Heat capacity of a solid using the Einstein model

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Homework Statement



Plot the heat capacity as a function of temperature for aluminium, using the Einstein model.

Homework Equations



The Einstein model for heat capacity:

b6ae86f1d6f5881e5c3582f77dfd8e04.png


be968b7166a250b07b92e04c2cb0702e.png


The Attempt at a Solution



The model assumes that the frequencies of all the harmonic oscillators in the material are the same. But does it mean "same for all temperatures" or "same for a given temperature"? And if the latter is true, will I need to find a function \epsilon (T)? Because otherwise the right hand side of the Cv equation wil have two free variables. Thankful for help, my textbook is very unclear about this.
 
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In this model, the frequency of each oscillator is the same at all temperatures, but the energy varies with temperature. Define

\frac{1}{x}=\frac{\epsilon}{kT}

Plot C(1/x) / 3Nk vs. x which is a dimensionless plot, good for any choice of specific values. Here, it's the shape that counts.
 

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