A. Michels

Contribution to the quantum-mechanical theory of the equation of state and the law of corresponding states. Determination of the law of force of helium

Summary Starting from a suitable expression for the potential of molecular interaction, the theoretical expression for the second virialcoefficient B can be expressed in the form of a law of corresponding states, based on volume and temperature units derived from the molecular field. The influence of quantummechanics is discussed by integrating the expressions for the quantum-mechanical correction terms of B, given by Uhlenbeck and Beth and by Kirkwood, which are valid for high temperatures. From comparison of these expressions for B, with the experimental B-values as a function of temperature, new values for the molecular field-constants of helium and hydrogen are obtained. These values are compared with the figures of Lennard-Jones and the theoretical data of Slater, Kirkwood and Margenau for helium.

Quantum-mechanical calculation of the second virial-coefficient of helium at low temperatures

Summary Using the interaction energy between two helium atoms, obtained in a previous paper by comparison of the quantum-mechanical expressions for the second virial-coefficient B with the .experimental data at temperatures above 40°K, the phases are evaluated by numerical integration of the wave-equation of the relative motion of two helium atoms. The integration of the wave-equation for E = 0 showed that it is highly probable that no discrete level exists. The phases are used to evaluate the expression for B, which has been given by Uhlenbeck and Beth. The values obtained are compared with the experimental values of Keesom and Kraak at 2.59, 3.09 and 4.22°K. The behaviour of B at very low temperatures, is discussed especially as regards the influence of the existence of a discrete level. Finally, the cross-section for the scattering of helium on helium atoms has been calculated by substituting the phases in the formula given by Massey and Mohr.

The influence of the interaction of more than two molecules on the molecular distribution-function in compressed gases

Summary Starting from the usual expression for the molecular distribution function g(r), a series expansion into powers of 1/ν is given. The second approximation has been evaluated numerically for a Lennard-Jones potential field in the revised form V(r) = 4e(R−12 — R−6) (where R = r/σ), which allows the results to be applied to all gases, for which the molecular field constants are known. The results obtained are compared with the experimental curves for liquid Hg, Ga and K and the general behaviour is interpreted, using the relations between g(r) and the potential of the mean force acting between two molecules. Finally, using the virial-theorem and the calculated g(r)-values, the third virial-coefficient has been evaluated theoretically, the results being compared with the experimental figures for nitrogen and argon.

Isotherms of nitrogen between 200 and 3000 atm. and 0° and 150°

Summary The isotherms of N2 have been measured at 0°, 25° etc. up to 3000 atm. A series evaluation of the type: p (v - α) = A + βd + γd2 + δd3 + ∈d4 fitted the experimental values better than a series of the usual type, but the deviations were still outside the experimental accuracy.

Properties of liquid helium II

Summary The theory of the degeneration phenomena of an ideal Bose-Einstein gas is modified so as to make it more in accordance with the thermal phenomena of liquid helium II. At the lowest temperatures the specific heat can be brought in agreement with the experimental data when the plausible assumption is made, that an excitation energy is required for the conversion of a “condensed” molecule in a “moving” one. The abnormally thick surface films of He II are explained by a wave-mechanical treatment as being due to an additional zeropoint energy, which depends on the dimensions of the vessel and which predominates the effect of intermolecular forces in the surface layers. The flow phenomena in very thin layers and narrow capillaries are discussed; it is shown that the experiments point definitely in the direction of a slip of the liquid along the wall. The maximum slipvelocity as determined from the experiments must depend on the thickness d of the layer according to the formula vmax ∼ h/md. The same formula can be applied to the flow through narrow capillaries when d is replaced by the diameter of the capillary. Finally a proof is given that an excitation energy appears in the quantum mechanical perturbation theory of an ideal gas, when a small repulsive force between the molecules is introduced.

Calculation of thermodynamic properties of nitrogen up to 3000 atm. between 0 and 150

Summary From the isotherm data of N2 the change of internal energy, specific heat, entropy and free energy have been calculated.

Influence of pressure on the curiepoint of a 70–30% Ni−Cu alloy

Summary The effect of pressure on the resistance phenomena near the Curiepoint of a Cu−Ni alloy has been determined. The Curie temperature increases by increasing pressure 6.10−5 degree per Atm. The result is discussed in connection with recent theories on ferromagnetism.

Average values of a group of mechanical quantities in quantum statistics of monatomic gases

Abstract The expansion of the partition function of a monatomic gas given by Ursell and Mayer and adapted to quantum mechanics by Uhlenbeck and Kahn, has been generalised to obtain a series-expansion into powers of the reciprocal volume for a group of quantities, as for instance the potential energy and the virial of the intermolecular forces of a monatomic gas. The expressions obtained are applied to calculate the deviations from the law of equipartition in quantum mechanics in the temperature region, where the deviations from classical statistics are small.

A suggested explanation for some properties of liquid He II.

Summary A possible mechanism for the heat conduction in liquid He II is indicated. In this connection the abnormal velocity of flow is also discussed.