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No. 2.I4 THE SPECIFIC HEAT OF SOLIDS AND THE PRINCIPLE OF SIMILITUDE. BY RICHARD CHACE TOLMAN. HE writer has already presented' a number of derivations in widely different fields of physical science, all of which are based on a single postulate which may be called the principle of similitude. In the present article we shall make use of this same principle in deriving a formula for the specific heat of homogeneous, isotropic, elastic substances. We shall find that the formula thus obtained for specific heat agrees with that of Debye2 for the specific heat of solids and liquids at low temperatures. In our proof, however, it will not be necessary to make use of any of the various forms of quantum theory. In particular, the derivation of Debye rests on the special assumption borrowed from the quantum theory of Planck that hv t ,v fpT - I is the energy in an elastic sphere at temperature T associated with modes of vibration whose frequencies lie between v and v + dv. In our deri- vation, however, we shall make no assumptions as to the form of the relation connecting energy with temperature and frequency of vibration. This possibility
Physical Review – American Physical Society (APS)
Published: Aug 1, 1914
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