# Heat capacity of a solid using the Einstein model

by Antti
Tags: capacity, einstein, heat, model, solid
 P: 25 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.
 HW Helper PF Gold P: 3,440 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.