10.1 INTRODUCTION

It is not uncommon nowadays to require students in engineering to take a course in statistical mechanics. The present chapter does not intend to provide such a course. Our aim is more modest. We plan to provide the necessary background for the students to be able to follow with ease a more demanding course in statistical mechanics.

In the first few sections, we shall extend the analytical mechanics introduced in Chapter 9. Hamiltonian mechanics will be introduced. This can also be used to pave the way for a course in chaos, a topic which is gaining widespread popularity. Next, we shall consider probability. It will be at an elementary level, but we shall emphasize the interpretation of probability. Students used to deterministic concepts find it hard to think in terms of probability. The idea of an ensemble average will be discussed. Finally, some topics in thermodynamics and Brownian motion will be examined.

10.2 PHASE SPACE

Consider a system consisting of N particles. Let the vector position of particle i be denoted by r _i relative to an origin O. In a three-dimensional space, each particle is defined by three coordinates. If there is no constraint between the particles, we need 3N quantities to describe the configuration of the system. We denote these 3N quantities by q ¹, q ², , q ^3N. The q ⁱ are independent variables and are known as generalized coordinates. We may regard the system to be...