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Heat capacity of a solid using the Einstein model

  1. Aug 23, 2009 #1
    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:

    [​IMG]

    [​IMG]

    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.
     
  2. jcsd
  3. Aug 23, 2009 #2

    kuruman

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    Homework Helper
    Gold Member

    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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