THE EXPANSION O F A GAS INTO A VACUUM AND THE KINETIC THEORY O F GASES' BY P E T E R FIREMAN
It is a fundamental fact that when a gas expands into a vacuum there is, roughly speaking, no evolution or absorption of heat in the whole body of the gas. But while the passing of a gas into an empty vessel is not accompanied by any change in the total quantity of heat in the gas, a change in the distribution of the heat takes place. If the experiment is carried outa with the aid of ,two metallic vessels of equal capacity communicating by means of a tube provided with a stop-cock, and if one vessel is filled with a gas under considerable pressure while the other is vacuous, then on opening the stop-cock and allowing the gas to pass into the empty vessel until equilibrium is established, we observe a considerable rise of temperature in the vessel which was vacuous and a nearly equal fall in the other. What is the cause of this simultaneous rise and fall of temperature, a rise and fall which seem to compensate one another 3 An attempt to give a clear answer to this question is the object of the present paper. Let us dwell for a little while on the important theoretical bearings of the experiment described. In the first place, it at once leads to the thermodynamical principle that the energy of a gas is independent of its volume. In the second place, the fact that there is no change in the total energy when a gas expands into a vacuum clearly shows that there is no repulsive force between its molecules. For if there were a repulsive force the expansion would involve a decrease of potential energy, wliich decrease would have to be made good by the increase of kinetic energy, by an absolute increase of the temperature of the entire mass of the gas. Since this is not the case, it follows that there Read before the Chemical Section of the American Association for the Advancement of Science, Pittsburg, July 2, 1902. e J. P. Joule. Phil. Mag. May, 1845,p. 377.
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is no repulsive force between the molecules of the gases. The proof of the absence of a repulsive force in the gases is an indirect support of the kinetic theory of gases, the only other doctrine regarding the nature of the gaseous state. According to this theory, the tendency of a gas to expand and to fill any space that is assigned to it is not due to a repulsive force between the molecules of the gas, but to the kinetic energy of the moving molecules under the influence of heat. In the third place, a most accurate study of the energy changes when a gas expands without doing work supplies the experimental basis for one of the corrections made in the gas equation by van der Waals and embodied in the so-called van der Waals equation. Joule and Thomsonl on causing gases to expand from a high pressure vessel through a porous plug ” found a slight loss of heat. This loss leads to the assumption that there is an attractive force between the molecules and that the loss of heat is due to the work done in overcoming this attraction. This attraction is taken into account in the van der Waals equation. I have dwelt at some length on the theoretical bearings of the phenomenon under consideration in order to emphasize more the importance of finding an adequate interpretation of it. The phenomenon is this : When a gas passes from one vessel into another which is vacuous, there results an increase of heat in the empty vessel and a decrease in the other. Why ? A plausible explanation would appear to be this : As soon as some of the gas has entered the vacuous vessel the rest of the gas does work on it, causing the rise of temperature in one vessel and the lowering in the other. But this explanation is very vague, and if not properly qualified, can be refuted as follows : You start with the molecules at a given temperature, i. e., with a certain mean kinetic energy ; you start with the molecules which are perfectly elastic bodies. Now what can be the result of collisions of that portion of the molecules which first entered the empty vessel and the remaining portion which is pressing after and on ((
-__\l’illiam Thomson’s Mathematical and Physical Papers, Vol. I., Article 49, P. 333.
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the former? The molecules of both portions have the same average velocity. Nothing else can result than an exchange of a certain mean kinetic energy with the same mean kinetic energy. Hence in consequence of the increase of volume, only the free mean path of the molecules will increase, which has nothing to do with the magnitude of the kinetic energy, with the magnitude of the heat. The proper explanation, without bringing in any notions which themselves require elucidation, can be, in my opinion, found as follows : Consider the molecules of the gas as they are ready to pass into the vacuous vessel. They arrive with various degrees of velocity. Consider, first, a swift molecule. In the empty vessel it will evidently retain its high velocity. Next, consider a slow molecule. Before it will have made much progress it will be overtaken by a fast one and exchange velocities with the latter, according to the law of impacts of elastic bodies ; it will continue on its way, but with a high velocity. And so with all the molecules or, at least, with the greatest part of the molecules which enter the enipty vessel ; they will either have possessed a high velocity and retain it or acquire it as explained. The result will be a congregation of swift molecules in the vessel which was vacuous and a lagging behind of the slow ones in the vessel which was filled with the gas at the beginning. We have here as it were a separation of molecules with high velocities from those with low velocities. Hence a rise of temperature in one vessel and a fall in the other. But this result is only possible owing to the fact that in the body of a gas at a given temperature there are molecules with widely different velocities. If the gas molecules in a given vessel at a constant temperature moved all with the same velocity then the expansion of a gas into a vacuum could not bring about a new distribution of the heat in the body of the gas. Thus the experiment of the expansion of a gas into a vacuum throws further light on the kinetic theory of gases, cor-
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roborating the view that the molecules in a closed vessel at a constant temperature move with various degrees of velocity. Further, in the light of the above reasoning, the cold produced by the escaping of a gas from under a high pressure into the atmosphere is due to the swift molecules rushing away far into space and the slow ones lagging behind.
