General formula for the representation of specific heats

General Formula for the Representation of Specific Heats.— In concluding this discussion, we shall also deal briefly with the question, important in the sequel, as to how the variations of the mean atomic heats may be expressed for compounds (and also for elements which, like sulphur, behave similarly to compounds). 

The following considerations from molecular theory give ns a hint on the subject.  

It is immediately obvious that the conception of molecular weight requires a definition for the solid state essentially different from that for gases probably no suitable definition will be possible until we have a precise knowledge of the energy at the absolute zero. But it is, at any rate, certain that crystals, in which no atom differs from another in its mode of attachment or of motion and in which there are no definite groupings of several atoms, may conveniently be treated as monatomic the diamond is a particularly instructive example in this respect. 

For the sake of shortness we shall speak of any such grouping as a molecule, and we arrive at the following conceptions. We shall have to suppose that in compounds the cohesion of the molecules in the crystal results from forces which reach from molecule to molecule, and it is reasonable to suppose that the cohesion is produced by valence forces of a nature similar to that assumed for the so-called molecular compounds. The molecules will execute thermal movements analogous to those of atoms in monatomic crystals. 

In addition, the atoms within the coniines of the molecule will oscillate to and from one another at temperatures sufficiently high to exclude the quantum theory, each atom has an energy of vibration 3RT (law of Kopp-Neumann) at lower temperatures the mean energy of vibration per 

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