# Heat capacity of a solid using the Einstein model

1. ### Antti

26
1. The problem statement, all variables and given/known data

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

2. Relevant equations

The Einstein model for heat capacity:

3. 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.

2. ### kuruman

3,447
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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