## Saturday, October 4, 2008

### Statistical Mechanics

For my first instalment of class descriptions I have chosen to write about the undergraduate course I am taking as a "filler". Now, it's deemed a filler due to the fact that I have taken Thermodynamics already, at Oswego, but have not had Statistical Mechanics (Stat. Mech.), so in order to prepare for my graduate level Stat. Mech. course in the Spring, I need to fill in the gaps.

You may be wondering, if you're not a physicist, which I'm guessing most people aren't, what is the difference between Thermodynamics and Stat. Mech.? Or, for that matter, what about them is the same; how are they related? This takes a little prior background knowledge to explain, so let me teach you a little qualitative physics which explain the two topics. Thermodyanics is the study of energy, and for that part, so is Stat. Mech. Mainly, the conversion of energy and the transformation of energy from one form to another is the primary focus of both topics. For example, heating a cup of coffee in the microwave turns electrical energy into waves which in turn vibrate the water molecules in the coffee, thus increasing the average kinetic energy of the particles. As a result, this increases the temperature of the coffee. During this whole process, though, energy is conserved in one form or another. We know that in the Universe energy can not be created or destroyed, only converted into different forms. So in manner of speaking, thermodynamics is the study of the conservation of energy.

The primary difference between Stat. Mech. and what I had, Classical Thermodynamics, is the treatment of the system which they study. In Classical Thermodynamics, the treatment of the processes are done on a macroscopic scale (large). When working in this area, we are not concerned with the physics of the individual molecules, only the system as a whole. This is great for engineering, but from the aspect of a physicist, we want to know everything that is happening with in the system. We take a look at the microscopic state (microstate) of the system and how that relates to the macroscopic state (macrostate). In order to do this, though, we can't describe each particle or molecule individually, that would be ridiculous considering that one mole of gas contains 6.023x1023 molecules! Also, since we are dealing with microstates and with molecules and particles we have to treat the system quantum mechanically. In order to circumnavigate the difficulties of the shear size of our system, we utilize statistical tools for study the molecules. Molecules and particles don't all act in the same manner, but, they do act similarly based on probabilities. Thus, we may not be able to say exactly what a particle is doing before we observe it, but we can calculate a probability for what it is doing. In this fashion we can evaluate a large number of particles very easily and thus formulate the physics of the macrostate from knowledge of the microstate.

The course, thus far, is fairly straight forward and honestly, rather easy. It helps that the textbooks we are using are very verbose and contain great descriptions of the physics, not only in terms of mathematics (quantitatively) but also in basic words (qualitatively). The two text books for the class are as follows:

"Fundamentals of Statistical and Thermal Physics" by Frederick Reif (1965)
"An Introduction to Thermal Physics" by Daniel Schroeder (2000)

Both are good books, very descriptive - but I find that Reif is the more thorough book. This is mostly because it is clearly meant for upper division undergraduate course work where Schroeder could be utilized for a Sophmore level class. Schroeder, though, is a much better writer in terms of "dumbing" the material down and creating an active reading environment, whereas Reif is a little more dull in his writing but is very thorough and intensive. I personally enjoy reading Reif more (incorporates more quantum aspects). This course is definitely a good relief from the rigor of Classical Mechanics and Mathematical Methods, both of which are intensive graduate courses.