Classical Statistical Thermodynamics

9780137792085

0137792085

Preface This book is intended as a text for a one-semester undergraduate course in thermal physics. Its objective is to provide third- or fourth-year physics students with a solid introduction to the classical and statistical theories of thermodynamics. No preparation is assumed beyond college-level general physics and advanced calculus. An acquaintance with probability and statistics is helpful but is by no means necessary. The current practice in many colleges is to offer a course in classical thermodynamics with little or no mention of the statistical theory--or vice versa. The argument is that it is impossible to do justice to both in a one-semester course. On the basis of my own teaching experience, I strongly disagree. The standard treatment of temperature, work, heat, entropy, etc. often seems to the student like an endless collection of partial derivatives that shed only limited light on the underlying physics and can be abbreviated. The fundamental concepts of classical thermodynamics can easily be grasped in little more than half a semester, leaving ample time to gain a reasonably thorough understanding of the statistical method. Since statistical thermodynamics subsumes the classical results, why not structure the entire course around the statistical approach? There are good reasons not to do so. The classical theory is general, simple, and direct, providing a kind of visceral, intuitive comprehension of thermal processes. The physics student not confronted with this remarkable phenomenological conception is definitely deprived. To be sure, the inadequacies of classical thermodynamics become apparent upon close scrutiny and invite inquiry about a more fundamental description. This, of course, exactly reflects the historical development of the subject. If only the statistical picture is presented, however, it is my observation that the student fails to appreciate fully its more abstract concepts, given no exposure to the related classical ideas first. Not only do classical and statistical thermodynamics in this sense complement each other, they also beautifully illustrate the physicist's perpetual striving for descriptions of greater power, elegance, universality, and freedom from ambiguity. Chapters 1 through 10 represent a fairly traditional introduction to the classical theory. Early on emphasis is placed on the advantages of expressing the fundamental laws in terms of state variables, quantities whose differentials are exact. Accordingly, the search for integrating factors for the differentials of work and heat is discussed. The elaboration of the first law is followed by chapters on applications and consequences. Entropy is presented both as a useful mathematical variable and as a phenomenological construct necessary to explain why there are processes permitted by the first law that do not occur in nature. Calculations are then given of the change in entropy for various reversible and irreversible processes. The thermodynamic potentials are broached via the Legendre transformation following elucidation of the rationale for having precisely four such quantities. The conditions for stable equilibrium are examined in a section that rarely appears in undergraduate texts. Modifications of fundamental relations to deal with open systems are treated in Chapter 9 and the third law is given its due in Chapter 10. The kinetic theory of gases, treated in Chapter 11, is concerned with the molecular basis of such thermodynamic properties of gases as the temperature, pressure, and thermal energy. It represents, both logically and historically, the transition between classical thermodynamics and the statistical theory. The underlying principles of equilibrium statistical thermodynamics are introduced in Chapter 12 through consideration of a simple coin-tossing experiment. The basic concepts are then defined. The statistical interpretation of a system containing many molecu