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The Production of Low Temperatures Down to Hydrogen Temperature

  • Chapter
Low Temperature Physics I / Kältephysik I

Part of the book series: Encyclopedia of Physics / Handbuch der Physik ((HDBPHYS,volume 3 / 14))

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Abstract

The purpose of this article is to give the fundamental physical principles involved in the many techniques for the production of low temperatures down to temperatures attainable with liquid hydrogen. In carrying through this aim, emphasis is laid on the evolution and establishment of new ideas and methods. However, it is not my purpose to detail the technological and mechanical developments attendant on each process of refrigeration, which can be found more suitably in engineering publications. In other words, each process of refrigeration is treated at the stage in which it was or is a problem in physics laboratories; but those aspects of the techniques which are concerned with their engineering or commercial development are omitted.

A condensed bibliography of the most essential books on the subject is given at the end of the Preface.

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References

  1. J. A. Ewing: The Mechanical Production of Cold. Cambridge Univ. Press 1908. A classic giving detailed references to 19th century work.

    Google Scholar 

  2. M. and B. Ruhemann: Low Temperature Physics. Cambridge Univ. Press 1937. Chap. I, Part I, gives an historical picture of the development of low temperature physics.

    Google Scholar 

  3. H. Lenz: Handbuch der Experimentalphysik, vol. IX/I, p. 47. 1929. Liquefaction of gases and its thermodynamical foundation. Good account of early work on Joule-Thomson expansion.

    Google Scholar 

  4. W. Meissner: Handbuch der Physik, vol. XI, p. 272. 1926. Production of low temperatures and the liquefaction of gases. Excellent survey of the field to 1926.

    Google Scholar 

  5. M. Ruhemann: The separation of gases. Oxford Press 1940. Chap. V gives good outline of refrigeration to low temperatures.

    Google Scholar 

  6. J. A. van Lammeren: Technique of Low Temperatures. Springer 1941. Besides detailing methods of production of low temperatures, this gives a useful chapter on cryostats and a full bibliography.

    Google Scholar 

  7. M. Davies: The physical principles of gas liquefaction and low temperature rectification. Longmans Green & Co. 1949. A short but authoritative book from a modern standpoint.

    Google Scholar 

  8. H. Hausen: Wärmeübertragung in Gegenstrom, Gleichstrom and Kreuzstrom. A detailed account of interchangers, regenerators, etc.

    Google Scholar 

  9. R. Plank: Handbuch der Kältetechnik, vol. I. Springer 1954. Excellent historical article.

    Google Scholar 

  10. H. J. Macintire and F. W. Hutchinson: Refrigeration Engineering. Wiley & Sons Inc. 1937. Good text from engineering point of view of refrigeration to — 50° C.

    Google Scholar 

  11. See R. Plank: Handbuch der Kältetechnik, vol. I., Berlin: Springer 1954.

    Google Scholar 

  12. See J. A. Ewing: The Mechanical Production of Cold. Cambridge Univ. Press 1908.

    Google Scholar 

  13. J. W. L. Köhler and C. O. Jonkers: Philips Techn. Rev. 16, 69, 105 (1954).

    Google Scholar 

  14. G. J. Ranque: Bull, bi-mensuel Soc. Française de Phys. June 2, 1933, p. 112. Publication bound with J. Phys. Radium (7) 4 (1933). See also, for example, U.S. Patent No. 1952281. Dec. 6, 1932.

    Google Scholar 

  15. R. Hilsch: Z. Naturforsch. 1, 203 (1946). English translation in Rev. Sci. Inst. 18, 108 (1947).

    ADS  Google Scholar 

  16. A. F. Johnson: Canad. J. Res. F 25, 299 (1947).

    Google Scholar 

  17. K. Elser and M. Hoch: Z. Naturforsch. 6a, 25 (1951).

    ADS  Google Scholar 

  18. R. MacGee jr.: Refrig. Engng. 58, 975 (1950).

    Google Scholar 

  19. For a full bibliography see W. Curley and R. MacGee Jr.: Refrig. Engng. 59, 166 (1951).

    Google Scholar 

  20. See M. P. Blaher: J. Sci. Instrum. 27, 168 (1950) for a neat construction using plastics.

    ADS  Google Scholar 

  21. R. Hilsch: Z. Naturforsch. 1, 203 (1946).

    ADS  Google Scholar 

  22. A. F. Johnson: Canad. J. Res. F 25, 299 (1947).

    Google Scholar 

  23. K. Elser and M. Hoch: Z. Naturforsch. 6a, 25 (1951).

    ADS  Google Scholar 

  24. D. ter Haar and H. Wergeland: Forh. Kong. Norske. Vid. Selskat. 20, 55 (1947).

    Google Scholar 

  25. G. Burkhardt: Z. Naturforsch. 3a, 46 (1948).

    ADS  MATH  Google Scholar 

  26. J. A. Prins: Nederl. Tijdschr. Natuurk. 14, 241 (1948).

    Google Scholar 

  27. D. S. Webster: Refrig. Engng. 58, 163 (1950).

    Google Scholar 

  28. C. D. Fulton: Refrig. Engng. 58, 473 (1950).

    Google Scholar 

  29. G. W. Sheper: Refrig. Engng. 59, 985 (1951).

    Google Scholar 

  30. J. J. van Deemter: Appl. Sci. Res. A 3, 174 (1952).

    Google Scholar 

  31. See W. Curley and R. MacGee Jr.: Refrig. Engng. 59, 166 (1951) for a fuller bibliography.

    Google Scholar 

  32. J. Gorrie: US Patent 8080. May 1851. See also

    Google Scholar 

  33. W. Siemens: Min. Proc. Instn. Civ. Engrs. 68, 179 (1882).

    Google Scholar 

  34. A. Kirk: Min. Proc. Instn. Civ. Engrs. 37, 244 (1873/74).

    Google Scholar 

  35. See J. A. Ewing: Mechanical Production of Cold. Cambridge Univ. Press 1908 and

    Google Scholar 

  36. R. Plank: Handbuch der Kältetechnik, vol. I. Berlin: Springer 1954.

    Google Scholar 

  37. J. W. L. Köhler and C. O. Jonkers: Philips Techn. Rev. 16, 69, 105 (1954).

    Google Scholar 

  38. G. Claude: Liquid Air, Oxygen and Nitrogen. Paris 1913. See also section G.

    Google Scholar 

  39. See Rinia, du Pré, de Brey and van Weenen: Philips Techn. Rev. 8, 2, 129 (1946),

    Google Scholar 

  40. See Rinia, du Pré, de Brey and van Weenen: Philips Techn. Rev. 9, 97, 125 (1947).

    Google Scholar 

  41. J. W. H. Köhler and C. O. Jonkers: Philips Techn. Rev. 16, 69 (1954).

    Google Scholar 

  42. J. Perkins: English Patent No. 6662, 1834. See also “Mechanical production of cold” by J. A. Ewing. Cambridge Univ. Press 1908.

    Google Scholar 

  43. See, for example, R. Plank: Handbuch der Kältetechnik, vol I. Berlin: Springer 1954.

    Google Scholar 

  44. See, for example, K. v. Linde: English Patent No. 1458 (1876) and see also

    Google Scholar 

  45. R. Plank: Handbuch der Kältetechnik, vol. I. Berlin: Springer 1954.

    Google Scholar 

  46. R. Pictet: C. R. Acad. Sci. Paris 85, 1214, 1220 (1877) and see also

    Google Scholar 

  47. R. Plank: Handbuch der Kältetechnik, vol. I. Berlin: Springer 1954.

    Google Scholar 

  48. R. Mollier: Z. ges. Kälteind. 3 (1896), which paper gives the T-S diagram for CO2.

    Google Scholar 

  49. The pioneer thermodynamic analysis was carried out by K. v. Linde (Z. ges. Kälteind. 28. Jan. 1895 and Z. VDI 2. Febr. 1895) and may be studied in detail in many textbooks on Refrigeration Engineering as for example: J. A. Ewing: „The Mechanical Production of Cold“, Cambridge Univ. Press 1908;

    Google Scholar 

  50. M. Davies: “The Physical Principles of Gas Liquefaction and Low Temperature Rectification”, Longmans, Green & Co. 1949;

    Google Scholar 

  51. R. G. Owens and F. Ophuls: ASRE Refrigerating Data Book, 7th Ed. 1951, Part I, p. 3 and p. 11.

    Google Scholar 

  52. ASRE Refrigerating Data Book, 7th Ed., Part II, p. 105 and ff. 1951.

    Google Scholar 

  53. Publications of Kinetic Chemicals Inc. Wilmington Delaware. (Colored Charts may be obtained from this company.)

    Google Scholar 

  54. R. and H. Chemicals Dept. E. I. du Pont de Nemours Co. Wilmington. Delaware. (Charts may be obtained from this company.)

    Google Scholar 

  55. ASRE Circular No. 12. Publ. Amer. Soc. Refrig. Engng. 40 W. 40 St. New York, N. Y.

    Google Scholar 

  56. D. F. Rynning and C. O. Hurd: Trans. Amer. Inst. Chem. Engr. 41, 465 (1945).

    Google Scholar 

  57. Nat. Bur. Stand., Circular 1923, No. 142.

    Google Scholar 

  58. W. H. Keesom and D. J. Houthoff: Leiden Comm. Suppl. 65a, b (1928).

    Google Scholar 

  59. Dana, Jenkins, Burdick and Timm: Refrig. Engng. 12, 403 (1926).

    Google Scholar 

  60. R. York and E. F. White: Trans. Amer. Inst. Chem. Engr. 40, 227 (1944).

    Google Scholar 

  61. R. W. Waterfill: Industr. Engng. Chem. 24, 616 (1932).

    Google Scholar 

  62. H. J. MacIntire and F. W. Hutchinson: Refrigerating Engineering. New York: J. Wiley & Sons 1950.

    Google Scholar 

  63. W. H. Keesom, A. Bijl and L. A. J. Monte: Leiden Comm. Suppl. 108b (1954) and Appl. Sci. Res. 4, 25 (1954).

    Google Scholar 

  64. Barkelew, Valentine and Hurd: Trans. Amer. Inst. Chem. Engr. 43, 25 (1947).

    Google Scholar 

  65. C. S. Matthews and C. O. Hurd: Trans. Amer. Inst. Chem. Engr. 42, 55 (1946).

    Google Scholar 

  66. Such diagrams were first introduced by R. Mollier: Z. VDI 48, 271 (1904). Diagrams of p - H, which are also of value in determining the characteristics of refrigerators, etc., and which were also introduced by Mollier, are referred to also as Mollier diagrams.

    Google Scholar 

  67. R. Mollier: Z. VDI 48, 271 (1904). For references to such diagrams for common refrigerating substances see Table 3.

    Google Scholar 

  68. F. Ophuls: ASRE Refrigerating Data Book, 7th Ed., Part. I, p. 11. 1951.

    Google Scholar 

  69. Some of this data is taken from L. S. Morse. 7th Int. Cong. Refrig. 3, 718 (1937).

    Google Scholar 

  70. Enthalpy measured from -40° C.

    Google Scholar 

  71. For ideal Carnot cycle operating between these temperatures, ξ max = 5.75. A value of ξ = 1 corresponds to an efficiency of 0.212 “tons” per h.p.

    Google Scholar 

  72. See E. Griffiths and J. H. Asbery: Proc. Brit. Assoc. Refrig. Mar. 1925 for references to early literature.

    Google Scholar 

  73. W. H. Keesom: Leiden Comm. Suppl. 76 a (1933).

    Google Scholar 

  74. R. Plank: Z. ges. Kälteind. 47, 81 (1940).

    Google Scholar 

  75. In refrigerating engineering the common unit of refrigerating capacity is the “ton”, derived from the average rate of heat absorption required to freeze 2000 lbs. (1 ton) of ice from water at the melting point every twenty four hours. The “ton” therefore is equivalent to 840 cals/sec. or 200 b.t.u./min. It is common also to express the coefficient of performance, in “tons” per horse-power. A value of ξ = 1 corresponds to 0.212 “tons”/h.p.

    Google Scholar 

  76. M. Davies: The physical principles of gas liquefaction and low temperature rectification. London: Longmans, Green & Co. 1949.

    Google Scholar 

  77. T. Midgley and A. L. Henne: Industr. Engng. Chem. 22, 542 (1930). See also

    Google Scholar 

  78. R. J. Thompson: Industr. Engng. Chem. 24, 620 (1932) for further early description.

    Google Scholar 

  79. See for example T. Midgley: J. Industr. Engng. Chem., Feb. 1937, and publications of Kinetic Chemicals (E. I. duPont de Nemours and Company).

    Google Scholar 

  80. See also publications of R. and H. Chemical Dept. E. I. du Pont de Nemours and Company.

    Google Scholar 

  81. See for example N. R. Sparks: Theory of Mechanical Refrigeration. New York: McGraw Hill (1938) for a discussion of the relative efficiencies of multi-stage compression, single expansion, systems.

    Google Scholar 

  82. See for example H. E. Rex: Refrig. Engng. 58, 566 (1950).

    Google Scholar 

  83. W. H. Keesom: Leiden Comm. Suppl. 76a (1933).

    Google Scholar 

  84. H. Kamerlingh-Onnes: Leiden Comm. 14 (1894); 87 (1903). H. Kamerlingh-Onnes: Leiden Comm. Suppl. 35 (1913). See also C. A. Crommelin: Leiden Comm. Suppl. 45 (1922).

    Google Scholar 

  85. W. H. Keesom: Leiden Comm. Suppl. 76a (1933).

    Google Scholar 

  86. A. Huguenin: Festschrift zum 70. Geburtstag von Prof. A. Stodola, p. 272, Zürich 1929.

    Google Scholar 

  87. See also R. Plank: Handbuch der Kältetechnik, Vol. I. 1954.

    Google Scholar 

  88. R. Pictet: C. R. Acad. Sci. Paris 85, 1214, 1220 (1877).

    Google Scholar 

  89. R. Pictet: C. R. Acad. Sci. Paris 85, 1214, 1220 (1877).

    Google Scholar 

  90. K. Olszewski: Ann. Phys. u. Chem. 31, 58 (1887). See also Phil. Mag. 39, 188 (1895).

    ADS  Google Scholar 

  91. J. Dewar: Proc. Roy. Inst., June 1886. — Phil. Mag. 39, 298 (1895).

    Google Scholar 

  92. H. Kamerlingh-Onnes: Leiden Comm. 14 (1894); 87 (1903). — Leiden Comm. Suppl. 35 (1913). See also C. A. Crommelin: Leiden Comm. Suppl. 45 (1922).

    Google Scholar 

  93. W. H. Keeson: Leiden Comm. Suppl. 76a (1933). + Bath of CO2 “snow” and ether was employed. * An attempt to liquefy the 02 by expansion at a valve after cooling to about 143° K was made. Only a “mist” emerged.

    Google Scholar 

  94. K. Olszewski: Ann. Phys. u. Chem. 31, 58 (1887). See also Phil. Mag. 39, 188 (1895) for a review of their work.

    ADS  Google Scholar 

  95. J. Dewar: Proc. Roy. Inst., June 1886. — Phil. Mag. 39, 298 (1895).

    Google Scholar 

  96. H. Kamerlingh-Onnes: Leiden Comm. 14 (1894); 87 (1903). — Leiden Comm. Suppl. 35 (1913). See also C. A. Crommelin: Leiden Comm. Suppl. 45 (1922).

    Google Scholar 

  97. J. P. Joule and W. Thomson: Phil. Mag. 4, 481 (1852). (William Thomson assumed the name of Lord Kelvin in 1892.)

    Google Scholar 

  98. J. P. Joule: Sci. Pap. 2, 216.

    Google Scholar 

  99. See for example J. K. Roberts and A. R. Miller: Heat and Thermodynamics, p. 105. London: Blackie & Son 1951.

    Google Scholar 

  100. Some representative experimental work has been done by the following authors. K. Olszewski: Ann. Phys. 7, 818 (1902) on H2.

    Google Scholar 

  101. F. E. Rester: Phys. Rev. 21, 260 (1905) on CO2.

    ADS  Google Scholar 

  102. K. Olszewski: Phil. Mag. 13, 722 (1907) on air and N2.

    Google Scholar 

  103. W. P. Bradley and C. F. Hale: Phys. Rev. 29, 258 (1909) on air.

    ADS  Google Scholar 

  104. J. Dalton: Leiden Comm. 109c (1909) on air.

    Google Scholar 

  105. F. Noell: Forsch. Ing.-Wes. 184 (1916) on air.

    Google Scholar 

  106. L. C. Hoxton: Phys. Rev. 13, 438 (1919) on air.

    ADS  Google Scholar 

  107. E. S. Burnett: Phys. Rev. 22, 590 (1923) on CO2.

    ADS  Google Scholar 

  108. J. R. Roebuck: Proc. Amer. Acad. Arts Sci 60, 537 (1925) on air.

    Google Scholar 

  109. N. Eumorfopoulos and J. Rai: Phil. Mag. 2, 961 (1926) on air.

    Google Scholar 

  110. H. Hausen: Forsch. Ing.-Wes. 274 (1926) on air.

    Google Scholar 

  111. J. R. Roebuck: Proc. Amer. Acad. Arts Sci. 64, 287 (1930) on air.

    Google Scholar 

  112. J. R. Roebuck and H. Osterberg: Phys. Rev. 43, 60 (1933) on He.

    ADS  Google Scholar 

  113. J. R. Roebuck and H. Osterberg: Phys. Rev. 46, 785 (1934) on A.

    ADS  Google Scholar 

  114. J. R. Roebuck and H. Osterberg: Phys. Rev. 48, 450 (1935) on N2.

    ADS  Google Scholar 

  115. J. L. Zelmanov: J. Phys. USSR. 3, 42 (1940) on He.

    Google Scholar 

  116. Roebuck, Murrell and Miller: J. Amer. Chem. Soc. 64, 400 (1942) on CO2.

    Google Scholar 

  117. Johnston, Bezman and Hood: J. Amer. Chem. Soc. 68, 2367 (1946) on H2.

    Google Scholar 

  118. Johnston, Swansen and Wirth: J. Amer. Chem. Soc. 68, 2373 (1946) on D2.

    Google Scholar 

  119. Charnley, Isles and Townley: Proc. Roy. Soc. Lond., Ser. A 218, 133 (1953) on N2, C2H4, CO2, N2O. — For a detailed review of the experimental work up to 1929 see

    ADS  Google Scholar 

  120. H. Lenz, Handbuch der Experimentalphysik, vol. 9/1, p. 47, 1929 and

    MathSciNet  Google Scholar 

  121. A. Eucken, Handbuch der Experimentalphysik, vol. 8/1, p. 511, 1929.

    Google Scholar 

  122. H. Hausen: Forsch. Ing.-Wes. 274, 1 (1926).

    Google Scholar 

  123. J. R. Roebuck and H. Osterberg: Phys. Rev. 48, 450 (1935).

    ADS  Google Scholar 

  124. J. R. Roebuck: Proc. Amer. Acad. Arts Sci. 64, 287 (1930).

    Google Scholar 

  125. * Calculated. See E. F. Hammel: J. Chem. Phys. 18, 228 (1950).

    ADS  Google Scholar 

  126. Owing to the paucity of adequate data this value is not too accurate. See W. H. Keesom: Helium. Amsterdam: Elsevier 1942.

    Google Scholar 

  127. * Meissner [Z. Physik 18, 12 (1923)] used the following values: p c = 12.80 atm., T c = 33 18°K, r = 3.276, obtained by Kamerlingh-Onnes, Crommelin and Cath [Leiden Comm. 151c (1917)]. Woolley, Scott and Brickwedde [J. Res. Nat. Bur. Stand. 41, 379 (1948)] give the following values: p c = 12.98 atm.; T c = 33.19° K, and r = 3.13.

    Google Scholar 

  128. ** These data come from Zelmanov’s work [J. Phys. USSR. 3, 43 (1940)].

    Google Scholar 

  129. M. Jacob: Phys. Z. 22, 65 (1921).

    Google Scholar 

  130. J. R. Roebuck and H. Osterberg: Phys. Rev. 46, 785 (1934).

    ADS  Google Scholar 

  131. J. de Boer et al.: Physica, Haag 14, 139, 149, 520 (1948).

    ADS  Google Scholar 

  132. Woolley, Scott and Brickwedde: J. Res. Nat. Bur. Stand. 41, 379 (1948).

    Google Scholar 

  133. J. L. Zelmanov: J. Phys. USSR. 3, 43 (1940). This work superceeds the earlier work of Keesom and Houthoff: Leiden Comm. Suppl. 65f (1928).

    Google Scholar 

  134. See J. K. Roberts and A. R. Miller: Heat and Thermodynamics, p. 105. London: Blackie & Son 1951.

    Google Scholar 

  135. For a van der Waals gas, the inversion temperature, T i , defined as that where α h = 0 for p → 0, is such that T i = 2T Boyle.

    Google Scholar 

  136. H. Hausen: Z. techn. Phys. 7, 444 (1926).

    Google Scholar 

  137. T - S and H - S diagrams for air due to Hausen: Forsch. Ing.-Wes. 274, 1 (1926).

    Google Scholar 

  138. T - S diagram for H2 due to Woolley, Scott and Brickwedde: J. Res. Nat. Bur. Stand. 41, 379 (1948).

    Google Scholar 

  139. T - S diagram for He due to Zelmanov: J. Phys. USSR. 8, 129 (1944). — For thermodynamic properties of O2 and N2 see for example U.S. Bur. Mines Paper 424, 1928.

    Google Scholar 

  140. See curves of Figs. 39, 40 and 41.

    Google Scholar 

  141. For tabulations of enthalpy see for example: for air Hausen [Forsch. Ing.-Wes. 274 (1926)]. For H2 see Woolley et al [J. Res. Nat. Bur. Stand. 41, 379 (1948)]). For He see S. W. Akin [Trans. Amer. Soc. Mech. Engrs. 72, 751 (1950)]. See also Table 10.

    Google Scholar 

  142. K. v. Linde: German patent 88 824 and Z. ges. Kälteind. 4, 23 (1897)- See also The Engineer. Nov. 13. and 20. 1896.

    Google Scholar 

  143. Hampson: May 1895. English Patent, 10165.

    Google Scholar 

  144. W. Siemens: English Patent, No. 2064. 1857. See also Min. Proc. Inst. Civ. Engrs. 68, 179 (1882).

    Google Scholar 

  145. If the compressed air is treated as a perfect gas, then for isothermal compression (math).

    Google Scholar 

  146. W. Meissner: Z. Physik 18, 12 (1923).

    ADS  Google Scholar 

  147. Woolley, Scott and Brickwedde: J. Res. Nat. Bur. Stand. 41, 379 (1948).

    Google Scholar 

  148. Zelmanov: J. Phys. USSR. 3, 43 (1940).

    Google Scholar 

  149. Johnston, Bezman and Hood: J. Amer. Chem. Soc. 68, 2367 (1946).

    Google Scholar 

  150. R. Linde: Z. VDI 65, 1357 (1921).

    Google Scholar 

  151. Data taken from R. Linde: Z. VDI 65, 1357 (1921).

    Google Scholar 

  152. H. Lenz: Handbuch der Experimentalyphisk, vol. 9/1, p. 127. 1929; see also

    Google Scholar 

  153. M. Davies: Gas Liquefaction and Rectification. London: Longmans 1949.

    Google Scholar 

  154. M. Ruhemann: Gas Separation. Oxford Press 1940.

    Google Scholar 

  155. Johnston, Bezman and Hood: J. Amer. Chem. Soc. 68, 2367 (1946).

    Google Scholar 

  156. Keyes, Gerry and Hicks: J. Amer. Chem. Soc. 59, 1426 (1937).

    Google Scholar 

  157. Keesom and Houthoff: Leiden Comm. 65 (1928).

    Google Scholar 

  158. For very complete details of the exact sizes of tubing, dimensions of the apparatus see, for example, K. Olszewski: Ann. Phys. 10, 768 (1903).

    Google Scholar 

  159. See for example I. Roberts: Refrig. Engng. 60, 950 (1952).

    Google Scholar 

  160. See for example ref. 1 above; A. M. Clark: Bull. Inst. Internat. Froid. Annexe 1954, p. 2, 39. R. Schlatterer: Bull. Inst. Internat. Froid. Annexe 1954, p. 2, 21.

    Google Scholar 

  161. B. H. van Dyke: Steel 123, 103 (1948). —

    Google Scholar 

  162. B. H. van Dyke: Chem. Eng. News. 54, 126 (1947).

    Google Scholar 

  163. For example, the so-called Linde-Frankl system as reported by Hochgesand, Mitt. Forsch. Anst. GHH Konzern. 4, Part 1 (1935), and by J. Wucherer, Iron Coal Tr. Rev. 159, 723 (1949).

    Google Scholar 

  164. J. Dewar: J. Chem. Soc. 73, 529 (1898).

    Google Scholar 

  165. J. Dewar: C. R. Acad. Sci. Paris 126, 1408 (1898). —

    Google Scholar 

  166. J. Dewar: Proc. Roy. Soc. Lond. 63, 256 (1898).

    Google Scholar 

  167. F. G. Brickwedde: Ohio State Univ. Eng. Exp. Station, News 18, No. 3, 30 (1946).

    Google Scholar 

  168. M W. Travers: Phil. Mag. 1, 411 (1901), see also „Experimental Study of Gases“, p. 198, New York: MacMillan & Co. 1901, and Encyclopedia Britannica 14, 184 also by Travers.

    Google Scholar 

  169. For description of others see for example K. Olszewski: Ann. Phys. 10, 773 (1903). — Bull. int. Acad. Cracovie 1908, 389; 1912.

    Google Scholar 

  170. See also Lilienfeld: Z. kompr. flüss. Gase 13, 186 (1911).

    Google Scholar 

  171. H. Kamerlingh-Onnes: Leiden Comm. 94 (1906).

    Google Scholar 

  172. H. Kamerlingh-Onnes (Posthumous publication): Leiden Comm. 158 (1926). — C. A. Crommelin: Leiden Comm. Suppl. 45 (1922).

    Google Scholar 

  173. J. C. McLennan: Roy. Soc. Can. Trans. 15, 31 (1931).

    Google Scholar 

  174. J. C. McLennan and G. M. Shrum: Roy. Soc. Can. Trans. 16, 181 (1922).

    Google Scholar 

  175. W. Meissner: Phys. Z. 29, 610 (1928).

    MathSciNet  Google Scholar 

  176. Jones, Larsen and Simon: Research 1, 420 (1948).

    Google Scholar 

  177. K. Clusius: Z. Naturforsch. 8, 479 (1953).

    ADS  Google Scholar 

  178. R. Spoendlin: J. Res. CNRS. 28, 1 (1954).

    Google Scholar 

  179. R. Spoendlin: J. Res. CNRS. 3, 309 (1951).

    Google Scholar 

  180. De Modernisering van het Kamerlingh Onnes Laboratorium te Leiden. 1953.

    Google Scholar 

  181. Private communication from Prof. K. W. Taconis.

    Google Scholar 

  182. † The liquefaction coefficient, e, given in this table may in some instances refer to the rate of provision of liquid H2 outside the liquéfier. For such situations the transfer loss must be known, before comparison of ε with theory can be made.

    Google Scholar 

  183. * Vapor pressure of 2 mm for precooling bath stated only.

    Google Scholar 

  184. ** Compressor displacement only quoted.

    Google Scholar 

  185. Travers: Phil. Mag. 1, 411 (1901).

    Google Scholar 

  186. K-Onnes: Leiden Comm. 94 f (1906).

    Google Scholar 

  187. Olzewski: Krakauer Anz. 1912.

    Google Scholar 

  188. K-Onnes: Leiden Comm. 158 (1926); Suppl. 45 (1922).

    Google Scholar 

  189. Meissner: Phys. Z. 29, 610 (1928).

    MathSciNet  Google Scholar 

  190. Blanchard and Bittner: Rev. Sci. Instrum. 13, 394 (1942).

    ADS  Google Scholar 

  191. Jones, Larsen and Simon: Research 1, 420 (1948).

    Google Scholar 

  192. Clusius: Z. Naturforsch. 8, 479 (1953).

    ADS  Google Scholar 

  193. Spoendlin: J. Res. CNRS. 28, 1 (1954).

    Google Scholar 

  194. Gorter: De Modernisering van het Kamerlingh-Onnes Laboratorium te Leiden. 1953.

    Google Scholar 

  195. E. R. Blanchard and H. W. Bittner: Rev. Sci. Instrum. 13, 394 (1942).

    ADS  Google Scholar 

  196. W. Meissner: Phys. Z. 29, 610 (1928).

    MathSciNet  Google Scholar 

  197. Jones, Larsen and Simon: Research 1, 420 (1948).

    Google Scholar 

  198. C. B. Hood and E. R. Grilly: Rev. Sci. Instrum. 23, 357 (1952).

    ADS  Google Scholar 

  199. H. Kamerlingh-Onnes: Leiden Comm. 94 f. (1906).

    Google Scholar 

  200. P. Kapitza and J. D. Cockroft: Nature, Lond. 129, 224 (1932).

    ADS  Google Scholar 

  201. E. R. Blanchard and H. W. Bittner: Rev. Sci. Instrum. 13, 394 (1942).

    ADS  Google Scholar 

  202. H. M. Huffman: Chem. Rev. 40, 1 (1947).

    Google Scholar 

  203. K. Clusius: Z. ges. Kälteind. 39, 94 (1932).

    Google Scholar 

  204. C. B. Hood and E. R. Grilly: Rev. Sci. Instrum. 23, 357 (1952).

    ADS  Google Scholar 

  205. E. Cremer and M. Polanyi: Z. phys. Chem., Abt. B 21, 459 (1933).

    Google Scholar 

  206. Scott, Brickwedde, Urey and Wahl: J. Chem. Phys. 2, 454 (1934).

    ADS  Google Scholar 

  207. Larsen, Simon and Swenson: Rev. Sci. Instrum. 19, 266 (1948).

    ADS  Google Scholar 

  208. E. R. Grilly: Rev. Sci. Instrum. 24, 1 (1953).

    ADS  Google Scholar 

  209. Jones, Larsen and Simon: Research 1, 420 (1948).

    Google Scholar 

  210. E. R. Grilly: Rev. Sci. Instrum. 24, 1 (1953).

    ADS  Google Scholar 

  211. W. Nernst: Z. Elektrochem. 17, 735 (1911)- See

    Google Scholar 

  212. J. E. Lilienfeld: Z. kompr. fliiss. Gase 13, 165 (1911).

    Google Scholar 

  213. W. M. Latimer: J. Amer. Chem. Soc. 44, 90 (1922).

    Google Scholar 

  214. Latimer, Buffington and Hoenshel: J. Amer. Chem. Soc. 47, 1571 (1925).

    Google Scholar 

  215. M. Ruhemann: Z. Physik 65, 67 (1930).

    ADS  Google Scholar 

  216. Keyes, Gerry and Hicks: J. Amer. Chem. Soc. 59, 1426 (1937).

    Google Scholar 

  217. Ahlberg, Estermann and Lundberg: Rev. Sci. Instrum. 8, 422 (1937).

    ADS  Google Scholar 

  218. H. A. Fairbanks: Rev. Sci. Instrum. 17, 473 (1946).

    ADS  Google Scholar 

  219. De Sorbo, Milton and Andrews: Chem. Rev. 39, 403 (1946).

    Google Scholar 

  220. F. R. Bichowsky: J. Ind. Chem. Soc. 14, 62 (1922).

    Google Scholar 

  221. B. V. Rollin: Proc. Phys. Soc. Lond. 48, 18 (1936).

    ADS  Google Scholar 

  222. K. Seiler: Ann. Phys. 39, 129 (1941).

    Google Scholar 

  223. A. Schallamach: J. Sci. Instrum. 20, 195 (1943).

    ADS  Google Scholar 

  224. J. Ashmead: Proc. Phys. Soc. Lond. 63, 504 (1950).

    ADS  Google Scholar 

  225. R. Spoendlin: J. Res. CNRS. 28, 1 (1954).

    Google Scholar 

  226. G. Claude: Air liquide, Oxygène, Azote, Gaz rares. Paris 1926.

    Google Scholar 

  227. G. Claude: C. R. Acad. Sci. Paris 134, 1568 (1902).

    Google Scholar 

  228. G. Claude: Liquid air, Nitrogen and Oxygen. Paris 1926.

    Google Scholar 

  229. S. C. Collins: Rev. Sci. Instrum. 18, 157 (1947). See also Collins, Nason and Cannady: Refrig. Engng. 59, No. 12 (1951).

    ADS  Google Scholar 

  230. B. C. P. Hochgesand: Mitt. Forsch. Anst. GHH Konzern 4, Part I (1935).

    Google Scholar 

  231. P. L. Kapitza: J. Phys. USSR. 1, 7 (1939).

    Google Scholar 

  232. M. Davies: The Physical Principles of Gas Liquefaction and Low Temperature Rectification. London: Longmans, Green & Co. 1949.

    Google Scholar 

  233. H. Lenz: Handbuch der Experimentalphysik, Bd. 9/1, p. 135. 1929.

    MathSciNet  Google Scholar 

  234. M. Davies: Physical Principles of gas liquefaction and low temperature rectification. London: Longmans, Green & Co. 1949.

    Google Scholar 

  235. M. Davies: The Physical Principles of Gas Liquefaction and Low Temperature Rectification. London: Longmans Green & Co. 1949.

    Google Scholar 

  236. P. L. Kapitza: J. Phys. USSR. 1, 7 (1939). This was a small machine. For similar machines on a larger scale the power required can be made to approach 1.1 kW-hr/liter liquid.

    Google Scholar 

  237. R. Linde: Z. ges. Kälteind. 41, 183 (1934).

    Google Scholar 

  238. B. C. P. Hochgesand: Mitt. Forsch. Anst. GHH. Konzern 4, Part I (1935). See also: J. Wucherer: Iron and Coal Trades Rev. 159, 723 (1949).

    Google Scholar 

  239. P. L. Kapitza: J. Phys. USSR. 1, 7 (1939)

    Google Scholar 

  240. J. J. Coleman: Min. Proc. Inst. Civ. Engrs. 68 (1882).

    Google Scholar 

  241. E. Solvay: C. R. Acad. Sci. Paris 121, 1141 (1895).

    Google Scholar 

  242. G. Claude: C. R. Acad. Sci. Paris 134, 1568 (1902). See also G. Claude: Liquid Air, Oxygen and Nitrogen. Paris 1926.

    Google Scholar 

  243. This is called by Kapitza [J. Phys. USSR. 1, 7 (1939)] the “technical efficiency”.

    Google Scholar 

  244. Rayleigh: Nature, Lond. 58, 199 (1898).

    ADS  Google Scholar 

  245. Thrupp: English Patent 26767, 1898.

    Google Scholar 

  246. R. Linde: Z. ges. Kälteind. 41, 183 (1934). See also

    Google Scholar 

  247. M. Ruhemann: Separation of Gases. Oxford Univ. Press 1940.

    Google Scholar 

  248. B. C. P. Hochgesand: Mitt. Forsch. Anst. GHH. Konzern 4, Part I (1935).

    Google Scholar 

  249. J. S. Swearingen: Trans. Amer. Inst. Chem. Engr. 43, 85 (1947).

    Google Scholar 

  250. P. Kapitza: J. Phys. USSR. 1, 7, 29 (1939). See also

    Google Scholar 

  251. M. M. Levitin and O. A. Stetzkayov: Avtogennoe. Delo 12, Nr. 5, 25 (1941).

    Google Scholar 

  252. H. Hausen [Z. ges. Kälteind. 48, 24 (1941)] has reinterpreted Kapitza’s data to give an adiabatic efficiency of from 76.5 to 78.5%.

    Google Scholar 

  253. J. S. Swearingen: Trans. Amer. Inst. Chem. Engr. 43, 85 (1947).

    Google Scholar 

  254. J. H. Rushton and E. P. Stevenson: Trans. Amer. Inst. Chem. Engr. 43, 61 (1947).

    Google Scholar 

  255. H. Kottas: Refrig. Engng. 59, 762 (1951).

    Google Scholar 

  256. Bleyle, Hinckley and Jewett: See A. D. Little Inc. reprint.

    Google Scholar 

  257. J. Wucherer: Bull. Inst. Internat. Froid. Annexe 1954, p. 2, 69.

    Google Scholar 

  258. A. Bose: Indian J. Phys. 23, 433 (1949).

    Google Scholar 

  259. P. Kapitza: Nature Lond. 133, 208 (1934). —

    Google Scholar 

  260. P. Kapitza: Proc. Roy. Soc. Lond., Ser. A 147, 189 (1934).

    ADS  Google Scholar 

  261. S. C. Collins: Rev. Sci. Instrum. 18, 157 (1947).

    ADS  Google Scholar 

  262. S. C. Collins: Rev. Sci. Instrum. 18, 157 (1947).

    ADS  Google Scholar 

  263. Collins, Nason and Cannaday: Refrig. Engng. 59, No. 12 (1951). Also private communication from Professor S. C. Collins.

    Google Scholar 

  264. S. C. Collins: Rev. Sci. Instrum. 18, 157 (1947).

    ADS  Google Scholar 

  265. Collins, Nason and Cannaday: Refrig. Engn. 59, No. 12. Also Private Communication from Professor S. C. Collins.

    Google Scholar 

  266. On reversal, the air instaneously in any one channel must be reversed in flow direction. If the quantity of air thus reversed in flow is large compared with the total flow, serious inefficiency is introduced.

    Google Scholar 

  267. W. E. Lobo: Chem. Ind. 59, 53 (1946).

    Google Scholar 

  268. A. D. Little Inc. Hydrogen liquéfier specifications. 1953.

    Google Scholar 

  269. P. L. Kapitza: Nature, Lond. 133, 208 (1934). —

    Google Scholar 

  270. P. L. Kapitza: Proc. Roy. Soc. Lond., Ser. A 147, 189 (1934).

    ADS  Google Scholar 

  271. S. C. Collins: Rev. Sci. Instrum. 18, 157 (1947). —

    ADS  Google Scholar 

  272. S. C. Collins: Science, Lancaster, Pa. 116, 289 (1952).

    ADS  Google Scholar 

  273. W. Meissner: Phys. Z. 43, 261 (1952).

    Google Scholar 

  274. C. T. Lane: Rev. Sci. Instrum. 12, 326 (1941).

    ADS  Google Scholar 

  275. Nicol, Smith, Heer and Daunt: Rev. Sci. Instrum. 24, 16 (1953).

    ADS  Google Scholar 

  276. S. C. Collins: Science, Lancaster. Pa. 116, 298 (1952).

    ADS  Google Scholar 

  277. H. M. Long and F. E. Simon: Nature, Lond. 172, 581 (1953).

    ADS  Google Scholar 

  278. H. M. Long and F. E. Simon: Appl. Sci. Res. A 4, 237 (1954).

    Google Scholar 

  279. H. M. Long and F. E. Simon: Z. Kältetechn. 6, 150 (1954).

    Google Scholar 

  280. L. Cailletet: C. R. Acad. Sci. Paris 85, 1213 (1877).

    Google Scholar 

  281. K. Olszewski: Ann. Phys. u. Chem. 31, 58 (1887). —

    ADS  Google Scholar 

  282. K. Olszewski: Wiener Ber. 95, 1 (1887). See also

    Google Scholar 

  283. K. Olszewski: Phil. Mag. 39, 188 (1895).

    Google Scholar 

  284. F. Simon: Z. ges. Kälteind. 39, 89 (1932).

    Google Scholar 

  285. F. Simon: Also Phys. Z. 34, 232 (1932).

    Google Scholar 

  286. F. Simon and J. E. Ahlberg: Z. Physik 81, 816 (1933).

    ADS  Google Scholar 

  287. See article on “Helium Liquefaction” below by S. C. Collins for fuller details.

    Google Scholar 

  288. Simon, Cooke and Pearson: Proc. Phys. Soc. 47, 678 (1935).

    ADS  Google Scholar 

  289. G. L. Pickard and F. E. Simon: Proc. Phys. Soc. 60, 405 (1948).

    ADS  Google Scholar 

  290. Simon, Cooke and Pearson: Proc. Phys. Soc. 47, 678 (1935).

    ADS  Google Scholar 

  291. G. L. Pickard and F. E. Simon: Proc. Phys. Soc. 60, 405 (1948).

    ADS  Google Scholar 

  292. F. Simon and J. E. Ahlberg: Z. Physik 81, 816 (1933).

    ADS  Google Scholar 

  293. Simon, Cooke and Pearson: Proc. Phys. Soc. 47, 678 (1935).

    ADS  Google Scholar 

  294. J. W. L. Köhler and C. O. Jonkers: Philips techn. Rev. 16, 69, 105 (1954).

    Google Scholar 

  295. H. Kamerlingh-Onnes: Leiden Comm. 14 (1894); 87 (1903); Leiden Comm. Suppl. 35 (1913).

    Google Scholar 

  296. K. v. Linde: Z. ges. Kälteind. 4, 23 (1897).

    Google Scholar 

  297. Hampson: English Patent 10165. 1895.

    Google Scholar 

  298. W. Siemens: English Patent 2064. 1857.

    Google Scholar 

  299. G. Claude: Liquid air, oxygen and nitrogen. Paris 1913.

    Google Scholar 

  300. M. Fränkl: German Patent. 490878. 1928.

    Google Scholar 

  301. S. C. Collins: Chem. Eng. 53, 106 (1946).

    Google Scholar 

  302. K. von Linde: Z. ges. Kälteind. 4, 23 (1897).

    Google Scholar 

  303. See for example. S. C. Collins and F. G. Keyes: J. Phys. Chem. 43, 5 (1939).

    Google Scholar 

  304. Hampson: English Patent 10165. 1895.

    Google Scholar 

  305. J. W. Cook: Bur. Stand. Sci. Papers. 17, No. 419 (1921).

    Google Scholar 

  306. R. Spoendlin: J. Res. CNRS. 15, 1 (1951).

    Google Scholar 

  307. See, for example, the design of W. F. Giauque used by J. G. Daunt and H. L. Johnston. [Rev. Sci. Instrum. 20, 122 (1949).]

    ADS  Google Scholar 

  308. In this section and in Sect. 46 some basic information on heat transfer between fluids and solids is given. For more detail the reader is referred to the many texts on this subject, including for example W. H. McAdams: Heat Transfer. New York: John Wiley & Sons. 1942. —

    Google Scholar 

  309. R. C. L. Bosworth: Heat transfer Phenomena. New York: John Wiley & Sons 1952. —

    MATH  Google Scholar 

  310. M. Jacob and G. A. Hawkines: Elements of Heat Transfer and Insulation. New York: John Wiley & Sons 1950. — Also reference is recommended to the very complete monograph by

    Google Scholar 

  311. H. Hausen: Wärmeübertragung in Gegenstrom, Gleichstrom und Kreuzstrom. Berlin: Springer 1950.

    Google Scholar 

  312. For further discussion of the term “effective” see Sect. 45.

    Google Scholar 

  313. W. H. Keesom: Helium, p. 86. Amsterdam: Elsevier 1942.

    Google Scholar 

  314. R. B. Jacobs and S. C. Collins: J. Appl. Phys. 11, 491 (1940).

    ADS  Google Scholar 

  315. H. Hausen: Wärmeübertragung im Gegenstrom, Gleichstrom und Kreuzstrom. Berlin: Springer 1950.

    Google Scholar 

  316. See general references given in Sect. 42 for further detail.

    Google Scholar 

  317. W. Nusselt: Z. VDI 53, 1750, 1809 (1909). —

    Google Scholar 

  318. W. Nusselt: Phys. Z. 12, 285 (1911).

    Google Scholar 

  319. W. H. McAdams: Heat Transmission, p. 145. New York: McGraw Hill 1951.

    Google Scholar 

  320. See data given by J. A. van Lammeren (Technik der tiefen Temperaturen, p. 55. Berlin: Springer 1941) for air, H2 and He at various temperatures.

    Google Scholar 

  321. See T. A. Hall and P. H. Tsoa [Proc. Roy. Soc. Lond., Ser. A 191, 6 (1947)] for low temperature measurements. See also

    ADS  Google Scholar 

  322. B. H. Schultz [Appl. Sci. Res. A 1, 287, 400 (1947/49)] for theoretical discussion of these factors in their application to heat interchangers.

    Google Scholar 

  323. C. Starr: Rev. Sci. Instrum. 12, 193 (1941).

    ADS  Google Scholar 

  324. H. Blasius: Phys. Z. 12, 1175 (1911).

    MATH  Google Scholar 

  325. C. Starr [Rev. Sci. Instrum. 12, 193 (1941)] gives this formula in consideration of hydrogen liquefier interchangers. His numerical constant, however, is incorrect by a factor of ten.

    ADS  Google Scholar 

  326. R. v. Linde: Z. ges. Kälteind. 41, 161 (1934).

    Google Scholar 

  327. R. B. Jacobs and S. C. Collins: J. Appl. Phys. 11, 491 (1940).

    ADS  Google Scholar 

  328. P. Kapitza: Proc. Roy. Soc. Lond., Ser. A 147, 189 (1934).

    ADS  Google Scholar 

  329. F. R. Bichowski: J. Industr. Engng. Chem. 14, 62 (1922).

    Google Scholar 

  330. McMahon, Bowen and Bleyle, jr.: Trans. Amer. Soc. Mech. Engrs. 72, 623 (1950).

    Google Scholar 

  331. S. C. Collins: Rev. Sci. Instrum. 18, 157 (1947).

    ADS  Google Scholar 

  332. Nicol, Smith, Heer and Daunt: Rev. Sci. Instrum. 24, 16 (1953).

    ADS  Google Scholar 

  333. J. Ashmead: Proc. Phys. Soc. Lond. 63, 504 (1950).

    ADS  Google Scholar 

  334. M. Fränkl: German Patents 490878 and 492431. 1928. US. Patents 1890646. 1932. -1970299. 1934.

    Google Scholar 

  335. See for example R. Linde: Z. ges. Kälteind. 41, 183 (1934). —

    Google Scholar 

  336. B. C. P. Hochgesand: Mitt. Forsch. GHH. Konzern 4, 14 (1935). —

    Google Scholar 

  337. J. Wucherer: Iron Coal Tr. Rev. 159, 723 (1949).

    Google Scholar 

  338. P. Borchard: Proc. VIII. Int. Congr. Refrig. London, p. 118 (1951).

    Google Scholar 

  339. See footnote to p. 84 for the effect of dead volume on the range of operational pressures.

    Google Scholar 

  340. H. Hausen: Z. ges. Kälteind. 39, 1 (1932).

    Google Scholar 

  341. G. Lund and B. F. Dodge: Industr. Engng. Chem. 40, 1019 (1948).

    Google Scholar 

  342. H. Glaser: Z. VDI 53, 925 (1939).

    Google Scholar 

  343. Time averages are denoted by a superscipt bar. Averages over configurational space are denoted by a subscript m.

    Google Scholar 

  344. H. Hausen: Z. ges. Kälteind. 39, 1 (1932).

    Google Scholar 

  345. H. Hausen: Z. ges. Kälteind. 39, 1 (1932).

    Google Scholar 

  346. Hausen: Wärmeübertragung in Gegenstrom, Gleichstrom und Kreuzstrom, pp. 262 to 452. Berlin: Springer 1950.

    Google Scholar 

  347. H. Hausen: Wärmeübertragung in Gegenstrom, Gleichstrom und Kreuzstrom. Berlin: Springer 1950.

    Google Scholar 

  348. B. H. Schultz: Appl. Sci. Res. 3, 173 (1952).

    Google Scholar 

  349. S. C. Collins: Chem. Engng. 53, 106 (1946).

    Google Scholar 

  350. P. R. Trumpler and B. F. Dodge: Chem. Engng. Progr. 43, 75 (1947).

    Google Scholar 

  351. For detailed discussion of this, which is outside the scope of this article, see W. E. Lobo and G. T. Skaperdas: Chem. Engng. Progr. 43, 69 (1947).

    Google Scholar 

  352. J. H. Rushton and E. P. Stevenson: Chem. Engng. Progr. 43, 61 (1947).

    Google Scholar 

  353. See reference 4 below.

    Google Scholar 

  354. W. E. Lobo and G. T. Skaperdas: Chem. Engng. Progr. 43, 69 (1947).

    Google Scholar 

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Daunt, J.G. (1956). The Production of Low Temperatures Down to Hydrogen Temperature. In: Flügge, S. (eds) Low Temperature Physics I / Kältephysik I. Encyclopedia of Physics / Handbuch der Physik, vol 3 / 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-39773-2_1

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