COMPRESSIBILITY OF METALS. 239 



less rigid bodies with definite shapes. We now see that this point of 

 view is of restricted usefulness, and in particular is not suited to 

 account for the behavior of the compressibility. 



We have up to the present followed Born in entirely disregarding the 

 effect of temperature. This may now be taken into consideration in 

 the following way in the domain in which the temperature is high 

 enough for the classical dynamics to apply, so that we may ascribe 

 to each atom a kinetic energy equal to (3/2) kt. The condition of 

 equilibrium may be conveniently expressed in terms of the " total 

 heat" per unit cell of the lattice, and we will restrict the discussion to 

 substances for which the complete lattice structure of both ions and 

 electrons is like NaCl. For the total heat, H, we have in general 

 the expression II — E -\- yV. Here V is to be taken as the volume 

 of the cell of the lattice or 8 3 . E, the energy of the cell of the lattice, 

 is made up of two parts, a potential part, which we write as before as 



— - + /(<5), plus the kinetic part, due to temperature agitation, which 

 o 



is 6kt., since there are in the cell 4 atoms, each with energy (3/2)kt. 

 (we suppose that the kinetic energy of the electrons may be disre- 

 garded) . Hence 



. E= - ^ +/(5) + 6kt. 



The equilibrium condition is that the total heat is constant for 

 changes at constant entropy, and constant pressure. Hence we have 



d (E + p 5 3 ) = 



where we are to change 8 at constant pressure and entropy. This 

 gives 



!+/W + 6«(f) j+ 3^ = 0. 



To evaluate ( — ) it is convenient to make connection with the ordi- 



\d0/ a 



nary formulas of thermodynamics for ( — ) , where v is the volume of 

 material which under standard conditions occupies 1 c.c. We have 



