The monatomic solid

It is customary to define a characteristic temperature for the oscillator, 6 = hv/k. Then 

If the temperature is either very high or very low, this equation takes on a simpler form. 

Case I. T is very low O/T 1. Then, is negligible compared with unity in the denominator of Eq. (29.42), and we have 

Case II. T is very high djT 1. Then the exponential in the denominator can be expanded = 1 — 0/T, and we have 

The monatomic solid has only vibrational motion. The partition function can be written as a product of the partition functions of the atoms composing the solid and an exponential factor that includes the interaction energy W of the atoms in the solid  

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