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CHAPTER VI

MOLECULAR FREE PATHS

61. Objections to the Kinetic Theory

THE theory of gases developed in the foregoing investigations has been shown to be in agreement with experimentally determined laws in a series of important points; Boyle's law and Dalton's law respecting the pressure of gases are necessary consequences of the theory, which explains also the law of effusion and justifies important laws of theoretical chemistry by furnishing Avogadro's law with a convincing foundation. In spite of this, however, its admissibility would lie open to justifiable doubts and objections if we confined the investigation to the points so far considered, and omitted to pursue the consequences of our hypothesis in other directions also.

As soon, indeed, as Krönig and Clausius 2 had roused the attention of the learned world in 1857 by their first memoirs, many replies and objections were raised against the hypothesis that combated the views hitherto held. But the considerations that were urged against it, far from refuting the theory against which they were marshalled, have served but to promote its development by causing Clausius to publish the important works in which, by enlarging into a scientific system the fundamental conceptions of the theory that had frequently been brought forward before his time, he made himself the real founder of the kinetic theory of gases.

The doubts put forward by Buys-Ballot,3 Hoppe,

1 Pogg. Ann. 1856, xcix. p. 315.

3 Ibid. 1858, ciii. p. 240.

2 Ibid. 1857, c. p. 353.

Ibid. 1858, civ. p. 279.

Jochmann, and others related to a series of very different phenomena, which were apparently irreconcilable with the theory, but are all referable to one and the same point of the theory that is easily liable to misconception.

Starting from the hypothesis that the particles of a gas are in a state of forward motion in straight lines, we have found ourselves forced to the conclusion that, for the elasticity and pressure of a gas to be explained, these motions are executed with enormous speed. A particle of air traverses a path of more than 400 metres in a second, and a molecule of hydrogen a path even four times greater. If these paths are really traversed in a single straight line, as the hypothesis of the theory seems to require, many phenomena are at once unintelligible.

Smoke can hang in still air for a long time almost immovable like a cloud. But it would be dispersed in a moment if the air molecules tore the particles of smoke away from each other, and carried them off in all directions nearly 500 metres in a second.

Sulphuretted hydrogen, generated in the corner of a room, must at once be scented everywhere in the whole room if its molecules hastened through the room in straight lines with the speed of 409 metres per second as calculated in § 28. On the contrary, we observe that the diffusion of this and other gases proceeds with the utmost slowness.

Still more convincingly than by this objection the theory seems to be refuted by the fact that gases conduct heat very slowly. For if heat consists in that rapid motion, and if this proceeds in straight lines, it must be propagated so fast by its own agency that a rise of temperature occurring at one point of a gas would be discoverable 400 metres away in no longer than a second; it must travel, in fact, quite as fast as sound.

For the same reason it would not be conceivable that the equilibrium of temperature that exists in the earth's atmosphere, where the higher layers are much colder than the lower, could be maintained; indeed there would be all the appearance of the earth's being surrounded by such good

Pogg. Ann. 1859, cviii. p. 153.

conductors that it could not maintain a temperature in which life could exist.

62. Refutation of the Objections

There would, indeed, have been no need of such a piling up of objections to bring the conviction that in a theory that has already obtained confirmation in so many points there must be some conception liable to be misunderstood.

The molecules of gas certainly move with that furious speed, and also move in nearly straight paths, but only till they strike some obstacle or collide with other particles. This, however, occurs very often-so often, indeed, that the case in which a molecule of the atmosphere enveloping us traverses a path of 400 metres without actual disturbance hardly ever occurs; but each air particle collides with some other exceedingly often, indeed many million times a second.

2

This remarkable behaviour, which was brought to light by a theoretical calculation carried out successfully by Clausius' and was confirmed by Maxwell in a theoretical 2 and experimental3 investigation closely connected with that of Clausius, puts our theory in quite a different light. We have not to consider the rectilinear backward and forward motion of the molecules as a translatory motion, bound up with enormous change of place and proceeding within wide limits of space, but as consisting of a motion of molecules among each other, proceeding tumultuously hither and thither in straight zigzags and confined within a narrow space; the molecules thus execute such a motion that the best representation of it is that of grains of corn shaken about in a closed box.

By this explanation of the character of the molecular motion the objections that have been raised fall at once to the ground; for the supposition at the bottom of each, viz. that a particle of air can in a second reach a place

'Ueber die mittlere Länge der Wege u.s.w.,' Pogg. Ann. 1858, cv. p. 239; Collected Works, 2. Abth. 1867, p. 260; transl. Phil. Mag. [4] xvii. 1859, p. 81. 2 Phil. Mag. 1860 [4] xix. p. 19; xx. p. 21.

3 Phil. Trans. 1866, clvi. p. 249.

distant by more than 400 metres, is not at all made in the kinetic theory.

How in accordance with this we have to explain the slowness with which the diffusion of gases proceeds is clear and intelligible without further words. The reason for the slowness of the conduction of heat is also easily seen if we look more closely into the process in the way in which Stefan has first examined it.

A heating of one region in a gas consists, according to our theory, in an increase of the molecular speeds in this region. The warmer particles therefore collide with greater momentum against the colder ones near them, and thereby impart a portion of that greater momentum, or, what is the same thing, of their higher temperature, to their environment. In this transference of the energy of motion consists the conduction of heat. This conduction would take place with the speed of the molecular motion if at each collision the striking particle so hit the one struck that the latter moved on in the same direction as that in which the blow occurred. But this happens only on the direct collision of two molecules which were moving in the same or opposite directions; they then simply exchange their velocities, and the whole excess of motion and heat is transferred from the one particle to the other. Mostly, however, the particles collide against each other obliquely; then the particle struck is thrust off in quite a different direction, and it follows that it also receives a much less share of the excess of energy of the other. The transference of heat is therefore not only impeded by its having to follow a zigzag path hither and thither, instead of proceeding in a straight line, but also by only a small fraction of any excess of energy being in general imparted at each collision. It is thus intelligible why a sensible heating cannot spread with the speed of sound in the space occupied by a gas, but only very slowly.

The objections raised are not, therefore, hard to remove. But the raising of them was of great importance for the development of the kinetic theory, and was very beneficial

'Pogg. Ann. 1863, cxix. p. 492; Wiener Sitsungsber. xlvii.