Abstract
In this paper I will attempt to discuss certain methodological and historical issues related to the development of the theory of liquids. What are liquids really? Are they denser gases or diluted solids? This last question may appear to be rather pedantic, yet its answer, at least partially, reflects the particular attitude one adopts for the reading of some of the more dramatic developments in physics and chemistry during the last one hundred years. Ever since the experiments of Thomas Andrews in the 1860’s where it was shown that the transition from the liquid state to the gaseous state is continuous, there were attempts to develop a theory of liguids based on the newly established kinetic theory of gases, and more specifically on Clausius’s virial theorem.
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Notes
J. D. van der Waals, Over de Continuiteit van den gas en vloeistoftoestand (University of Leiden, 1873). It was translated into German in 1881, English in 1890, and French in 1894.
The only detailed biograpy of van der Waals is in Russian, by A. Ya. Kipnis and B. E. Yavelow, Johannes Diderik van der Waals 1837–1923 (Leningrad, Nauka, 1985). Oxford University Press plans to publish an English edition.
Also see S. G. Brush, The Kind of Motion We Call Heat, 2 volumes (New York, 1976)
J. S. Rowlinson, On the Continuity of the Gaseous and Liquid States (Amsterdam, 1988), especially the introduction.
T. Andrews, ‘On the continuity of the gaseous and liquid states’, the first Bakerian Lecture (1869), in Scientific Papers, pp. 296–317; edited with a memoir by P. G. Tait and Grum Brown (London, 1896). Andrews had shown that carbon dioxide, when above 30.9 degrees centrigrade cannot be converted to a liquid however large the applied pressure is; for temperatures below, liquefaction is achieved by an increase in pressure. This temperature was termed the critical temperature.
Van der Waals’s thesis, p. iv.
Kostas Gavroglu, ‘The reaction of the British physicists and chemists to van der Waals’s early work and the law of corresponding states’, to be published in Historical Studies in The Physical Sciences, 1990.
See, for example, E. Sarrau’s introductory essay to the French translation of van der Waals’s thesis.
J. C. Maxwell, ‘Capillary Action’, Encyclopedia Britannica, 9th edition, 1879
J. S. Rowlinson, ‘Legacy of van der Waals’, Nature 244 (1973), pp. 414–417
J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity (Oxford, 1982)
M. J. Klein, ‘The Historical Origins of the van der Waals Equation’, Physica 73 (1974), pp. 28–47.
See Brush, The Kind of Motion… and Rowlinson Continuity….
R. J. E. Clausius, ‘Ueber einen auf die Warme anwendbaren mechaniachen Satz’, Annalen der Physik 141 (1870), pp. 124–130.
J. D. Van der Waals, ‘The Equation of State for Gases and Liquids’, in Nobel Lectures (Physics) 1901–1921 (New York, 1910), p. 256.
This is Chapter 12 in all the translations of his thesis and was included with van der Waals’s consent.
Ibid., p. 454.
Quoted in E. Cohen, ‘Kamerlingh Onnes Memorial Lecture’, Chemical Society Memorial Lectures (London, 1933), p. 1203.
James Clerk Maxwell, ‘van der Waals on the continuity of the gaseous and liquid states’, Nature 10 (October 15 1874), p. 478.
Ibid., p. 477.
Ibid., p. 471.
Ibid., p. 478.
Ibid., p. 478.
Ibid., p. 479.
J. C. Maxwell, ‘On the Dynamical Evidence of Molecular Constitution of Matter’, Journal of The Chemical Society 13 (1875), pp. 493–508.
Maxwell, see note 11.
Maxwell, ‘Van der Waals on the continuity…’, p. 477.
J. Dewar, ‘Liquid Hydrogen’, Proc. Roy. Soc. XVI (1899), p. 13.
Kostas Gavroglu and Yorgos Goudaroulis, ‘Heike Kamerlingh Onnes’s researches at Leiden and their methodological implications’, Studies in the History and Philosophy of Science 19 (1988), pp. 243–274.
F. E. Simon, ‘Zum Prinzip von der Unerreichbarkeit des absoluten Nullpunktes’, Zeit. Fur Physik 41 (1927), pp. 806–809
In 1934 he pointed out that the high zeropoint energy of helium was responsible for keeping the substance, under saturation pressure, in the liquid phase down to absolute zero, See also F. E. Simon, ‘Behaviour of condensed helium near absolute zero’, Nature 133 (1934), p. 527.
For details of both the experimental and theoretical developments see W. H. Keesom, op. cit.
F. London, Superfluids (New York, Wiley, 1950)
K. Gavroglu and Y. Goudaroulis, Methodological Aspects of Low Temperature Physics 1881–1956 (Dordrecht, Kluwer Academic Publishers, 1988).
The first hint of such an idea is found in W. H. Keesom and M. Wolfke, ‘Two different liquid states of helium’, Communications from the Physical Laboratory at the University of Leiden 190b (1927), pp. 17–22.
W. H. Keesom, ‘Quelques remarques en rapport avec l’anomalie de la chaleur specifique de l’helium au point lambda’, Communications from the Physical Laboratory at the University of Leiden (Supplement), 71e (1932), pp. 47–52.
K. Clusius, paper read in Breslau, 1933.
The zero-point energy may be estimated theoretically in two limiting cases: when the interatomic distance is less than an atomic diameter and when the interatomic distance is much greater than the atomic dimaeter. F. London used an interpolation formula between these limiting cases. See R. B. Dingle, Theories of helium IF, Philosophical Magazine (Supplement) 1 (1952), pp. 111–168.
F. London, ‘On condensed helium at absolute zero’, Proceedings of the Royal Society of London Al53 (1936), pp. 576–586.
“It is perhaps characteristic of the trend of thought at the time that F. London avoided the term ‘liquid’ in the title of his paper, referring to ‘condensed’ helium”, K. Mendelssohn, ‘Superconductivity’, Reports on Progress in Physics 10 (1946), p. 376.
F. London, ‘Superconductivity’, Reports on Progress in Physics 10 (1946), p. 581.
Ibid., pp. 582–583.
Heinz London, ‘Superfluid helium’, Year Book of the Physical Society of London (1960), pp. 34–48.
F. London’s first step was analogous to Sommerfeld’s treatment of the free electron gas. See A. Sommerfeld, ‘Zur Elektrontheorie der Metalle auf Grund der Fermischen Statistik’, Zeitschrift fur Physik 47 (1928), pp. 1–32. Many years before London proposed his theory, M. C. Johnson discussed the ‘degeneracy’ of the helium gas at a meeting of the Physical Society of London on February 14, 1930. Johnson used Fermi’s correction to the pressure of the ideal gas. J. E. Lennard-Jones pointed out that he should have used Bose-Einstein statistics: “the author considers only Fermi-Dirac statistics, whereas the theory indicates that helium atoms should obey the Bose-Einstein statistics. It would add to the value of his work if the author could consider the effect of the latter statistics on helium near the critical point”. This suggestion, however, was not taken up. M. C. Johnson, ‘A method of calculating the numerical equation of state for helium below 6 degrees absolute and of estimating the relative importance of gas degeneracy and interatomic forces’, Proceedings of the Physical Society of London 42 (1929–1930), pp. 170–179.
A. Einstein, ‘Quantentheorie des einatomigen idealen Gases’, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-Matematische Klasse (1924), pp. 261–267
A. Einstein, ‘Quantentheorie des einatomigen idealen Gases’, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-Matematische Klasse (1925), pp. 3–16. Uhlenbeck in his doctoral thesis questioned Einstein’s result, and no one paid any attention to this odd phenomenon until London’s letter to Nature, and Uhlenbeck’s and Kahn’s paper in Physica where Uhlenbeck withdrew his objections.
F. London, ibid., (1925), p. 644.
F. London, ‘On the Bose-Einstein condensation’, Physical Review 54 (1938), pp. 947–954.
L. Tisza, ‘Transport phenomena in helium II’, Nature 141 (1938), p. 913.
L. Tisza, ‘Sur la supraconductibilité thermique de l’helium II et le statistique de Bose-Einstein’ Comptes Rendus 207 (1938), pp. 1035–1037.
J. F. Allen, ‘Liquid helium’, in F. Simon et al., Low Temperature Physics, Four Lectures (New York, Academic Press, 1952), p. 90.
International Conference on Fundamental Particles and Low Temperatures, Cavendish Laboratory, Cambridge 22–27 July 1946. Proceedings published by the Physical Society, 1947.
F. London, ‘The present state of the theory of liquid helium’, International Conference on Fundamental Particles and Low Temperatures, Cavendish Laboratory, Cambridge 22–27 July 1946. Proceedings published by the Physical Society, 1947, p. 1.
L. D. Landau, ‘The theory of superfluidity of helium II’, Journal of Physics (USSR) 5 (1941), pp. 71–79.
F. London to L. Tisza, May 8, 1946.
Ibid.
L. Tisza to F. London, November 26, 1946.
V. Peshkov, op. cit., note 25.
F. London to L. Tisza, September 10, 1946.
L. Tisza to F. London, October 10, 1946.
L. Tisza to F. London, October 17, 1946.
F. London to L. Tisza, November 21, 1946.
F. London, op. cit., note 25, p. 8.
V. Peshkov, ‘Determination of the velocity of propagation of the second sound in Helium II’ Journal of Physics (USSR) 10 (1946), pp. 389–398.
L. D. Landau, ‘On the theory of superfluidity of Helium II’, Journal of Physics (USSR) 11 (1947), pp. 9–92.
F. London to L. Tisza, March 10, 1949.
W. Osborne, B. Weinstock and B. M. Abraham, ‘Comparison of the flow of isotopically pure liquid Helium 3 and Helium 4’, Physical Review 75 (1949), p. 988.
Ibid., p. 988.
F. London to L. Tisza, February 24, 1949.
L. Tisza to F. London, March 13, 1949.
F. London, ‘The rare isotope of helium 3; A key to the strange properties of ordinary liquid helium 4’, Nature 163 (1949), pp. 694–696.
L. D. Landau, ‘On the theory of superfluidity’, Physical Review 75 (1949), pp. 884–885.
L. Tisza, ‘On the theory of superfluidity’, Physical Review 75 (1949), pp. 885–886.
Ibid., p. 885.
Ibid., p. 886.
F. London to L. Tisza, March 17, 1949.
F. London to L. Tisza, November 28, 1950.
Ibid.
Ibid.
L. Tisza to F. London, December 5, 1950.
Ibid.
L. Tisza to F. London, August 10, 1951.
F. London, ‘Limitations of the two-fluid theory’, in R. Powers, editor, Proceedings of the International Conference on Low Temperature Physics (held in Oxford August 22–28, 1951), pp. 2–6.
Ibid., p. 3.
Ibid., p. 4.
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Gavroglu, K. (1990). From Gases and Liquids to Fluids: The Formation of New Concepts during the Development of Theories of Liquids. In: Nicolacopoulos, P. (eds) Greek Studies in the Philosophy and History of Science. Boston Studies in the Philosophy of Science, vol 121. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2015-6_17
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