where n is the number of vibrations per second, λ the wave-length of sound, and a the coefficient of the expansion of a gas for a rise of 1° in temperature, t, viz. 0·00367. Now if the expression p (1 + at) can be shown to be identical for argon and for air, the value of γ for argon can be calculated by the very simple proportion—
λ2dair : λ2dargon :: 1·408 : γargon.
This involved a measurement of the rate of rise of pressure of argon, p, per degree of rise of temperature, t; or, in other words, the verification of Boyle’s and Gay-Lussac’s laws for argon; and this research was successfully carried out by Dr. Randall of the Johns Hopkins University of Baltimore, U.S.A., and Dr. Kuenen, of Leyden, working in Professor Ramsay’s laboratory.[29] They made use of a constant volume thermometer, and measured the rise of pressure corresponding to a definite rise of temperature, comparing the gases argon and helium in this respect with air. The values found between 0° and 100° for air, argon, and helium were—
| One volume air, heated from 0° to 100°, raises | |
| pressure in the proportion of 1 to | 1·3663 |
| Argon | 1·3668 |
| Helium | 1·3665 |
It may therefore be taken for certain that, within the limits of experimental error, the value of the expression p(1 + at) is identical for all three gases.
We see, then, that for argon, as for mercury gas, the value of γ, the ratio between the specific heats at constant volume and at constant pressure, is 1 to 1·66, whereas for air, hydrogen, oxygen, nitrogen, carbon monoxide, and nitric oxide, it is 1 to 1·4.
We have now to consider what conclusion can be drawn from this difference.
On the usually accepted theory of the constitution of matter, it is held that atoms may be regarded as spheres, hard, elastic, smooth, and practically incompressible. True, we really know little or nothing regarding the properties of such particles, if particles there be; but in considering their behaviour it is necessary to make certain suppositions, and to see whether observed facts can be pictured to our minds in accordance with such postulates. If, from the known behaviour of large masses, conclusions can be drawn regarding small masses, and if these conclusions harmonise with what is found to be the behaviour of large numbers of small masses acting at once, the justice of the supposition is, although not proved, at least rendered defensible as one mode of regarding natural phenomena.
Molecules, on this supposition, may consist of single atoms, or they may consist of pairs of such atoms, joined in some fashion like the bulged ends of a dumb-bell; or lastly, they may consist of greater numbers of atoms arranged in some different manner, the arrangement depending on their relative size and attraction for each other. It must be clearly understood, however, that such mental pictures are not to be taken as actually representing the true constitution of matter, but merely as attempts to picture such forms as will allow of our drawing conclusions regarding their behaviour from known configurations of large masses.
The molecules of gases are imagined to be in a state of continual motion, up and down, backwards and forwards, and from side to side. It is true that they must also move in directions which cannot be described by any of these expressions, but such other directions may be conceived as partaking more or less of motions in the three directions specified; i.e. in being resolvable into these. To these motions have been applied the term “degrees of freedom.” Such motions through space, in which the molecule is transported from one position in space to another, form three of the possible six degrees of freedom which a molecule may possess, and the molecules are said to possess “energy of translation” in virtue of this motion. The other three consist in rotations in three planes at right angles to each other.