﻿Theory of the Metallic State. 135 



heat by a diamond at 20° Abs. Its conductivity is almost 

 as great as that of copper, although its specific heat is 

 negligible. The specific heat of the electron space-lattice 

 may probably be calculated fairly accurately from Debye's 

 formula, which has proved so successful in the case of solids *. 

 The atomic heat is 



= 3R 





In our case, as shown above, the velocity of sound, 1/2 1/2 , 

 is very large f, on account of the small density, so that c v 



1 9_4 ^3 



reduces to the form ^^- R — = — ^ , and the specific heat of 



the electrons is well below the limits of measurement. 

 Taking one electron per atom and k equal to the compressi- 

 bility of silver, for instance, v m would be 



436 . 4-42 . 10 12 =l-93 . 10 15 or /3v m = 94000. 



Thus the atomic heat at 300° would be 1*51 . 10~ 5 cal. or 

 the specific heat 7 = 0*266 cal. 



This explains, too, why those phenomena which depend 

 upon the energy-content of the electrons are so minute. 



Contact potential. — The electrons in the metal will have 

 many points of similarity with a solution in spite of forming 

 a space-lattice. Their mutual repulsion must be counter- 

 balanced by the attraction of the more distant ions. We 

 thus have an analogous phenomenon to the internal pressure 

 in liquids in the theories of van der Waals and Reinganum, 

 or to the osmotic pressure in solutions. 



If two metals are placed in contact, the electrons will flow 

 from the metal with higher internal pressure into that with 

 lower until the potential difference balances the difference in 

 pressure. 



Other things being equal, the work necessary to remove 

 an electron will be inversely proportional to the cube root 

 of the atomic volume. Hence, in general, the metals with 

 large atomic volumes, such as the alkali metals, will become 



* Ann. d. Phys. (4) xxxix. p. 789 (1012). 



t It is interesting- to find that the velocity calculated by this formula 



is of the order 10 s ', which is about the value found for the trans- 

 sec. 



mission of energy through a cable. It is difficult to see how these high 



velocities can be explained on the old electron theory, for a wave can 



never travel foster in a mis than the velocity of the molecules, 



