Heat capacity of a solid using the Einstein model

[Antti]

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:

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.

 

[kuruman]

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.