The Problem:

A UF graduate student has experimentally measured the heat capacity of a new material at low temperature. She gives you her data (T, Cv) and asks you to determine the Debye frequency of the solid ... that is, find the maximum frequency of the harmonic oscillations that contribute to the heat capacity of the atomic lattice in this material.

The Data:

       T (Kelvin)   Cv (J/mole/K)

      0.11179  1.1789e-007
     0.078809  3.4577e-008
      0.27886  1.3129e-006
      0.50844  8.9417e-006
      0.55114  8.0345e-006
      0.76963  3.2444e-005
       1.6793   0.00028973
       1.9645   0.00050979
        4.542    0.0036385
        8.127     0.044397
       17.107       0.3204
       20.629       0.2112
       26.481       1.1997

You need to fit the data to a theoretical model for Cv. This means finding the value of the Debye frequency that gives the best match between the experimental points and the theoretical model. You could do this with a linear (or nonlinear) least squares method, if you are equipped for this type of thing. Otherwise the simplest way is to use a spreadsheet. For example ...

• Pick a value for the Debye frequency.
• Create two columns showing the theoretical T versus Cv for that value of the Debye frequency.
• Add a column showing the experimental T versus Cv
• Plot your calculated versus experimental values on the same graph
• Adjust the Debye frequency to give the best match

The Solution:

When you have it figured out, hand in the following on a sheet (or two) of paper:

1. Your computer program or spreadsheet, clearly showing all methodology and all formulas used
2. A plot showing the experimental data and the theoretical curve that passes nearest to the data
3. An explanation of your method and your result. Give your best estimate of the Debye frequency and the Debye Temperature. Do not forget to include your estimate of the uncertainty in these values. Do not delude yourself by reporting too many significant figures.
4. Identify all your collaborators.

Hand in your quiz in class on Friday. Because this is a quiz, there can be no extensions or makeups for this assignment!