**Physics-432**

**Homework Set (4)**

This homework set is due on Monday (11^{th} of Muharram) at 10.00
p.m.

If you need help, please e-mail me or visit me in my office.

Please solve fully and clearly, state assumptions, circle final answers, and comment wisely (when applicable).

You are free to discuss with your colleagues, but makes sure your
solution is truly *yours*.

**Question #1:**

The Debye model gives a T^{3} dependence on temperature of the
lattice heat capacity for a crystal. This agrees quite well with theory. Argue
how this agreement is expected based on the assumptions made in the model.

**Question #2:**

In a few statements, in your own words, describe why the thermal conductivity of the lattice increases and then decreases as the temperature is lowered.

**Question
#3:**

In class, we explained that the Debye model gives a T^{3}
dependence on temperature of the lattice heat capacity in 3-dimensional
systems.

Show that according to the Debye model, the heat capacity has a T^{2}
temperature dependence, at low temperatures, in 2-dimensional systems.

**Question #4:**

e-mail me (zhyamani@kfupm.edu.sa) two web-site URLs that describe the contribution of phonons to heat capacity according to the models studies in class (including the Dulong Petit value).