 18, 817 (1950).

    Article  MathSciNet  ADS  Google Scholar 

  35. Jaffe, G.: Ann. der Phys. 6, 195 (1930).

    Article  ADS  MATH  Google Scholar 

  36. Jeans, J. H.: The Dynamical Theory of Gases. Cambridge 1916.

    Google Scholar 

  37. Kac, M.: Proceedings of Third Berkeley Symposium on Mathematical Statistics and Probability. U. of Cal. Press 1956.

    Google Scholar 

  38. Keller, J. B.: Comm. Pure Appl. Math. 1, 275 (1948).

    Article  MATH  Google Scholar 

  39. Kennard, E. H.: Kinetic Theory of Gases. New York: McGraw-Hill 1938.

    Google Scholar 

  40. Kirkwood, J. G.: J. Chem. Phys. 15, 72 (1947).

    Article  ADS  Google Scholar 

  41. Kohler, M.: Théorie moléculaire de l’onde de choc dans les gaz monoatomiques. Laboratoire d’etudes balistiques de Saint Louis, 1946.

    Google Scholar 

  42. Kohler, M.: Z. Physik 124, 772 (1947).

    Article  MathSciNet  ADS  Google Scholar 

  43. Kohler, M.: Z. Physik 27, 215 (1950).

    Article  MathSciNet  ADS  Google Scholar 

  44. Jamb, H.: Hydrodynamics. New York: Dover Publ. 1945.

    Google Scholar 

  45. Lebowitz, J. L., and H. L. Frisch: Phys. Rev. 107, 917 (1957).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. Maxwell, J. C.: Scientific Papers. New York: Dover Publ. n. d.

    Google Scholar 

  47. Merlic, E., and F. C. Hurlbut: The Determination of slip flow coefficients for various Histories. Inst. of Engineering Res., U. of Calif., 1956.

    Google Scholar 

  48. Morducaow, M., and P. A. Libby: J. Aer. Sci. 16 (1949).

    Google Scholar 

  49. Morgenstern, D.: Proc. Nat. Acad. Sci. 40, 719 (1954).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  50. Morgenstern, D.: J. Rat. Mech. Analysis 4, 533 (1955).

    MathSciNet  MATH  Google Scholar 

  51. Morrey, C. B.: Comm. Pure a. Appl. Math. 8, 279 (1955).

    Article  MathSciNet  MATH  Google Scholar 

  52. Mott-Smith, H. M.: Phys. Rev. 82, 885 (1951).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  53. Mott-Smith, H. M.: A New Approach in the Kinetic Theory of Gases. Lincoln Laboratory, M.I.T. 1954.

    Google Scholar 

  54. Nom, W.: J. Rat. Mech. Analysis 4, 627 (1955).

    Google Scholar 

  55. Rankine, W. J. M.: Trans. Roy. Soc. 160 (1870).

    Google Scholar 

  56. Rayleigh, J.: Proc. Roy. Soc. Lond., Ser. A 84 (1910).

    Google Scholar 

  57. Rogosinski, W. W.: Volume and Integral. New York: Interscience 1952.

    MATH  Google Scholar 

  58. Rose, M. (Heineman) : Comm. Pure Appl. Math. 1, 259 (1948).

    Article  Google Scholar 

  59. Rose, M. (Heineman): Phys. Rev. 91, 469 (1953).

    Google Scholar 

  60. Shannon, C. E., and W. Weaver: The Mathematical Theory of Communication. Univ. of Illinois Press 1949.

    Google Scholar 

  61. Taylor, G. I.: Proc. Roy. Soc. Lond., Ser. A 84 (1910).

    Google Scholar 

  62. Thomas, L. H.: J. Chem. Phys. 12, 449 (1944).

    Article  ADS  Google Scholar 

  63. Titchmarsh, E. C.: The Theory of Functions. Oxford University Press 1939.

    Google Scholar 

  64. Truesdell, C.: J. Rat. Mech. Analysis 5, 55 (1956).

    MathSciNet  MATH  Google Scholar 

  65. Van Hove, L.: Physica, Haag 15, 951 (1949).

    Article  ADS  MATH  Google Scholar 

  66. Van Hove, L.: Physica, Haag 21, 517 (1955).

    MATH  Google Scholar 

  67. Wang Chang, C. S.: On the Theory of the Thickness of Weak Shock Waves. Dept. of Engr. Research, U. of Mich., 1948.

    Google Scholar 

  68. Wang Chang, C. S., and G. E. Uhlenbeck: On the Propagation of Sound in Monotonic Gases. Engr. Research Inst., U. of Mich., 1952.

    Google Scholar 

  69. Wang Chang, C. S. and G. E. Uhlenbeck: The Heat Transport Between two Parallel Plates as Functions of the Knudsen Number. Engr. Research Inst., U. of Mich., 1953.

    Google Scholar 

  70. Wild, E.: Proc. Cambridge Phil. Soc. 47, 602 (1951).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  71. Yang, H. T., and L. Lees: Rayleigh’s problem at low mach number according to the kinetic theory of gases. Guggenheim Aeron. Lab., Cal. Inst. of Tech. 1955.

    Google Scholar 

  72. Zoller, K.: Z. Physik 130, 1 (1951).

    Article  MathSciNet  ADS  MATH  Google Scholar 

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S. Flügge

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© 1958 Springer-Verlag OHG. Berlin · Göttingen · Heidelberg

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Grad, H. (1958). Principles of the Kinetic Theory of Gases. In: Flügge, S. (eds) Thermodynamik der Gase / Thermodynamics of Gases. Handbuch der Physik / Encyclopedia of Physics, vol 3 / 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45892-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-45892-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

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