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Heat capacity of a solid using the Einstein model

by Antti
Tags: capacity, einstein, heat, model, solid
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Antti
#1
Aug23-09, 03:53 AM
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 [tex]\epsilon (T)[/tex]? 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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kuruman
#2
Aug23-09, 06:30 AM
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P: 3,443
In this model, the frequency of each oscillator is the same at all temperatures, but the energy varies with temperature. Define

[tex]\frac{1}{x}=\frac{\epsilon}{kT}[/tex]

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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