Abstract
Any one, who has not studied seriously any branch of physics, glancing occasionally in our physical periodicals and noticing the subjects experimental research is concerned with, will very likely feel inclined to the opinion, that a great part of these investigations is perfectly useless. It may be that he will not object to determinations of the elasticity of metals, the tension of water-vapour, the electromotive force of galvanic cells and the like, but then he will have in mind the important applications of physics. Our uninitiated reader will, however, be at a complete loss to explain, how one can possibly be interested in the small deviations, shown by the gases, from Boyle’s law, in the specific heat of a metal like cerium, which has only be obtained in quantities of a few grains, or in the optical constants of some rare mineral or other. When, moreover, he is told that physicists actually exist, who devote a large part of their life to investigating the shape of liquid drops and membranes or determining refractive indices of all kinds of materials, he is sure to consider their work rather trifling and but little stimulating.
Inaugural address, Leiden, 25th January 1878.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Notes
The following quotation from his „Discours sur l’utilité des mathématiques dans toutes les sciences, et particulièrement dans la physique” (Oeuvres philosophiques et mathématiques de ‘s Gravesande, publiées par Allamand, II p. 323) may serve to give ‘s Gravesande’s opinion about universal gravitation. After a few preliminary considerations concerning that force he goes on: „Quelle que soit cette force, il faut lui donner un nom. Si nous ne faisons attention qu’au corps vers lequel l’autre est porté on l’appelle attraction; mais à l’égard du corps qui est porté on la nomme gravitation. Ces noms désignent des effets et non des causes; ceux qui ont reproché à Newton qu’il désignait par eux des qualités occultes n’ont pas eu une idée juste de la philosophie.
Phil. Mag. 3, 401, 1877, brings an article of Hicks on this subject. In his computations he starts from the following suppositions: 1. That when a molecule experiences a blow greater than a certain blow c, it breaks up into its component atoms, 2. that when two atoms impinge with a blow less than c, they combine to form a molecule. It will be clear that the results deduced from these suppositions can at most be only a rough image of reality.
The internal state of a monatomic gas (or of a mixture of two such gases) at rest at uniform temperature and density is known very accurately. It can now be required from the kinetic theory to determine, what laws must be obeyed by small deviations from that state. In order to know these deviations completely, one would have to know how the various velocities are distributed over the various molecules, also in the case when turbulent motions take place in the gas or when the latter does not possess a uniform density, composition or temperature. If the gas-particles repel each other with a force, inversely proportional to the fifth power of their distance, Maxwell succeeded (Phil. Mag. 35, 129, 185, 1868) even without knowing the velocity-distribution in question, to deduce from the kinetic theory of gases the aerodynamical equations and to compute the coefficient of friction and the conduction of heat. Later on Boltz-mann (Wiener Sitzungsberichte, 66, 275, 1872) treated on the same supposition the law of the velocity-distribution for non-stationary states. When, however, the particles do not act on each other in this particular way, when, for example, they behave like elastic spheres, the knowledge of the velocity-distribution in the non-stationary state is indispensable for a rigorous solution of the problems on internal friction and suchlike, but for that very case the distribution law has not been discovered. So long as this gap is not filled the theory of internal friction, developed under this condition, must be considered as only an approximate one.
If the gas-molecules may be considered as elastic spheres one is able, supposing that the theory of internal friction were developed completely, to deduce from the coefficient of internal friction of a gas some information on the diameter of its particles, and if this had been worked out for two gases, one would possess also the data, necessary for taking into account the mutual collisions of the particles of these two, gases, so that one could then compute their diffusion and the internal friction of a mixture of the two gases. Besides, there must then exist a definite connection between the coefficients of diffusion of a number of gases, taken in pairs. So soon, however, as the particles act on each other in a different way, one cannot draw any conclusion from the mutual action of particles of one and the same gas, as to the interaction of molecules of different gases, and all of the computations, mentioned above, are then cancelled. This is why the diffusion and the internal friction of a gaseous mixture are of such great theoretical importance. So far as one is able to judge at present, it would seem that the conception of the particles of a gas as behaving like elastic bodies, has the greater probability in its favour. See Stefan, Wiener Sitzungsberichte, 65, 323, 1872; Maxwell, Nature, 8, 298, 1873.
Van der Waals imagines the molecules to be elastic spheres, which attract each other at a distance. The distance at which, when colliding, their centres of gravity remain apart, in other words, the extension of the particles, is taken into account by him by investigating how much the path between two successive collisions is shortened by the extension of two molecules in the direction of their relative motion and by then deducing in what proportion the number of collisions against the walls of the containing vessel is thereby increased. Later on, the shortening in question of the path between two collisions has been computed more rigorously by Korteweg (K.A.W. 10, 349, 363, 1876) but in this way he obtains the same result as van der Waals. Maxwell (Nature, 10, 477, 1874) objects to van der Waals’ computation. He remarks that it must be possible to find the influence of the spatial extention of the molecules by taking into account in the well-known expression for the virial, also the virial of the repulsive forces that the molecules exert on each other at a collision. He only gives the result of his computation and this differs from van der Waals’ result. In the meantime, I have found that, at any rate if the molecules of a gas fill only a small fraction of the space in which they are contained, one does arrive at van der Waals’ equation by considering the virial of the forces of repulsion in question. (See Coll. Papers, vol. 6, p. 40. Editors’ note).
Since then experiments of Mendeléeff on these deviations have been published (Nature, 15, 455, 498, 1877), the explanation of which is still wanting.
It is not difficult in this problem either, to take into account the influence of molecular attraction, if one may suppose, as Laplace did in his theory of capillarity, that the radius of the sphere of attraction, though very small, yet is still very large compared with the average distance of the molecules, so that the sphere of attraction circumscribed round any particle still contains a great number of molecules. It fol-’ lows then that, when a space is filled partly with a liquid and partly with its vapour, no force acts on a molecule in the interior of the vapour or of the liquid, but that on a molecule in the boundary-layer a force does act, which depends solely on the position of that particle. Everything comes in this case to the same as if there were no attraction at all, but as if the molecules were acted on by external forces, which are a function of the position of the particles. When, however, external forces of such a nature act and when one neglects the spatial extension of the particles, the problem of determining their motion has already been solved in a general way. It would not be difficult to take into account in this solution also, the extension of the particles, and in this way one would be able to establish for the tension of saturated vapours an expression, wholly deduced from the kinetic theory. But, unfortunately, it is apparently not allowed to assume each molecule to be attracted by a great many other molecules. Van der Waals arrives at the result, that molecules attract each other appreciably only shortly before their collision, and if this be true, the rigorous treatment of molecular attractions becomes much more difficult and it will not then be allowed to consider the expression, which in the way indicated above can be obtained for the tension of saturated vapours as a entirely correct theoretical formula.
It can be proved, namely, that in the case of particles at rest in the position of equilibrium of the body, the pressure or stress between contiguous parts must be zero. By introducing this into the equations of the problem, one obtains between the constants, determining the elasticity of the body, a relation which does not agree with experiment. The magnitude of the deviation from that relation must in some way or other be connected with the intensity of the heat-motion.
Considering our deficient knowledge of the heat-motion in solid bodies, there is as yet only little hope for a completely developed theory of elastic after-working. For the time being, one will probably not be able to go any further than Boltzmann (Pogg. Ann. Ergänzungsband, 7, 624, 1876). The only question is how far the fundamental theorem, used by him, can be considered a necessary consequence of the molecular theory.
I am thinking here more in particular of the measurements of Baumgarten on the elasticity of Iceland-spar (Pogg. Ann. 152, 369, 1874) and of those of Woldemar Voigt and Groth on the elasticity of rocksalt (Pogg. Ann. Ergänzungsband, 7,1, 177, 1876, and Pogg. Ann. 157, 115, 1876). The last mentioned experiments are especially remarkable, because it appears from them that even in crystals of the regular system the elasticity is not the same in all directions. The way, however, in which it changes with direction, must be closely connected with the law, according to which the mutual action of two molecules depends on distance.
Rights and permissions
Copyright information
© 1939 Martinus Nijhoff, The Hague, Netherlands
About this chapter
Cite this chapter
Lorentz, H.A. (1939). Molecular Theories in Physics. In: Collected Papers. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-3443-7_2
Download citation
DOI: https://doi.org/10.1007/978-94-015-3443-7_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-015-2213-7
Online ISBN: 978-94-015-3443-7
eBook Packages: Springer Book Archive