Kapitsa Explains Superfluidity

Pyotr Leonidovich Kapitsa developed ideas relating to superfluidity in liquid helium and techniques that remain basic to modern low-temperature physics.

Summary of Event

A thorough and systematic study of the properties of materials whose temperature is close to absolute zero was made possible when, in 1908, Heike Kamerlingh Onnes of the University of Leiden succeeded in liquefaction of helium. Among many unexpected properties, it was found that electrical resistance of many metals approached a constant as the temperature was lowered, and in some cases it vanished entirely at some characteristically low temperature, found to depend on the magnetic field. Kamerlingh Onnes thus had discovered superconductivity in liquefying helium, and for his many achievements in the area of low-temperature physics, he was awarded the Nobel Prize in Physics in 1913. Nobel Prize recipients;Heike Kamerlingh Onnes[Kamerlingh Onnes]
[kw]Kapitsa Explains Superfluidity (Jan., 1938)
[kw]Superfluidity, Kapitsa Explains (Jan., 1938)
Low-temperature physics[Low temperature physics]
Physics;low-temperature[low temperature]
[g]Russia;Jan., 1938: Kapitsa Explains Superfluidity[09670]
[c]Science and technology;Jan., 1938: Kapitsa Explains Superfluidity[09670]
[c]Physics;Jan., 1938: Kapitsa Explains Superfluidity[09670]
Kapitsa, Pyotr Leonidovich
Kamerlingh Onnes, Heike
Rutherford, Ernest
Landau, Lev Davidovich

By 1920, as the properties of various metals near liquid helium temperature (4.20 Kelvins) were being investigated, it became evident that liquid helium exhibits strange and unusual properties around 2.20 Kelvins, thus making it a subject of intense study. In 1924, Kamerlingh Onnes and coworkers found that liquid helium density has a maximum at around 2.30 Kelvins, and a graph of density versus temperature shows a cusp rather than a smooth curve as in the analogous case of water. After several attempts, Willem Hendrik Keesom Keesom, Willem Hendrik of Leiden succeeded in solidifying liquid helium under several atmospheric pressures and showed that the melting curve (pressure versus temperature) bends at the lower end so as to appear almost parallel to the temperature axis. This led Kamerlingh Onnes to surmise that under atmospheric pressure, helium may remain a liquid down to absolute zero temperature. By 1927, Keesom and coworkers observed an increase in the dielectric constant of liquid helium, as well as peculiar variations in the specific heat at around 2.20 Kelvins. It was suggested that a phase change in liquid helium occurs at 2.19 Kelvins such that normal “liquid helium I” prevails at higher temperature and stable “liquid helium II” exists at lower temperature. A curve of specific heat of liquid helium as a function of temperature resembles the Greek letter lambda, and the critical temperature at which phase transition occurs is known as the “lambda point.” Lambda point

In addition to these accumulated perplexing properties of liquid helium, in 1935, Keesom and his daughter A. P. Keesom discovered that helium II exhibits a seemingly infinite thermal conductivity. At the University of Cambridge, John Frank Allen Allen, John Frank and his collaborators, in addition to confirming Keesom’s result, showed that the thermal conductivity of helium II differed from the ordinary because of its dependence on the temperature gradient. In 1938, Allen and his coworkers were to find two of the three important properties of helium II.

Pyotr Leonidovich Kapitsa arrived at Cambridge’s Cavendish Laboratory in 1921. After initially working under the supervision of Ernest Rutherford, he received his Ph.D. in 1923 and remained at Cambridge until 1934. By early 1930, he was honored by the Royal Society of Science and installed as a Royal Society Professor and as director of the newly constructed Mond Laboratory. During this time, Kapitsa had achieved “liquefaction of helium by an adiabatic method without precooling with liquid hydrogen,” a common procedure since Kamerlingh Onnes’s work. Kapitsa returned to the Soviet Union in 1934 for a visit and was not permitted to leave (until 1965); he was named director of the new Institute for Physical Problems in Moscow in 1935.

The apparent lack of “explanation to the abnormal thermal conductivity of helium II” evident from Keesom’s experimental results, confirmed by Allen and collaborators, provided the setting for Kapitsa’s work. In an article that appeared in Nature in January, 1938, he suggested that the thermal conductivity of helium II, below the lambda point, occurs via the convection currents rather than the normal conduction process. He pointed out that such convection current can be maintained only if the viscosity of helium II is exceedingly low. The experimental data pointed to the fact that viscosity of helium II was at least eight times less than that slightly above the lambda point (2.20 Kelvins). Kapitsa showed experimentally that the viscosity of “helium II was at least ten thousand times less than that of gaseous hydrogen at low temperature,” supposedly the least viscous of fluids. Based on these supporting arguments, Kapitsa proposed that helium II “below the lambda point assumes a special kind of state,” which he called “superfluid.” He was able to demonstrate the low viscosity (the internal resistance to flow) by allowing helium to flow through a narrow slit of 5 × 10
meters formed by two polished glass disks. He found that helium II passed through the slit rapidly below the lambda point but scarcely flowed above it.

Pyotr Leonidovich Kapitsa.

A few months later, Allen and his collaborators at Cambridge discovered that around 1.08 Kelvins, a small heat flow, which was passed electrically, produced a rise in the liquid helium level in a closed bulb at the heated end. It should have fallen because of increased vapor pressure, and this was found to be the case for larger heat flows. When the experiment was repeated with a modified apparatus such that the top of the bulb at the hot end of the capillary was open, thus sharing the vapor pressure with the helium bath, no difference in the result was noted. They also found “fountain effect,” in which a hydrodynamic flow through a capillary resulted when liquid helium was heated by radiation. In 1938, John Gilbert Daunt Daunt, John Gilbert and Kurt Mendelssohn Mendelssohn, Kurt of the University of Oxford reported yet another property of superfluid, the phenomenon of the “creeping film.” They demonstrated that when an empty beaker was lowered into the liquid, it filled to the level of the helium bath even though the rim of the beaker was above the liquid level. It was observed that the level of the liquid in the beaker dropped at the same rate at which the beaker filled when it was partly lifted above the bath.

In a 1941 paper, Kapitsa proved, in addition to his original hypothesis, that helium II flow was composed actually of two currents: one flowing along the wall of the capillary and the other through the center in the opposite direction. He showed further that heat transfer in helium II is produced by these oppositely directed convection currents of different heat content. Kapitsa also assumed that the heat content of the flow of thin films along the wall was different, resulting from the molecular force of the surface, as opposed to the flow along the center. Through a series of experiments, Kapitsa established that below the lambda point, helium II is a mixture of normal fluid and superfluid and that the concentration of the latter increases as the temperature is lowered. He showed that superfluid has zero entropy and as one approaches absolute zero, helium II is transformed entirely into superfluid, which flows without friction, unlike the normal fluid, which experiences drag as it transports heat. He also confirmed Daunt and Mendelssohn’s result; namely, if the fluid is forced out through a fine capillary, its temperature falls as much as three- to four-tenths of a degree.

Seeking to demonstrate that heat transport in helium II is the result of movement of fluid, Kapitsa fashioned a movable vane and suspended it at the mouth of a flask filled with fluid so that any flow would be observable by the deflection of the vane. He then filled the electrically heatable flask with liquid helium and immersed it in a helium bath. By placing the movable vane at the mouth of the flask and applying heat to it, he was able to observe the deflection of the vane, proving conclusively that the liquid flows. During World War II, research activities in the area of low-temperature physics were suspended in the West, while in the Soviet Union, Kapitsa and other prominent physicists such as Lev Davidovich Landau progressed at a rapid rate, the latter formulating an elaborate quantum theory of liquid helium during 1940 to 1941.


In 1938, John Gilbert Daunt and Kurt Mendelssohn reported a property of superfluidity known as the “creeping film” phenomenon: When an empty beaker is lowered into a bath of liquid helium, it fills to the level of the helium bath even though the rim of the beaker is above the liquid level. Liquid helium, in otherwords, will “creep” along surfaces to find its own level.

Following Kapitsa’s hypothesis of superfluidity, numerous unexpected and puzzling properties of liquid helium were discovered, but none could be explained theoretically. From 1940 to 1941, Landau, of Kapitsa’s institute, advanced an elaborate quantum theory of liquid helium. Independently, Laslo Tisza Tisza, Laslo of the College de France advanced some of the qualitative aspects of the theory of helium II, such as zero entropy and “second sound.” Landau’s theory of superfluidity describes quantum mechanically all observed macroscopic properties of liquid helium below the lambda point at 2.19 Kelvins. The two fluids, each in a different state, are assumed to coexist as a mixture of separate quantum states capable of independent simultaneous motion, free of mutual drag, as if through each other. The new state—the superfluid state emerging through a phase change in the normal fluid—is nonviscous and has zero entropy. The transition from normal to superfluid increases with decreasing temperature and tends to complete at 0 Kelvins. The normal viscous fluid transports heat, and in a sense, it is heat itself, flowing against the background of superfluid at ground state or zero energy.

Kapitsa had shown in one of his experiments that although normal fluid escaping from a flask that was being electrically heated deflected the movable vane, the quantity of liquid helium remained unchanged. The explanation of this phenomenon is that superfluid countercurrent flowed back into the flask, keeping the quantity of fluid constant. Landau’s theory assumes the superfluid flow to be “irrotational,” and, according to the theory of hydrodynamics by the well-known eighteenth century Swiss mathematician Leonhard Euler, the flow of such nonviscous fluid past a solid surface should not exert a force on the body. Thus normal fluid current in one direction and the countercurrent in the opposite direction would keep the quantity of fluid in a container unchanged.

The theory of liquid helium predicts the so-called second sound. Based on the propagation of two different kinds of waves, one associated with the normal fluid and the other with the superfluid, both moving simultaneously in opposite directions with different velocities, Landau’s theory should lead to a second sound in addition to the ordinary sound. The initial effort to detect the “second sound” failed in 1940. It soon became evident, however, that whereas the ordinary sound waves are associated with cyclical compression and rarefaction of fluid that propagates through the fluid, the second sound waves oscillating in opposite directions would be too weak to detect. Such counteroscillations of normal and superfluid were realized as giving rise to oscillations of heat relative to cold superfluid background of ground state. Thermal waves can be expected to radiate and are susceptible to excitation (hence detection) by appropriately tuned temperature oscillators. A. P. Peshkov successfully confirmed the occurrence of second sound in helium II. In recognition of his theory of liquid helium, Landau was awarded the 1962 Nobel Prize in Physics. Nobel Prize recipients;Lev Davidovich Landau[Landau]

Eminent Soviet physicists such as Ilya Mikhailovich Lifshitz, Isaak Yakovlevich Pomeranchuk, and Nikolai Nikolaevich Bogoliubov continued to explore superfluidity after Landau’s death. The work done on liquid helium in the United States pointed to the fact that critical phase change in helium II is brought on by the formation of microscopic vortices, experimentally verified by William Frank Vinen of Mond Laboratory in Cambridge. It soon became obvious that as helium is composed of two stable isotopes—helium-4 and helium-3—it should exhibit different statistical characteristics. Helium-4 would obey Bose-Einstein statistics, whereas helium-3 atoms conform to Fermi-Dirac statistics, and therefore liquid helium composed of pure helium-3 isotope would show totally different characteristics. In 1949, Edward Roger Grilly, Edward Frederic Hammel, and Stephen George Sydoriak, of Los Alamos showed that helium-3 liquefies at 3.20 Kelvins. Experiments indicate that helium-3 does not become superfluid and that it is a new and even more interesting quantum fluid in comparison with helium-4.

The study of superfluid and low-temperature physics progressed at a rapid rate after Kapitsa formulated his hypothesis and conducted his experiments. Kapitsa is said to have believed firmly that the secrets of nature are revealed only at the limits of physical phenomena. After nearly half a century, he was awarded the 1978 Nobel Prize in Physics for his contribution to low-temperature and plasma physics. Nobel Prize recipients;Pyotr Leonidovich Kapitsa[Kapitsa]
Low-temperature physics[Low temperature physics]
Physics;low-temperature[low temperature]

Further Reading

  • Kapitza, P. L. The Collected Papers of P. L. Kapitza. Edited by D. ter Haar. 4 vols. Oxford, England: Pergamon Press, 1926-1970. Highly technical volumes demonstrate Kapitsa’s contributions to physics. Papers appearing in volume 2, pertaining to superfluidity, are relatively simple to follow.
  • Kedrov, Fedor B. Kapitza: Life and Discoveries. Translated by Mark Fradkin. Moscow: Mir, 1984. A journalistic account of Kapitsa’s scientific career and his life in the Soviet Union under Joseph Stalin. Includes a complete list of Kapitsa’s scientific and nontechnical writings and related works.
  • Lifshitz, Eugene M. “Superfluidity.” Scientific American 198 (June, 1958): 20. Well-written account of Kapitsa’s discovery of the phenomenon of superfluidity and the historical development of low-temperature physics. Written for the general reader by a well-known Soviet scientist.
  • Lubkin, Gloria B. “Nobel Prizes: To Kapitza for Low Temperature Studies.” Physics Today 31 (December, 1978): 17-19. Explains the essence and importance of Kapitsa’s work.
  • Perry, Albert. Introduction to Peter Kapitza on Life and Science, by Pyotr L. Kapitza. New York: Macmillan, 1968. Provides a brief sketch of Kapitsa’s life and discusses his work at the Cavendish Laboratory.
  • Spruch, Grace Marmor. “Pyotr Kapitza, Octogenarian Dissident.” Physics Today 32 (September, 1979): 34-36. Brief account of Kapitsa’s career shows the physicist’s development from a prisoner in a gilded cage to an effective dissident treading a narrow path.
  • Trigg, George L. Landmark Experiments in Twentieth Century Physics. 1975. Reprint. Mineola, N.Y.: Dover, 1995. Provides highly readable and accurate technical accounts of developments in low-temperature physics from 1908, when Kamerlingh Onnes succeeded in liquefaction of helium. Includes extensive excerpts from Kapitsa’s original papers that appeared in Nature.
  • Wilson, David. Rutherford: Simple Genius. Cambridge, Mass.: MIT Press, 1983. Interesting biography of a man who played a crucial role in Kapitsa’s life. Chapter 16 presents an account of the special bond that existed between Rutherford and his unique student.

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