A system of physical chemistry - Index of

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A system of physical chemistry - Index of

EQUIPARTITION OF KINETIC ENERGY 19

oscillations of particles with respect to a fixed centre of gravity. Vibration

is only possible when there is a restoring force acting upon the

particle which tends to make it take up a mean position. The existence

of the restoring force is the factor which distinguishes vibration from

translation and also from rotation to be mentioned later. We meet

with vibration in the case of the atoms inside a molecule of a gas, and

likewise in the case of the atoms composing a solid. Vibration is

always a constrained movement. We can conceive of vibration as

corresponding either to one or to two or to three degrees of freedom.

When we speak of vibration in connection with molecules it is always

to be understood that we are referring to the vibrations of the atoms

inside the molecule. One such atom can vibrate with respect to the

other in the case of a diatomic molecule. In this case the vibration

is linear, that is, it is along the line joining the two atom centres.

Since the vibration is linear there is one degree of freedom in this case.

Linear vibration is represented in diagram [a) Fig. 2.

Figure Axis.

-•• •-

Mean Position. Mean Position.

Fig. 2 (a). — Linear vibration of atoms in a diatomic Fig. 2 (b). — Circular

molecule. One degree of freedom. Energy, vibration or spiti of

kinetic + potential. an atom round a

centre of gravity.

Two degrees of freedom.

Energy, kinetic

+ potential.

It is also conceivable that the vibration of the particle, an atom

or an electron, may be circular. That is, the particle may describe a

circular path about a centre of gravity, the orbit being traced out on a

surface. Hence in such a case there are two degrees of freedom to be

attributed to the vibration. This is represented by the spinning motion

shown in diagrams (d) and (c), Fig. 2. Further, in the case of a monatomic

solid (such as a metal) the only type of motion which can be

ascribed to the atom is vibration. Free translation cannot exist, for

if it did the solid would not retain its crystalline form. In this case

the vibration of every atom can take place in three directions in space

with respect to the centre of gravity or mean position of the atom.

There are therefore three degrees of freedom to be attributed to the

vibrations of the ultimate particles in a solid. This is represented in

diagram (rt^). Fig. 2. The characteristic feature of all vibrations is the

As will be shown later

existence of potential as well as kinetic energy.

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