Newton solved the mechanics of the two-body problem; the last time I checked, a general solution to the three-body problem is wanting. And four is right out!
It would be perfectly logical to conclude that describing the motion of 1023 particles would be out of the question, but a surprising and marvelous simplification arises when the number of particles is large. Our goal in this course is to investigate the behavior of systems with large numbers of particles and to find how the standard concepts of thermal physics (temperature, entropy, free energy) arise from basic probability and simple mechanics.
You are all undoubtedly familiar with the notions of temperature and heating, and understand in a very empirical and practical way that energy flows from warmer objects to colder objects when they are placed in contact. You know that when an object is in thermal equilibrium with its surroundings, its temperature, volume, pressure, etc., do not change with time. You know that objects can store energy in "random" internal motions of atoms and molecules. You probably believe in the principle of energy conservation, and you know from mechanics that objects move in such a way as to lower their potential energy.
You may also know from chemistry that there is such a thing as entropy and that it is in some fashion related to randomness. It's tabulated in books and depends on the substance, phase, and temperature in question. Differences in things like entropy, enthalpy, Gibbs free energy, and Helmholtz free energy are what count, but you're probably not so sure what some of these things are and, even if you are, which one is important in which situation.
All the concepts I've just mentioned, with the exception of energy and potential energy, are politely ignored in a mechanics course. There you learned about conservation of mechanical energy, about the motions of point masses and rigid bodies, and systems of one, two, or at most three independent particles. You learned how Newton's laws (or some fancier energy variation, such as Lagrangian or Hamiltonian dynamics) were fantastically successful in predicting the motions of real objects (and that life was much easier when friction could be ignored).
An important goal of this course is to develop mechanical definitions of thermal quantities such as temperature, entropy, etc., and to deduce the laws of thermodynamics from basic mechanical principles. Sometimes we will use a classical mechanics description of a system, and sometimes a quantum mechanical one. Statistical mechanics arises from the application of basic probability to mechanical systems of large numbers of particles. We will first develop these ideas of probability and apply them to simple systems. Out of this will emerge the mechanical definitions of entropy, temperature, and equilibrium, as well as the laws of thermodynamics. Statistical mechanics also shows us how to calculate such thermal quantities as heat capacity (specific heat), entropy, vapor pressure, and others from first principles (at least for simple systems).
Some of the things you will learn in this course include:
Updated 8/29/02 .