THE QUANTUM PHYSICS OF SOLIDS 



703 



atom, and Cv the specific heat per gram atom at constant volume. 7 is 

 a parameter which measures the asymmetry of the curve and is defined 

 as follows : if we think of the solid as being compressed by an external 

 pressure, the forces between the atoms will change and the Debye 

 temperature will increase. If the curve were a parabola — ^that is, 

 perfectly symmetrical — the Debye temperature would not change. 

 7 is defined by the relationship 



aln«. (U) 



7 = 



a In V 



The 7, K, and V are nearly constant for a given substance. Hence the 

 thermal expansion curve is practically the same as the specific heat 

 curve except for a constant factor. In Fig, 25 we give the thermal 



XI0"6 



UJ 8 



O 



50 100 150 200 250 300 350 400 450 500 550 600 



ABSOLUTE TEMPERATURE IN DEGREES KELVIN, T 



Fig. 25 — Coefficient of thermal expansion versus temperature for copper. 



expansion of copper.^" The Debye temperature was chosen to give the 

 best fit. We see that the theory of thermal expansion gives as good 

 agreement with experiment as does the theory of specific heat. If 

 Griineisen's law were perfectly satisfied, the same Debye temperature 

 would be found for both the thermal expansion and the specific heat 

 curves. The relatively small difference between the two values, 325 

 for expansion and 315 for specific heat, is a measure of the validity of 

 Griineisen's law. 



5° E. Griineisen, Handbuch der Physik, X, p. 43 (1926). 



