The Lambda Effect in Liquid Helium

Prof. W. Keesom

Recently new measurements were made of the specific heat of liquid helium at the pressure of saturated vapors[^1]. As a result of these measurements it became clear that the principal change in the heat capacity at the lambda point occurs within an interval of \(0.002^\circ\), and it is quite probable that it is even \(0.0002^\circ\).

New evidence was also found that the transformation He I into He II is not associated with the formation of latent heat.

Measurements of the specific heat at constant volume, carried out at elevated pressure, likewise revealed the lambda effect, as had been expected on the basis of previous measurements of the relation between pressure, volume, and temperature.

A satisfactory way of indicating a definite value of the magnitude of the jump in specific heat at the lambda point is proposed.

It may be assumed that the difference in the forms of the specific-heat curves for the branch corresponding to He I should be attributed to the influence of fluctuations caused by thermal motion.

Both the viscosity and the thermal conductivity of liquid helium change discontinuously at the point of transformation of He I into He II.

Thermodynamic Temperature Scale below \(0.9^\circ\) K

The thermodynamic temperature scale for the region above \(0.9^\circ\) was established with the aid of a helium thermometer. For lower temperatures it can be established by means of adiabatic demagnetization of paramagnetic salts, accompanied by the measurement of the amount of heat required to restore the initial temperature. If this heat is denoted by \(dQ\),

whereas the decrease in entropy corresponding to magnetization of the salt at the initial temperature by \(dS\), then the temperature reached upon demagnetization is

\[ T=\frac{dQ}{dS}. \]

With this method it is necessary to know precisely the magnetic properties of the salt at the initial temperature; however, a modification of the method has also been proposed in which no such requirement is imposed.\(^2\)

Heat Capacity of Electrons in a Metal

The atomic heat capacity of silver and zinc at temperatures lying below approximately \(6^\circ\)K, in a certain part of it, can apparently be attributed to the heat capacity of free electrons, following from Sommerfeld’s formula for the number of free electrons equal to 1 per atom.\(^3\) Recently made measurements of the specific heat of KCl at temperatures below \(3^\circ\)K\(^4\) confirm this.

The atomic heat capacity of nickel considerably exceeds the value natural for the atomic lattice.\(^5\) The additional heat capacity in the interval between 1.1 and \(9.0^\circ\)K can be expressed by the formula

\[ C_{\mathrm{add}}=0.001744\,T. \]

It may be assumed that this heat capacity is associated with the energy of the conduction electrons. The fact that it is many times larger than follows from Sommerfeld’s formula for free electrons shows that in the corresponding energy band, at least at the level of the limiting energy, the density of possible energy states is especially large.

Calorimetry of Superconductors

Experiments carried out with tin and thallium show that the specific heat of a metal, upon transition from the superconducting state to the nonsuperconducting state, undergoes a jump.\(^6\) The magnitude of this jump in the absence of a magnetic field corresponds to the formula indicated by Rutgers. It can be written in the following form:

\[ \Delta C = T\frac{d^2}{dT^2}\left(\frac{H^2}{8\pi d}\right), \]

where \(H\) is the magnetic field that must be applied in order, at the given temperature \(T\), to destroy superconductivity, and \(d\) is the density.

If there is no external magnetic field, then the transition from the superconducting state to the nonsuperconducting state occurs without any manifestation of latent heat. In the presence of a magnetic field, the latent heat associated with the cessation of superconductivity\(^7\) is described by the following formula, derived under the assumption of ideal conditions:

\[ r=-T\frac{d}{dT}\left(\frac{H^2}{8\pi d}\right). \]

This formula was confirmed for thallium in those experiments in which the metal was brought into the superconducting state in the absence of a magnetic field. In those cases when the preliminary transition to the superconducting state was carried out in the presence of a magnetic field, the measurements took into account only a certain fraction of the latent heat. This indicates that some fraction of the magnetic flux was “frozen” inside the body.

Confirmation of the formula written above by experiment shows that, from the thermodynamic point of view, the transition from the superconduc-

of the state into the nonsuperconducting one is a reversible process even in the case when there are nondecaying currents. This suggests the idea that the disappearance of nondecaying currents observed in the transition to the nonsuperconducting state is not connected with the formation of Joule heat, but depends directly on the penetration of the magnetic field.

At present, new measurements on tin are being carried out under conditions more closely approaching the ideal.