A system of physical chemistry - Index of

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A system of physical chemistry - Index of

APPENDIX I 169

Here «i, n.^ are the molecular densities of each type of molecule

around a point where the potential energy is zero.

The formulae developed hitherto have postulated implicitly an

absence of intermolecular forces, except such as arise in a collision

between molecules, an event which, though absolutely very frequent

for a molecule, is relatively rare, since the time which a molecule

spends in its free paths is very much larger than the time spent in

collisions. When we introduce intermolecular forces, i.e. when we

approach the liquid or solid state, the formulae become more complex,

and as they are not required in the text of the chapter to which this

appendix refers, may be laid aside.

A more important case for our purpose is the case of a gas whose

molecules can no longer be considered as simple rigid bodies, but for

which an atomic and even a sub-atomic structure must be postulated.

It would take us too far afield to treat tiie formulae for this case in all

their generality, but we can deal with a few statements of service later.

As before, we take the number of molecules as N, and consider that

the general position of each molecule is given by the three Cartesian

co-ordinates of its centre of mass. Besides these three co-ordinates there

are other geometrical quantities (or co-ordinates in a more general sense)

necessary to define the structure of a molecule. These internal co-ordinates

can be most readily thought of as the least number of lengths

and angles necessary to specify the position of every distinct and conceivably

separate part of the molecule with regard to its centre of mass.

The number of these co-ordinates constitute the internal "degrees of

freedom " of the molecule. Suppose there are n of them, the necessary

n co-ordinates being denoted by the letters—

q\ q-i

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