Knowing the mass of a given volume of a gas, and the pressure that the gas exerts against the boundaries that confine it, we may cal culate the average speed that the constituent molecules of the gas must have, in order to produce the observed pressure. The formula by which the calculation is effected need not be given here, but some of the results are of interest. Thus it is found that at 32° F. the molecules of the more familiar gases have the following average velocities, in feet per second: Hydrogen, 5,571; oxygen, 1,394; nitrogen, 1,488; carbon monoxide, 1,491; carbon dioxide, 1,189. At higher temperatures, the velocities are greater, being proportional, for any one gas, to the square root of the absolute temperature.
A very important application of the kinetic theory of gases relates to the ratio of the spe cific heats of a gas. Boltzmann's theory shows that if the specific heat of a gas at constant pressure be divided by its specific heat at con stant volume, then the quotient can be ex pressed in the form 1 -1--n 2 , provided the effects of such forces as may exist between the differ ent molecules of the gas are negligible, n being the number of degrees of freedom of the mole cules of gas under consideration. This equa tion, it will be seen, affords a means of ascer taining the number of degrees of freedom of the molecule of a gas, by setting the foregoing expression equal to the observed value of the ratio of the specific heats, and then solving the equation for n. By this method, it has been inferred that the molecules of hydrogen, nitro gen, oxygen and carbon monoxide have each five degree of freedom; for the ratio of the specific heats of these gases approximates closely to 1.4, which is the value of the foregoing ex pression for n— 5. If the molecules of a gas were really smooth spheres,— so smooth that they could not be set in rotation by their collisions,— then we should have n = 3, and hence the ratio of the specific heats would be 1.667, a value which is actually observed in the cases of argon, helium, mercury vapor, cad mium vapor, and a few other substances. Hence it is inferred that argon and helium are ele mentary bodies; because it is difficult to con ceive of a compound body behaving, so far as collisions are concerned, as though its mole cules were smooth spheres; and if they had any other shape, it would be necessary to admit that they have at least five degrees of freedom (since it is impossible for any body in free space to have four degrees of freedom), and this would reduce the calculated value of the ratio of the specific heats to 1.400, a value
which it is apparently impossible to reconcile with the results of direct observation.
Most of the results of the kinetic theory, as given above, involve the assumption that the effects of the mutual attractions that may exist between the individual molecules of a gas are small, on the whole. The forces, when they exist, may be great; but we assume that under ordinary circumstances the radius of sensible action of these forces is small in comparison with the length of the average distance that the molecules travel, between successive collisions. When, by reason of the gas being greatly compressed, this assumption becomes of doubt ful validity, the foregoing conclusions become correspondingly weakened. The average dis tance that a molecule travels, between succes sive collisions, is known as its "free path)); and numerical estimates of the length of the free path have been obtained, by methods which cannot be given in the present article. Thus the free paths of some of the more familiar gases are as follows (expressed in ten-mil lionths of an inch), the gases being supposed to be at 32° F., and under ordinary atmospheric pressure: Oxygen, 38; nitrogen, 36; hydrogen, 67; carbon monoxide, 36; carbon dioxide, 25. When the density of a gas is diminished, the average free path of the molecules increases in direct proportion to the decrease in density. Thus in the high vacua that prevail in X-ray tubes, the mean free path may be measured in inches; the free path for hydrogen, for ex ample, being about 6.7 inches, when the density of the gas has been reduced to the millionth of the normal density at 32° F. and atmos pheric pressure.
The whole kinetic theory of gases is likely to be profoundly modified in the near future, when physicists have learned more about the "electrono (q.v.), which is now commonly re garded as the foundation unit in molecular architecture. For further details concerning the subjects touched in this article, consult Boltz mann, fiber Gastheorie) • Meyer, (Kinetic Theory of ; Risteen, and the Molecular Theory of Watson, Theory of Gases' ; Tait, (Foundations of the Kinetic Theory of Gases) See also