Motion of Electrons in Solids. 793 



We have seen that these two definitions lead to the same 

 temperature. The first definition explains at once the ten- 

 dency for the temperatures of two bodies to equalise by heat- 

 radiation ; the second definition explains the tendency for 

 their temperatures to equalise by conduction. 



In a gas the temperature is defined in only one way, 

 namely, by the mean energy of translation of its molecules. 

 The question arises as to whether the temperature of a solid 

 can also be defined in a similar way. 



So far as present evidence goes, it seems as though this 

 question must be answered in the negative, for the following 

 reasons. 



23. For almost all metals the atomic heat is, to within a 

 few per cent., equal to 5*88, the value required if each atom 

 had associated with it energy 3RT — i. e. twice the transla- 

 tional energy of a free electron or molecule of gas at 

 temperature T. 



If the energy of motion of the atom is governed by the 

 temperature T, each atom must, on account of this motion, 

 have associated with it energy exactly equal to 3RT, half of 

 this being contributed by its average kinetic energy (|RT), 

 and half by its average potential energy (§B.T). But it is 

 difficult to imagine the atoms moving freely as regards trans- 

 lational motion without at the same time being set into 

 rotation, and the energy of this rotation, if governed by the 

 temperature T, would be 3RT per atom. Each atom would 

 now have energy CRT associated with it*. 



Further, each atom has associated with it a number of 

 free electrons of which the average, according to Schuster's 

 tablef, is about two per atom. This adds a further contri- 

 bution 3RT to the energy to be associated with each atom. 



Thus the energy per atom would, under these circumstances, 

 seem to be about 9RT, made up of three equal contributions 

 of 3RT each from motion of atoms, rotation of atoms, and 

 motion of electrons. The value permitted by the specific heats 

 is uniformly 3RT. The uniformity of this number indicates 

 that we must attribute it to a similar origin in all substances. 



It seems as if the only permissible view is that the 3RT is 

 contributed by the motion of electrons. If we accept this, 

 the rejection of the contribution 6RT from the atoms means 

 that the energy of motion of these is very small in comparison 



* If we take the molecule ;is unit, each molecule would have energy 

 CRT, and therefore each atom, at least in diatomic substances, would 

 have energy 3RT, the required amount. But Dulong and Petit 1 s law 

 is not limited to diatomic elements, and seems to show conclusively that 

 the atom must he taken as unit. 



+ Phil. Mag. vii. p. 155. 



