A Thermodynamical Approximation Formula

General.—When I put forward my Heat Theorem, our information on the subject of the specific heats of solids at low temperatures was so scanty that it was quite impossible to make a direct test such as we have described in Chapter IX for condensed systems. In order to assure myself that I was on the right track, I attempted to make a test, which should be at least approximate, of the formula 

If this proved favourable, the Heat Theorem was thus proved at the same time for chemical equilibria in general, for from the foregoing formula the rule 

I recognized, of course, quite clearly that this could only be an approximate test. But if the regularities resulting from formula (77) were found to be actually confirmed in nature, this would constitute good support. As my colleague Planck once said to me in conversation, one cannot but assume that a law so general as this, that the entropy constant of matter is negligibly small at the absolute zero, is either as exactly true as the other Laws of Thermodynamics, or else is sometimes far removed from the truth. In spite of much search, no case has yet been found in which this 

It should be mentioned that some erroneous tendencies in recent chemical literature render the following warning necessary. The approximation formula must not be identified with my Heat Theorem, although it was found in connection therewith. Discrepancies between the approximation formula and the facts do not of course entail any contradiction of the strict validity of the Heat Theorem. This would only come in question if a discrepancy were found between an exact application of it and the facts such has never been the case hitherto, and is now hardly to be expected in view of the present vastly increased state of our knowledge. 

Derivation of a Vapour-Pressure Formula.—The following is the method which we select in order to find a useful approximation formula. We attempt first to obtain an 

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