Advertisement

Thermodynamic Properties of Fluids below 20 K*

  • William E. Keller
Chapter

Abstract

The title of this chapter is in one sense very restrictive and in another entirely open-ended. Below 20 K the only chemical species exhibiting fluid behavior are the isotopes of hydrogen and helium, often referred to as quantum fluids since quantum effects are responsible for many startling differences in behavior of these substances as compared with ordinary fluids. On the other hand, because both 3He and 4He are expected in the absence of externally applied pressure to remain as liquids even at the absolute zero of temperature, the temperature range permitted for discussion may extend downward without limit. In a third sense there are of course many additional degrees of freedom implicit in the words ‘thermodynamic properties’. These circumstances combine to set this chapter apart organizationally from other chapters in this volume; others tend to describe measurement methods for a single variable, or class of related variables, as may be applied to a variety of substances, whereas the present chapter is to deal with techniques for measuring several different variables—over perhaps wide ranges—as applied to a few special substances.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

VII. References

  1. 1.
    Abel, W. R, A. C Anderson, W. G. Black and J. G. Wheatley. Phys. Rev. Letters, 16, 273 (1966).CrossRefGoogle Scholar
  2. 2.
    Abel, W. R., A. G. Anderson, W. G. Black and J. G. Wheatley. Phys. Rev. 147, 111 (1966).CrossRefGoogle Scholar
  3. 3.
    Abraham, B. M., UTS*, p 37.Google Scholar
  4. 4.
    Ahlers, G., Phys. Rev. 171, 275 (1968).CrossRefGoogle Scholar
  5. 5.
    Ahlers, G., Phys. Rev. A3, 696 (1971).CrossRefGoogle Scholar
  6. 6.
    Anderson, A. C., UTS*, p 82.Google Scholar
  7. 7.
    Anufriev, Yu. D., Zh. Eksp. Teor. Fiz. Pis’ma, 1, 155 (1965); English translation. JETP Letters, 1, 155 (1965).Google Scholar
  8. 8.
    Bailey, A. C. (Ed.). Advanced Cryogenics, Plenum: New York (1970).Google Scholar
  9. 9.
    Baker, J. M., B. Bleaney, P. M. Llewellyn and P. F. D. Shaw. Proc. Phys. Soc. (London), 69A, 353 (1956).CrossRefGoogle Scholar
  10. 10.
    Barber, C. R., Fifth Symposium on Temperature†, p 99.Google Scholar
  11. 11.
    Bedford, R. E., M. Durieux, R. Muijlwijk and C. R. Barber. Metrologia, 5, 47 (1969).CrossRefGoogle Scholar
  12. 12.
    Bedford, R. E., H. Preston-Thomas, M. Durieux and R. Muijlwijk. Metrologia, 5, 45 (1969).CrossRefGoogle Scholar
  13. 13.
    Berglund, P. M., G. J. Ehnholm, R. G. Gylling, O. V. Lounasmaa and R. P. Søvik. UTS*, p 113; also in Proceedings of the Third International Cryogenic Engineering Conference (Berlin), p 473. Iliffe: Guildford, UK (1970).Google Scholar
  14. 14.
    Berman, R. and C. F. Mate. Phil Mag., Ser. III, 29, 461 (1958).Google Scholar
  15. 15.
    Berman, R. and J. Poulter. Phil Mag. 43, 1047 (1952).Google Scholar
  16. 16.
    Berry, K. H., Fifth Symposium on Temperature†, p 323.Google Scholar
  17. 17.
    Boghosian, C. and H. Meyer. Phys. Rev. 152, 200 (1966).CrossRefGoogle Scholar
  18. 18.
    Boghosian, C., H. Meyer and J. E. Rives. Phys. Rev. 146, 110 (1966).CrossRefGoogle Scholar
  19. 19.
    Buckingham, M. J. and W. M. Fairbank, in Progress in Low Temperature Physics, Vol. III (Gorter, C. J., Ed.), p 80. North-Holland: Amsterdam (1961).Google Scholar
  20. 20.
    Cataland, G. and H. H. Plumb. Fifth Symposium on Temperature†, p. 183.Google Scholar
  21. 21.
    Cetas, T. C. and C. A. Swenson. Phys. Rev. Letters, 25, 338 (1970); Fifth Symposium on Temperature†, p 57.CrossRefGoogle Scholar
  22. 22.
    Chapellier, M., M. Goldman, V. H. Chau and A. Abragam. CR Acad. Sci., Paris, 268, 1530 (1969).Google Scholar
  23. 23.
    Colclough, A. R., Fifth Symposium on Temperature†, p 365.Google Scholar
  24. 24.
    Croft, A. J., Cryogenic Laboratory Equipment, Plenum: New York (1969).Google Scholar
  25. 25.
    Dana, L. I. and H. K. Onnes. Leiden Commun. 179c (1926).Google Scholar
  26. 26.
    Das, P., R. De Bruyn Ouboter and K. W. Taconis. Low Temperature Physics LT9, Part B, p 1253. Plenum: New York (1965).CrossRefGoogle Scholar
  27. 27.
    Dash, J. G., R. D. Taylor, D. E. Nagle, P. P. Craig and W. M. Visscher. Phys. Rev. 122, 1116 (1961).CrossRefGoogle Scholar
  28. 28.
    Dearnaley, G., Contemp. Phys. 8, 607 (1967).CrossRefGoogle Scholar
  29. 29.
    De Bruyn Ouboter, R., K. W. Taconis, C. LePair and J. J. M. Beenakker. Physica, 26, 853 (1960).CrossRefGoogle Scholar
  30. 30.
    deGroot, S. R., H. A. Tolhoek and W. J. Huiskamp, in Alpha-, Beta-, and Gamma-Ray Spectroscopy, Vol. II, p 1199. (Siegbahn, K., Ed.), North-Holland: Amsterdam (1965).Google Scholar
  31. 31.
    Durieux, M., in Progress in Low Temperature Physics, Vol. VI, p 405. (Gorter, C. J., Ed.), North-Holland: Amsterdam (1970).Google Scholar
  32. 32.
    Edwards, D. O., E. M. Ifft and R. E. Sarwinski. Phys. Rev. 177, 380 (1969).CrossRefGoogle Scholar
  33. 33.
    Edwards, D. O., R. E. Sarwinski, P. Seligman and J. T. Tough. Cryogenics, 8, 392 (1968).CrossRefGoogle Scholar
  34. 34.
    Ehnholm, G. J. and R. G. Gylling. Cryogenics, 11, 39 (1971).CrossRefGoogle Scholar
  35. 35.
    Goldstein, L., Phys. Rev. 159, 120 (1967); 188, 349 (1969).CrossRefGoogle Scholar
  36. 36.
    Golovashkin, A. N. and G. P. Motulevich. Cryogenics, 3, 167 (1963).CrossRefGoogle Scholar
  37. 37.
    Goodkind, J. M. and D. L. Stolfa. Rev. Sci. Instrum. 41, 799 (1970).CrossRefGoogle Scholar
  38. 38.
    Goodwin, R. D., J. Res. Nat. Bur. Stand. 65C, 231 (1961).Google Scholar
  39. 39.
    Graf, E. H, D. M. Lee and J. D. Reppy. Phys. Rev. Letters, 19, 417 (1967).CrossRefGoogle Scholar
  40. 40.
    Grilly, E. R., J. Low Temp. Phys. 4, 615 (1971).CrossRefGoogle Scholar
  41. 41.
    Grilly, E. R. and R. L. Mills. Phys. Rev. 105, 1140 (1957); Ann. Phys. (NY), 8, 1 (1959).CrossRefGoogle Scholar
  42. 42.
    Halverson, G. and D. A. Johns. Fifth Symposium on Temperature†, p 803.Google Scholar
  43. 43.
    Hammel, E. F. and W. E. Keller. Phys. Rev. 124, 1641 (1961).CrossRefGoogle Scholar
  44. 44.
    Hirschkoff, E. C., O. G. Symko and J. C. Wheatley. J. Low Temp. Phys. 2, 653 (1970).CrossRefGoogle Scholar
  45. 45.
    Hirschkoff, E. C., O. G. Symko and J. C. Wheatley. J. Low Temp. Phys. 4, 111 (1971).CrossRefGoogle Scholar
  46. 46.
    Hoare, F. E., L. C. Jackson and N. Kurti. Experimental Cryophysics, Butterworths: London (1961).Google Scholar
  47. 47.
    Hoffer, J. K., Thesis (UCRL-18319), University of California, Berkeley (1968).Google Scholar
  48. 48.
    Hudson, R. P. and R. S. Kaeser. Physics, 3, 95 (1967).Google Scholar
  49. 49.
    International Practical Temperature Scale of 1968. Metrologia, 5, 35 (1969).CrossRefGoogle Scholar
  50. 50.
    Johnston, H. L., W. E. Keller and A. S. Friedman. J. Amer. Chem. Soc. 76, 1482 (1954).CrossRefGoogle Scholar
  51. 51.
    Johnson, R. T., O. V. Lounasmaa, R. Rosenbaum, O. G. Symko and J. C. Wheatley. J. Low Temp. Phys. 2, 403 (1970).CrossRefGoogle Scholar
  52. 52.
    Johnson, R. T. and J. C. Wheatley. J. Low Temp. Phys. 2, 423 (1970).CrossRefGoogle Scholar
  53. 53.
    Josephson, B. D., Phys. Letters, 1, 251 (1962).CrossRefGoogle Scholar
  54. 54.
    Kalvins, G. M., T. E. Katila and O. V. Lounasmaa, in Mössbauer Effect Methodology, Vol. 5, pp 231–261. (Gruverman, I. J., Ed.), Plenum: New York (1970).CrossRefGoogle Scholar
  55. 55.
    Kamper, R. A., Fifth Symposium on Temperature†, p 349.Google Scholar
  56. 56.
    Kamper, R. A., J. D. Siegwarth, R. Radebaugh and J. E. Zimmerman. Proc. I.E.E.E., 59, 1368 (1971).Google Scholar
  57. 57.
    Kamper, R. A. and J. E. Zimmerman. J. Appl. Phys. 42, 132 (1971).CrossRefGoogle Scholar
  58. 58.
    Keller, W. E., Helium-3 and Helium-4, Plenum: New York (1969).CrossRefGoogle Scholar
  59. 59.
    Keller, W. E., Phys. Rev. 97, 1 (1955); 98, 1571 (1955); 100, 1790 (1955).CrossRefGoogle Scholar
  60. 60.
    Kellers, C. F., Thesis, Duke University (1960).Google Scholar
  61. 61.
    Kerr, E. C. and R. H. Sherman. J. Low Temp. Phys. 3, 451 (1970).CrossRefGoogle Scholar
  62. 62.
    Kerr, E. C. and R. D. Taylor. Ann. Phys. (N.Y.), 20, 450 (1962).CrossRefGoogle Scholar
  63. 63.
    Kerr, E. G. and R. D. Taylor. Ann. Phys. (N.Y.), 26, 292 (1964).CrossRefGoogle Scholar
  64. 64.
    Kittel, C., Introduction to Solid State Physics, 4th ed., p 579. Wiley: New York (1971).Google Scholar
  65. 65.
    Kurti, N., F. N. H. Robinson, F. E. Simon and D. A. Spohr. Nature (London), 178, 450 (1956).CrossRefGoogle Scholar
  66. 66.
    Landau, J., J. T. Tough, N. R. Brubaker and D. O. Edwards. Phys. Rev. 2A, 2472 (1970); Rev Sci. Instrum. 41, 444 (1970).CrossRefGoogle Scholar
  67. 67.
    Lawless, W. N., Rev. Sci. Instrum. 42, 561 (1971); Fifth Symposium on Temperature†, p 1143CrossRefGoogle Scholar
  68. 68.
    Lawless, W. N., R. Radebaugh and R. J. Soulen. Rev. Sci. Instrum. 42, 567 (1971).CrossRefGoogle Scholar
  69. 69.
    Lee, D. M., H. A. Fairbank and E. J. Walker. Phys. Rev. 121, 1258 (1961).CrossRefGoogle Scholar
  70. 70.
    Liebenberg, D. H. and L. D. F. Allen. J. Appl. Phys. 41, 4050 (1970); Fifth Symposium on Temperature†, p 875.CrossRefGoogle Scholar
  71. 71.
    London, H., Proceedings of the International Conference on Low Temperature Physics, p 157. Oxford, August 1951.Google Scholar
  72. 72.
    London, H., G. R. Clarke and E. Mendoza. Phys. Rev. 128, 1992 (1962).CrossRefGoogle Scholar
  73. 73.
    Mills, R. L. and E. R. Grilly. Phys. Rev. 99, 480 (1955); 101, 1246 (1956).CrossRefGoogle Scholar
  74. 74.
    Mills, R. L., E. R. Grilly and S. G. Sydoriak. Ann. Phys. (N.Y.), 12, 41 (1961).CrossRefGoogle Scholar
  75. 75.
    Mitsui, K., H. Sakurai and T. Mochizuki. Fifth Symposium on Temperature†, p 333.Google Scholar
  76. 76.
    Mota, A. C., R. P. Platzeck, R. Rapp and J. G. Wheatley. Phys. Rev. 177, 266 (1969).CrossRefGoogle Scholar
  77. 77.
    Neganov, B. S., N. Borisov and M. J. Liburg. Zh. Eksp. Teor. Fiz. 50, 1445 (1966); English translation: Soviet Phys. JETP, 23, 959 (1966). See also, Neganov, B. S., Institute for Nuclear Problems, Dubna. Report P13, 4014 (1968) (in Russian).Google Scholar
  78. 78.
    Neiler, J. H. and P. R. Bell, in Alpha-, Beta-, and Gamma-Ray Spectroscopy, Vol. I, p 245. (Siegbahn, K., Ed.), North-Holland: Amsterdam (1965).Google Scholar
  79. 79.
    Nyquist, H., Phys. Rev. 32, 110 (1928).CrossRefGoogle Scholar
  80. 80.
    Onnes, H. K. and W. van Gulik. Leiden Commun. 184A (1926).Google Scholar
  81. 81.
    Plumb, H. H. and G. Cataland. Metrologia, 2, 127 (1966).CrossRefGoogle Scholar
  82. 82.
    Plumb, H. H. and G. Cataland, to be published.Google Scholar
  83. 83.
    Pomeranchuk, I., Zh. Eksp. Teor. Fiz. 20, 919 (1950).Google Scholar
  84. 84.
    Rogers, J. S., R. J. Tainsh, M. S. Anderson and G. A. Swenson. Metrologia, 4, 47 (1968).CrossRefGoogle Scholar
  85. 85.
    Rose-Innes, A. C., Low Temperature Techniques, English Universities Press: London (1964).Google Scholar
  86. 86.
    Roubeau, P., D. Le Fur and E. J. A. Varoquaux, in Proceedings of the Third International Cryogenic Engineering Conference, Berlin, p 315. Iliffe: Guildford, UK (1970).Google Scholar
  87. 87.
    Roubeau, P. and E. J. A. Varoquaux. Cryogenics, 10, 255 (1970).CrossRefGoogle Scholar
  88. 88.
    Rubin, L. G. and W. N. Lawless. Rev. Sci. Instrum. 42, 571 (1971).CrossRefGoogle Scholar
  89. 89.
    Sarwinski, R. E., UTS*, p 48.Google Scholar
  90. 90.
    Schooley, J. F. and R. J. Soulen. Fifth Symposium on Temperature†, p 169.Google Scholar
  91. 91.
    Scott, R. B. (Ed.). Technology and Uses of Liquid Hydrogen, Macmillan: New York (1964).Google Scholar
  92. 92.
    Scribner, R. A., M. F. Panczyk and E. D. Adams. J. Low Temp. Phys. 1, 313 (1969).CrossRefGoogle Scholar
  93. 93.
    Sherman, R. H., Proceedings of the Tenth International Conference on Low Temperature Physics, Vol. I, p 188. (Malkov, M. P., Ed.), VENETE: Moscow (1967).Google Scholar
  94. 94.
    Sites, J. R., D. D. Osheroff, R. C. Richardson and D. M. Lee. Phys. Rev. Letters, 23, 836 (1969).CrossRefGoogle Scholar
  95. 95.
    Sites, J. R., H. A. Smith and W. A. Steyert. J. Low Temp. Phys. 4, 605 (1971).CrossRefGoogle Scholar
  96. 96.
    Shore, F. J, V. L. Sailor, H. Marshak and G. A. Reynolds. Rev. Sci. Instrum. 31, 970 (1960).CrossRefGoogle Scholar
  97. 97.
    Sommers, H. S., W. E. Keller and J. G. Dash. Phys. Rev. 92, 1345 (1953).CrossRefGoogle Scholar
  98. 98.
    Steyert, W. A., Rev. Sci. Instrum. 38, 964 (1967).CrossRefGoogle Scholar
  99. 99.
    Steyert, W. A., UTS*, p 90.Google Scholar
  100. 100.
    Steyert, W. A., private communication.Google Scholar
  101. 101.
    Stolfa, D. L. and J. M. Goodkind. UTS*, p 120.Google Scholar
  102. 102.
    Suomi, M., A. G. Anderson and B. Holmstrom. Physica, 38, 67 (1968).CrossRefGoogle Scholar
  103. 103.
    Swenson, G. A. CRC Crit. Rev. Solid State Sciences, 1, 99 (1970).CrossRefGoogle Scholar
  104. 104.
    Sydoriak, S. G. and T. R. Roberts. Phys. Rev. 118, 901 (1960).CrossRefGoogle Scholar
  105. 105.
    Symko, O. G., J. Low Temp. Phys. 1, 451 (1969).CrossRefGoogle Scholar
  106. 106.
    Taylor, R. D., Fifth Symposium on Temperature, p. 1259.Google Scholar
  107. 107.
    Ter Harmsel, H., Thesis, Leiden (1966).Google Scholar
  108. 108.
    Ter Harmsel, H., H. Van Dijk and M. Durieux. Physica, 33, 503 (1967).CrossRefGoogle Scholar
  109. 109.
    Tiggelman, J. L. and M. Durieux. Fifth Symposium on Temperature†, p 849.Google Scholar
  110. 110.
    van Rijn, G. and M. Durieux. Fifth Symposium on Temperature†, p 73.Google Scholar
  111. 111.
    Wagner, R. R. and B. Bertman. Paper T-2 presented at Commission I, International Institute of Refrigeration, Tokyo (1970).Google Scholar
  112. 112.
    Wallace, B. and H. Meyer. Phys. Rev. A2, 1563 (1970).CrossRefGoogle Scholar
  113. 113.
    Walstedt, R. E., E. L. Hahn, G. Froidevaux and E. Geissler. Proc. Roy. Soc. A, 284, 499 (1965).CrossRefGoogle Scholar
  114. 114.
    Wansink, D. H. N. and K. E. Taconis. Physica, 23, 125 (1957).CrossRefGoogle Scholar
  115. 115.
    Wheatley, J. G, R. E. Rapp and R. T. Johnson. J. Low Temp. Phys. 4, 1 (1971).CrossRefGoogle Scholar
  116. 116.
    Wheatley, J. G, D. E. Vilches and W. R. Abel. Physics, 4, 1 (1968).Google Scholar
  117. 117.
    Wiebes, J., Thesis, Leiden (1969).Google Scholar
  118. 118.
    Wilks, J., Liquid and Solid Helium, Clarendon Press: Oxford (1967).Google Scholar
  119. 119.
    Wilson, M. F., D. O. Edwards and J. T. Tough. Phys. Rev. Letters, 19, 1368 (1967).CrossRefGoogle Scholar
  120. 120.
    Wilson, M. F., D. O. Edwards and J. T. Tough. Rev. Sci. Instrum., 39, 134 (1968).CrossRefGoogle Scholar
  121. 121.
    Wilson, M. F. and J. T. Tough. Phys. Rev. 1A, 914 (1970).CrossRefGoogle Scholar
  122. 122.
    Zimmerman, J. E., P. Thiene and J. T. Harding. J. Appl. Phys. 41, 1572 (1970).Google Scholar
  123. 123.
    Zinov’eva, K. N., as reported at the Grenoble Helium Conference (March 1970).Google Scholar

Copyright information

© Springer Science+Business Media New York 1968

Authors and Affiliations

  • William E. Keller
    • 1
  1. 1.Los Alamos Scientific LaboratoryUniversity of CaliforniaNew MexicoUSA

Personalised recommendations