Kinetic theory of gases

“ And I show that the kinetic theory of gases not only fails to satisfy this requirement, but is a complete reversal of a legitimate scientific procedure. This is the sense of the passage which Professor Newcomb parades before the unwary reader, whom he ought to have shocked still more with my horrible suggestion (which I now deliberately repeat) that a gas is in its nature a simpler thing than a solid, and that no attempt to account for its properties by taking those of a solid as a basis and making arbitrary additions to them is likely ever to succeed. ”

“ Highly superheated vapors can be treated as gases, and by appropriately mixing different substances one can always imagine a gas mixture being produced which has a finite absorptivity for all wavelengths. But one must not think here of the radiation which the gases emit under the influence of electrical or chemical processes.
If one assumes a gas as a radiating body, Maxw ell's law of the distribution of velocities will apply if we take as our basis the kinetic theory of gases. The absolute temperature will be proportional to the mean kinetic energy of the gas molecules. ”

“ The atomistic hypothesis shows itself remarkably fecund in the study of phenomena produced in gases, and here the mutual independence of the particles renders the question relatively more simple and, perhaps, allows the principles of mechanics to be more certainly extended to the movements of molecules.
The kinetic theory of gases can point to unquestioned successes ”

“ It should be observed that this self-adjustment of their motion by the particles is not a mere result of chance, but a rigid adjustment of such a character that, if the uniformity of the motion were artificially disturbed, the particles when left to themselves would immediately correct the irregularity. The above length of free path, though great in one sense, becomes small and suitable for a gas pervading the vast range of the visible universe. ”

“ The coefficient of resistance being found, the motion of each of the two gases may be discussed separately.
One of the most important consequences of the kinetic theory is that if the volume be kept constant the coefficient of diffusion varies as the square root of the absolute temperature. To prove this, we merely have to imagine the velocity of each molecule to be suddenly increased n fold; the subsequent processes, including diffusion, will then go on n times as fast ”

“ Thus, e. g., the law of Avogadro in pure thermodynamics is only a definition, while in the kinetic theory it is a necessary consequence; furthermore, the value of , the mol-heat of a gas, is completely undetermined by pure thermodynamics, but from the kinetic theory it is of equal magnitude for all monatomic gases and, in fact, equal to , corresponding to our experimental knowledge. ”

“ Were it not for this fundamental difficulty, the hydro-kinetic model gas would be exceedingly interesting; and, though we could scarcely adopt it as conceivably a true representation of what gases really are, it might still have some importance as a model configuration of solid and liquid matter, by which without elasticity the elasticity of true gas might be represented. ”

“ This proves that the particles of the gas attract one another slightly, and but very slightly. It follows that, when a gas is under pressure, what prevents it from collapsing is not any repulsion between the particles, since there is none. Now, there are only two modes of force known to us, force of position or attractions and repulsions, and force of motion. Since, therefore, it is not the force of position which gives a gas its expansive force, it must be the force of motion. In this point of view, the kinetical theory of gases appears as a deduction from the mechanical theory of heat. ”

“ That theory, in fact, shows that the more nearly identical the gases are, the slower will be the process of inter-diffusion, so that the mechanical energy will indeed be available, but only after a time that becomes indefinitely prolonged. It is a case in which the simple doctrine of energetics becomes inadequate before the limit is reached. The phenomena of highly rarefied gases provide other cases. ”

“ From the ascertained behaviour in certain respects of gaseous media we are able to construct their characteristic equation, and correlate their remaining relations by means of its consequences. Part of the experimental knowledge required for this purpose is the values of the gas-constants, which prove to be the same for all nearly perfect gases. The doctrine of energetics by itself can give no clue as to why this should be so; it can only construct a scheme for each simple or complex medium on the basis of its own experimentally determined characteristic equation. ”

“ It will be seen from these pressures that when combustion is complete, the force developed is 2·36 greater than when combustion is incomplete; and also that the increase of force is due to the larger quantity of heat liberated, since the volume of the gases is the same in both cases. If we suppose the carbon burned to carbonic oxide in the presence of a sufficient quantity of oxygen to make carbonic acid, we shall have 31·5 cubic feet of the oxide + 15·7 cubic feet of free oxygen, or a total volume of 42·7 cubic feet of gases. ”

“ It will be observed that when , the presence of the gas will not affect the pressure or density of the gas . When , the pressure and density of the gas are greater than if were absent, and when , the reverse is true. The properties of an ideal gas-mixture (according to the definition which we have assumed) when in equilibrium with liquids or solids have been developed at length, because it is only in respect to these properties that there is any variation from the properties usually attributed to perfect gases. ”

“ The simplest form of assimilation is seen when volumes of two different gases are brought together within a closed receptacle; for, though the molecules of the two gases may originally possess different "kinetic" energy, they undergo in association a change by which the molecules of both gases come to have a like degree of the energy of movement. What is true of gases is true also of matter in each of its states: heat communicated to an aggregate is more or less rapidly distributed through it until all the parts possess, roughly speaking, like degrees or amounts of movement ”

“ Thus, if we regard a mixture of hydrogen oxygen, and vapor of water as an ideal gas-mixture, for a mixture containing any given quantities of these three gases at any given temperature there will be a certain volume at which the mixture will be in a state of dissipated energy. In such a state no such phenomenon as explosion will be possible, and no formation of water by the action of platinum. (If the mass should be expanded beyond this volume, the only possible action of a catalytic agent would be to resolve the water into its components.) ”

“ In gases at atmospheric pressure, the commercially available thermal sources induce transition rates between quantum energy states which are small compared to those of the competing collisional relaxation processes, and cannot induce non-equilibrium energy state populations. ”

“ A still more striking experiment is that resulting from the liquefying of nitrous oxide—protoxide of nitrogen, or laughing-gas. This gas needs, as was said, great pressure to liquefy it at an ordinary temperature. At freezing point only a pressure of thirty atmospheres is needed to liquefy it. It then boils if exposed to the air, radiating cold—or, rather, absorbing heat—till it falls to a temperature low enough to freeze mercury. But it still, wonderful to say, retains the property which, alone of all the gases, it shares with oxygen—of increasing combustion. ”

“ Since β and α are each proportional to the pressure, the minimum potential is independent of the pressure of the gas. On this view the minimum potential depends upon the metal of which the cathode is made, since k measures the number of corpuscles emitted per unit time by the cathode when struck by positive ions carrying unit energy, and unless β bears the same ratio to α for all gases the minimum potential will also vary with the gas. ”

“ The emanation exhibits the characteristic properties of a gas, it obeys Boyle’s Law (i.e., its volume varies inversely with its pressure) , and it can be condensed to a liquid at low temperatures; its density as determined by the diffusion method is about 100. Attempts to prepare chemical compounds of the emanation have failed, and in this respect it resembles the rare gases of the atmosphere—helium, neon, argon, krypton, and xenon—whence it is probable that its molecules are monatomic, so that a density of 100 would give its atomic weight as 200. ”

“ The physical peculiarity from which this results is the intensity of its heat—commonly stated at 2,000 degrees, as to our common illuminating gas—acting instantaneously throughout its mass, just as in gunpowder. The gas goes up the flue in its own flash, like the ignited charge in the barrel of a gun: the burning coals can only send, and by a leisurely messenger, namely, the moderately heated gases, and contiguous air, that rise only by the gravitation or pressure of the surrounding atmosphere. ”

“ The chemical action takes place with much greater facility under these circumstances. The union of the carbon in the coal gas with the oxygen then takes place so thoroughly and instantaneously that the carbon never seems to have abandoned the gaseous form even for a moment in the course of the transformation. But in the case where air is not permitted to mingle with the gas, the supply of oxygen to unite with the incandescent gases can only be obtained from the exterior of the flame. ”