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Heat Capacity Numerical Problem

  1. Mar 10, 2013 #1
    1. The problem statement, all variables and given/known data

    I am working on a problem for my Thermal Physics course. In short, its a numerical problem. I had to go through some Excel calculations and end up with two columns of numbers. One, C/Nk, where C-heat capacity, k-boltzmann constant, N-number of particles and the other is kT/eps, where k-Boltzmann constant, T-temperature, eps-some unit of energy. I have sets of numbers in both of these columns, so I can plot C/Nk as a function of kT/eps.

    Then, I am am given an experimentally measured C(T) for some real materials and asked to estimate(roughly) the constant eps for each of the materials. How do I go about this? Any hints? I have tried doing some numerical methods, but end up with a mess. There has to be some quick and simple way.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 11, 2013 #2

    DrClaude

    User Avatar

    Staff: Mentor

    Assuming that only [itex]C[/itex] depends on [itex]T[/itex], you can write
    [tex]
    \frac{C}{Nk} = a \frac{k T}{\epsilon},
    [/tex]
    where [itex]a[/itex] is some proportionality constant. On your graph of [itex]C/Nk[/itex] vs [itex]k T/\epsilon[/itex], find some point where you can find an approximate value for [itex]a[/itex] (hint: the steeper the slope, the smaller the error).

    Then, do the same for the experimental values, with [itex]\epsilon[/itex] the unknown, instead of [itex]a[/itex].
     
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