The Einstein frequency is often expressed in terms of an equivalent temperature θE, where θE = hν/k....

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The Einstein frequency is often expressed in terms of an equivalent temperature θE, where θE = hν/k. Confirm that θE has the dimensions of temperature, and express the criterion for the validity of the high-temperature form of the Einstein equation in terms of it. Evaluate θE for (a) diamond, for which ν = 46.5 THz and (b) for copper, for which ν = 7.15 THz. What fraction of the Dulong and Petit value of the heat capacity does each substance reach at 25°C?

David · Accepted Answer

θE = hν/k 
kT=E 
k=E/T 
Dimensionally, θE = hν/k = E/k => [ML
2 
T
-2
]/[ML
2
T
-3
] =[T] 
The Einstein formula of heat capacity: 
……..eq (1) 
The High Temperature Limit of the Einstein Specific Heat 
 
Einstein’s formula approaches Dulong – Petit law at high T. For high temperatures,

The Einstein frequency is often expressed in terms of an equivalent temperature θ E , where θ E = h ν/ k . Confirm that θ E has the dimensions of temperature, and express the criterion for the...

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