A system of physical chemistry - Index of

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A system of physical chemistry - Index of

EQ UIPARTITION OF KINETIC ENERG V 2 1

atomic molecule were really represented by the diagram (c), Fig. 2,

i.e. if the atoms were massive spheres extending a sensible distance

from the axis, the energy of the motion represented in the diagram

would be sufficiently large to make its presence felt in the molecular

heat of the gas. As a matter of fact this type of circular vibration does

not affect the molecular heat sensibly. This arises from the now

accepted conclusion that practically the entire mass of any atom is

concentrated in a nucleus situated at the centre of the atom, the dimensions

of the nucleus being small even compared with those of the

atom (c/. Chap. V., the Rutherford-Bohr atomic model). Hence, in

the motion represented in diagram (c), Fig. 2, the mass of the two atoms,

i.e. the mass of the whole molecule is practically all concentrated i^/'o/i

the axis of circular vibration (the figure axis in this case), and the

moment of inertia of the atoms, and consequently the energy in respect

of this motion is negligible, because the r term referred to in the tootnote

is practically zero. Further, as shown in Chap. V., each molecule

possesses a number of electrons likewise spinning, as in diagram {c),

Fig. 2. In the case of the electrons the distance r is not negligible,

but on the other hand the mass of the electron is so small a fraction of

the total mass of the molecule that again the moment of inertia is

small and the energy of electronic spin does not enter sensibly into the

"ordinary" energy content of the molecule, the variation of which

(energy) with temperature is given by the molecular heat. The molecular

heat term is due to energy of translation, of linear vibration and

of molecular rotation or its equivalent, precessional vibration {c/. infra).

The electron spin enters into the question of the ultra-violet spectrum

of the gas, c/. Chap. V. It must be assumed, of course, that such a

spin as that represented in the diagram (c), Fig. 2, takes place in all

cases. It is scarcely affected by temperature, however, and conse-

quently does not enter into molecular heat values, except in the limit

when the temperature is very high.

3, Energy of Molecular Rotatiott.— If a molecule resemble a solid

sphere we would it expect to rotate in the manner indicated in Fig. 3,

diagram {a). The rotation of a sphere can be referred to three axes

ot rotation, i.e. there are three degrees of freedom. The energy is

entirely kinetic. Molecules, however, are not necessarily spherical

unless they contain a number of atoms. It is beheved that at least

three atoms must be present in a molecule before we can possibly

ascribe to the molecule as a whole the limiting number (3) of degrees

of freedom in respect of rotation.

It is a remarkable fact that monatomic gas molecules do not appear

to possess rotational energy. This conclusion rests upon the experimental

fact that the molecular heat of argon and other monatomic

gases and metallic vapours can be accounted for by simply assuming

translational energy. This point will be dealt with later. A monatomic

the particle in the above case are supposed to be small compared with r. In the

case of a solid sphere the moment of inertia of the sphere can be shown to be

2/5 . M

. r-, the axis of rotation passing through the centre of the sphere.

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