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Physical Properties of Helium

Helium is a colourless gas, and possesses neither taste nor odour.

The density of helium has been determined by many investigators. A study of the relation between the pressure and volume of the gas has shown that at 0° with pressures varying from 147 mm. to 838 mm. of mercury the product pv is absolutely constant, i.e. the compressibility coefficient is zero. Jaquerod and Scheuer give the compressibility coefficient at 0° as -0.00060 between pressures of 400 and 800 mm. of mercury.

In this respect, therefore, helium behaves as it might be expected to do were its critical temperature much higher than it actually is. It may be noted in this connection that when helium and hydrogen are mixed the volume of the mixture is greater than the sum of the original volumes. The pv isothermals for helium have been determined over wide ranges of temperature and pressure by Onnes.

The molecular weight of helium, calculated from Heuse's value for the density according to Berthelot's method of limiting densities, is 4.00.

As an example of the extreme lightness of helium it has been observed that by passing a stream of pure carbon dioxide through a porous tube sufficient helium diffuses in from the atmosphere to be detected spectroscopically after absorption of the carbon dioxide by caustic potash.

The coefficient of increase of pressure at constant volume is perfectly normal, and at temperatures from 0° to 100° C. has the value 0.0036616. This value is independent of the original pressure.

It was early discovered that helium does not obey Graham's Law of diffusion of gases, but passes through a porous diaphragm more slowly than is expressed by the law. Donnan observed later that the rate of effusion of helium through a small hole in a platinum plate was slower than one would expect from calculations based on the density, and suggested that the anomaly is probably due to the fact that at ordinary temperatures helium, like hydrogen, undergoes a rise in temperature on free expansion through a small orifice (Joule-Thomson effect). All other known gases, with the exception of hydrogen, diffuse more rapidly than is required by calculations based on the assumptions of the kinetic gas theory.

The solubility of helium in water was first determined by Estreicher, who found the following values for the absorption coefficient: 0.01487 at 0.5°, and 0.01404 at 50°, with a minimum at 25°. The experimental procedure adopted, however, has since been shown to be untrustworthy. More importance must be attached to the values obtained by Antropoff, who found for the absorption coefficient the value 0.0134 at 0°, and 0.0226 at 50°, with a minimum at 10°. The existence of a minimum has its counterpart in the case of other inert gases (q.v.) and of hydrogen. Helium is insoluble in absolute alcohol and benzene.

The viscosity of helium was first determined by Rayleigh by measurement of the rate of flow of the gas through a capillary tube. He obtained the value 0.96 (air=l). Later, Schultze repeated this determination, and found the viscosity of helium at 15° to be 1.086 times that of air.

viscosity of helium
Helium viscosity
Rankine has recently redetermined this constant, using an apparatus which may be described here, as it is particularly well adapted for use with very small amounts of gas, and therefore finds application in investigations on the rare gases. It consists of a tube in the form of an elongated O, one side of which, A (fig.), is a very fine capillary tube, while the other side, B, though much wider, is sufficiently narrow to allow a pellet of mercury, C, to remain intact. The driving pressure required to force the gas through the capillary is supplied by the weight of this pellet of mercury. Taps D and E allow the apparatus to be cleaned, evacuated, and filled with the gas under examination.

The results obtained with this apparatus confirmed Schultze's figure. Therefore, taking the absolute value for the viscosity of air at 15.5° as η = 1.803×10-4 C.G.S. units, it follows that the absolute value of the viscosity of helium at 15° is 1.958×10-4 C.G.S. units, which is in fair agreement with the figure 1.969×10-4 at 15.3° found experimentally by Tahzler.

Tanzler also found η = 2.348×10-4 at 99.6° and η = 2.699×10-4 at 184.6°. Assuming that the change of viscosity follows a linear law of the type

ηθ = η0(1+βθ),

where ηθ and η0 are the values of the viscosity at θ° and 0° respectively, the value of the temperature coefficient β for helium is 2.32×10-3.

The thermal conductivity of a gas, according to the kinetic gas-theory, is given by K in the equation

K = f.η.cv

where η and cv are the viscosity and the specific heat at constant volume respectively, and f is a constant. For helium the value of K at 0° C. is 0.00003386, from which it follows that f = 2.507 - a value which is in accordance with Boltzmann's development of Maxwell's theory, and therefore affords evidence of the molecular simplicity of the gas. The thermal conductivity at low pressures shows unexplained anomalies. The refractivity of helium was first determined by Rayleigh. The method used consisted in passing parallel beams of light from the same source through similar tubes containing helium and air respectively. The pressure of gas in these tubes was varied until a point was reached at which the retardation of light, as determined by observation of interference bands, was the same in both tubes. The ratio of the refractivities is then inversely as the ratio of the pressures in the tubes and, the refractivity of air being known, that of helium may readily be calculated.

Rayleigh's figure was inaccurate, but Ramsay and Travers subsequently repeated the measurements, and found the refractivity of helium (μ-1) to be 0.1238 times that of air. This gives for helium the value

μ = 1.0000361.

The above method or some modification of it has been used by other observers, the chief of whose results are tabulated below.

Wave Length.Refractive Index (μ)
(1)Visible spectrum (14°)1.0000340
5790, 5760, (N.T.P.)1.000034384

It has been the custom to express the refractive index of a gas by an equation of the type: -


which may be written:


The values of the constants in these equations for helium are as follows: -


C. and M. Cuthbertson prefer to employ an equation of the Sellmeier

where η0 is the frequency of the free vibration and η is the frequency of the light for which μ is to be calculated.

For helium at N.T.P. the constants in this equation are: -

C = 2.42476×1027; η02 = 34991.7×1027.

The dispersion of helium is extremely small, as may be seen by the small- ness of the constant b in equation (i.) above, as compared with its value in the case of hydrogen or argon (b = 4.3×10-11 for hydrogen, and b = 5.6×10-11 for argon). This is perhaps clearer if we express relative dispersion by the formula -

where μF, μC, μD are the refractive indices for the Fraunhofer lines F, C, and D. We then have the following values of v: - Air =98.0; Hydrogen = 65.9; Helium = 39.9;

The specific inductive capacity of helium has been determined by the electrostatic null-method of Hopkinson and Lebedeff, and has the value

K = 1.000074

at 0° and 760 mm. According to Maxwell's Law, K should be equal to (μ)2, where μ is the refractive index for radiations of large wave-length. Extrapolating from the values for the refractive index for light of various wavelengths within the range of the visible spectrum, we find μ = 1.0000375,

whence (μ)2 = 1.000075,

a value which agrees well with that given above for K. Bouty states that the dielectric cohesion of helium at 17° is represented by the number 18.3 (A = 38; air = 419; H2 = 205). In this connection the extraordinary length of the spark gap in helium may be mentioned. By experiments made with a vacuum tube of which one electrode was movable, it was found that under a certain fixed set of conditions as to potential difference, pressure, etc., the following lengths of spark were obtainable in helium, and in certain other gases: - Oxygen = 23.0 mm.;. Air = 33.0 mm.; Hydrogen = 39.0 mm.; Argon = 45.5 mm.; Helium = 250-300 mm.;

If VHe and Vair are the sparking potentials in helium and air respectively, then the ratio VHe/Vair is found to diminish with increase of sparking distance (δ) and with increase of pressure (P), while other gases compared with air show an increase of sparking potential with increase in δ and P. When V is plotted against δ, helium gives straight lines, while other gases give curves concave to the axis of δ. The minimum spark potential in helium is 184 volts, and the corresponding pressure is 2.4 mm.

inert gases spectra
Spectra produced in Ordinary Vacuum Tubes by the Uncondensed Discharge from an Induction Coil.
The spectrum of helium is complex, and was found by Runge and Paschen to contain six series of lines. These fall naturally into two groups in each of which we have a Principal Series, and two Subordinate Series which converge toward a common limit. (See Picture.)

One of these groups consists of doublet series, and the doublet D3, by which helium was discovered, is the first in the Principal Series. It is the lines of this group which characterise the solar spectrum of helium, and the spectrum obtained in a vacuum tube under moderately low pressures.

The chief line of the Principal Single Line Series is λ5016, in the green, and is prominent in the spectrum of helium under very low pressure. Generally all the lines of helium are visible in the spectrum under any conditions; but the relative intensity of the two groups characterised by D3 and λ5016 respectively can undergo great changes, so that the light emitted by a vacuum tube exhibits the following alterations as the pressure is reduced: -
  1. Orange yellow
  2. Bright yellow
  3. Yellowish-green
  4. Green
  5. Green X-ray vacuum
  6. Black vacuum

The infra-red spectrum of helium has been investigated by Paschen. A series of lines observed by Pickering in the spectrum of the star ζ Puppis, and ascribed for many years to hydrogen, has been shown to belong to the spectrum of helium by Fowler, who has also observed new lines in this series; and Fowler has observed still another series in the helium spectrum, beginning with the well-known solar line λ 4868.

Collie observed that in the presence of mercury a Plucker tube containing helium showed the full spectrum in the capillary portion, but in other parts of the tube gave a spectrum modified in a way which corresponded to the change produced by change of pressure. He suggests that a helium mercury tube containing a trace of hydrogen would form a useful spectroscopic standard as it gives a number of brilliant lines fairly evenly spaced throughout the visible spectrum.

The Doppler effect is the change in wave-length of light wave due to relative motion in the line of sight of the light source and the observer. If a source of light is approaching an observer with velocity v, the change in wave-length (dλ) is given by

dλ/λ = v/c

where c is the velocity of light, the wave-length being diminished; and vice versa for a receding source. Until 1905, observations of this effect were limited to astronomical work on spectra, but in that year Stark discovered that the Doppler effect could be observed with the spectra of the " positive rays " or " Kanalstrahlen " of gases. The discovery is an important one, as it promises to throw considerable light upon the question of the origin of series in spectra. The Doppler effect has been observed for certain lines in the spectrum of helium.

The light of a vacuum tube containing helium is easily affected by electrical waves, and this fact forms the basis of a suggested method for their detection.

The Zeeman effect for helium has been observed by Lohmann. When the glowing gas is placed in a magnetic field and the light issuing at right angles to the lines of force examined with an echelon diffraction grating, it is found that all the lines become triplets and that the fraction x/λ2, where x is the distance between the outside lines of a triplet and X is the mean wave-length, is the same for all lines. Measurements made with a Rowland grating give similar results. The simplest development of Lorentz's theory of the Zeeman effect leads to the anticipation that x/λ2 should be the same for all the lines of a spectrum and the above experimental results therefore indicate that the helium molecule has a very simple structure. This conclusion receives support from the fact that mercury vapour, which is known on quite other grounds to be monatomic, shows precisely the same relationship.

Helium as diamagnetic

Experiments on the absorption of cathode rays in helium and in other gases have shown that with all gases the absorption increases to a maximum with decreasing velocity of the rays. In the case of hydrogen this maximum occurs with much lower velocities and is attained more suddenly than in the case of other gases, and helium exhibits the peculiar behaviour of hydrogen, but in a much exaggerated form: the absorption curve rises but slowly down to very small velocities of the rays and then rises very abruptly to a maximum.

Numerous experiments have been made to find the ratio of the two specific heats (at constant pressure and constant volume). This determination is important, because from theoretical considerations and from measurements on the monatomic vapour of mercury, we believe that in any monatomic gas the value of the ratio Cp/Cv should be 1.667.

One of the most convenient methods for determining this quantity depends on the relation between the ratio of the specific heats (γ) and the velocity of sound in the gas.

The velocity v of the propagation of sound waves in an elastic medium, according to Newton's formula, is:

where K is the coefficient of elasticity and d the density of the medium. The value of K for a gas is the elasticity under adiabatic compression (without loss or gain of heat), and is greater than the isothermal elasticity, which is numerically equal to the pressure. The ratio between the two elasticities is equal to γ, the ratio of the specific heats.

If, therefore, in the gas under investigation, λ is the wave-length of a sound of frequency n, and if the isothermal elasticity is p and its density d, we have

where D is the density of the gas under unit pressure. Writing λ1 and D1 for the corresponding quantities in another gas for which the value of γ1 is known, the wave-length λ1 of a note of the same frequency n, will be given by


As the ratio p/d is independent of the pressure, we do not require to know the actual pressures and densities of the gases in the two cases, and any variation of temperature can be allowed for in the values of D and D', though it is usual, for the sake of simplicity, to adopt the same temperature in each case.

Air, for which γ = 1.408, is used as the standard gas, and the determination of γ for any other gas thus resolves itself into a comparison of the wave-lengths of the same sound in air and in the gas. This is usually accomplished by a method due to Kundt.

Ramsay Collie Travers apparatus
Ramsay Collie Travers apparatus
The particular form of apparatus used by Ramsay, Collie, and Travers (vide infra) is indicated in fig.

A long tube T, which may be of narrow bore (2 mm.) is closed at one end, and through this end is sealed a glass rod R, half of which is inside and half outside the tube. Some lycopodium powder is distributed along the tube, dry air is introduced, and the rod R is set into longitudinal vibration by rubbing it with a rag wet with alcohol. By moving the clip C on the thick-walled rubber tubing fitted to the open end of T, the length can be adjusted till it resounds to the note. The stationary waves thus set up in the tube by interference between the waves incident upon and reflected from the ends of the tube are made evident by the disposition of the lycopodium which is swept away from the points of greatest movement and heaped up at the nodes. The distance between adjacent nodes - the half wave-length - is determined by direct measurement. The tube is next evacuated and filled with the gas under examination and the measurement of wave-length repeated.

Owing to the lightness of helium it is extremely difficult to get good dust figures, and thus Ramsay at first found for y the high value 1.8. Subsequently it was found that in the particular apparatus used, for air,\tλ/2 = 19.60 mm.; while for helium λ/2 = 101.5 mm.; Whence, for helium γ = 1.652 mm.

This figure has been confirmed by other observers.

Scheel and Heuse have determined the specific heat of helium at constant pressure and the ratio of the specific heats at 18° and - 180° with the following results: -

Cp at 18° = 4.993; at -180° = 4.934

γ at 18° = 1.660; at -180° = 1.673
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