Concepts in Thermal Physics 2nd Edition

Book Preface

Thermal physics forms a key part of any undergraduate physics course. It includes the fundamentals of classical thermodynamics (which was founded largely in the nineteenth century and motivated by a desire to  understand the conversion of heat into work using engines) and also statistical mechanics (which was founded by Boltzmann and Gibbs, and is  concerned with the statistical behaviour of the underlying microstates of the system). Students often find these topics hard, and this problem is not helped by a lack of familiarity with basic concepts in mathematics,  particularly in probability and statistics. Moreover, the traditional focus of thermodynamics on steam engines seems remote and largely irrelevant to a twenty-first century student. This is unfortunate since an under standing of thermal physics is crucial to almost all modern physics and to the important technological challenges which face us in this century.

The aim of this book is to provide an introduction to the key concepts in thermal physics, fleshed out with plenty of modern examples  from astrophysics, atmospheric physics, laser physics, condensed matter  physics and information theory. The important mathematical principles, particularly concerning probability and statistics, are expounded  in some detail. This aims to make up for the material which can no longer be automatically assumed to have been covered in every school mathematics course. In addition, the appendices contain useful mathematics, such as various integrals, mathematical results and identities.  There is, unfortunately, no shortcut to mastering the necessary mathematics in studying thermal physics, but the material in the appendix provides a useful aide-m´emoire.

Many courses on this subject are taught historically: the kinetic theory of gases, then classical thermodynamics are taught first, with statistical mechanics taught last. In other courses, one starts with the principles of classical thermodynamics, followed then by statistical me chanics and kinetic theory is saved until the end. Although there is merit in both approaches, we have aimed at a more integrated treatment. For example, we introduce temperature using a straightforward  statistical mechanical argument, rather than on the basis of a somewhat abstract Carnot engine. However, we do postpone detailed consideration of the partition function and statistical mechanics until after we  have introduced the functions of state, which manipulation of the partition function so conveniently produces. We present the kinetic theory of gases fairly early on, since it provides a simple, well-defined arena in which to practise simple concepts in probability distributions. This has worked well in the course given in Oxford, but since kinetic theory is only studied at a later stage in courses in other places, we have designed the  book so that the kinetic theory chapters can be omitted without causing problems; see Fig. 1.5 on page 10 for details. In addition, some parts of  the book contain material that is much more advanced (often placed in boxes, or in the final part of the book), and these can be skipped at first reading.

The book is arranged in a series of short, easily digestible chapters, each one introducing a new concept or illustrating an important application. Most people learn from examples, so plenty of worked examples  are given in order that the reader can gain familiarity with the concepts as they are introduced. Exercises are provided at the end of each chapter to allow the students to gain practice in each area. In choosing which topics to include, and at what level, we have aimed for a balance between pedagogy and rigour, providing a comprehensible introduction with sufficient details to satisfy more advanced readers. We  have also tried to balance fundamental principles with practical applications. However, this book does not treat real engines in any engineering depth, nor does it venture into the deep waters of ergodic theory.  Nevertheless, we hope that there is enough in this book for a thorough grounding in thermal physics and the recommended further reading gives pointers for additional material. An important theme running through  this book is the concept of information, and its connection with entropy.

The black hole shown at the start of this preface, with its surface covered in ‘bits’ of information, is a helpful picture of the deep connection  between information, thermodynamics, radiation, and the Universe. The history of thermal physics is a fascinating one, and we have provided a selection of short biographical sketches of some of the key pi oneers in thermal physics. To qualify for inclusion, the person had to have made a particularly important contribution or had a particularly interesting life – and be dead! Therefore one should not conclude from  the list of people we have chosen that the subject of thermal physics is in any sense finished, it is just harder to write with the same perspective  about current work in this subject. The biographical sketches are necessarily brief, giving only a glimpse of the life-story, so the Bibliography  should be consulted for a list of more comprehensive biographies. However, the sketches are designed to provide some light relief in the main narrative and demonstrate that science is a human endeavour.