This book is intended as a thorough but concise course on the fundamentals of classical thermodynamics. My overriding objective in writing has been to achieve a clear and stimulating exposition: to give an account of the subject that is easy to learn from.

There are many ways of writing a textbook on thermodynamics because the subject is relevant to so many branches of science. The terms of reference of Equilibrium thermodynamics are primarily those of the undergraduate physicist; but it is also suitable for use in materials sciences, engineering and chemistry. The subject is usually taught in the first or second year of a UK undergraduate course but the book takes the student to degree standard and beyond. Prerequisites are a knowledge of elementary mechanics, calculus and electromagnetism, and a familiarity with school-level thermal physics. In overseas universities, thermodynamics may be taught somewhat later in an undergraduate course to allow more time for preparatory work.

Many books and courses on thermal physics attempt to develop classical thermodynamics and statistical mechanics side by side. Although it is essential that the relationship between the two be established at some stage of a scientific undergraduate's education, it is best to teach classical thermodynamics first and separately, for the ability to use it well depends largely on knowing what it can achieve without appealing to the microscopic nature of things.

Introductory remarks

In the last two chapters, we have stated and developed the second law of thermodynamics along traditional lines. The statements of the law asserted the impossibility of certain processes which are easily visualized and readily believed. However, to arrive at the real substance of the matter, we had to equip ourselves with the paraphernalia of idealized heat engines and wade through lengthy arguments about efficiencies and cyclic processes. Only then did we discover that we had arrived, as if by good fortune, at a new function of state, the entropy, on which depends all the subsequent development of the subject. In fact, the essential function of the second law is to enable us to define this quantity and to derive its properties. It seems desirable, therefore, to adopt a formulation of the law which achieves this end with greater economy. That put forward early this century by Caratheodory does precisely that (see Caratheodory, 1909 and 1925).

One may well enquire why, if it has this advantage, Carathéodory's statement of the second law is not more widely used. There are two reasons for this. In the first place, any formulation which makes it possible to avoid the use of cycles and heat engines in the basic development must necessarily be framed in somewhat more abstract terms than the Kelvin or Clausius statements which refer to specific processes.

Background to the first law

The first law of thermodynamics is essentially an extension of the principle of the conservation of energy to include systems in which there is flow of heat. Historically, it marks the recognition of heat as a form of energy.

The work which led up to this is well known. There were two rival theories of the nature of heat. According to the caloric theory, heat, or caloric, was an indestructible fluid which permeated matter and flowed from hot bodies to colder ones. According to the molecular motion theory, heat was associated with rapid vibrations of the molecules of which matter was composed. Of the two, the caloric theory had the greater support until the middle of the last century, although some of the most significant experiments were done much earlier.

In 1761 Black had studied the melting of ice. He noted that the temperature of a pail of ice-cold water placed in a warm room rose quite quickly, whereas, if the pail contained ice, the temperature remained constant for many hours while the ice melted. If caloric flowed into the pail from the surroundings when it contained ice-cold water, it must also do so when it contained ice. Therefore, he argued, ice-cold water must contain more caloric than ice. In 1799 Davy showed that both wax and ice could be made to melt by rubbing two pieces together.

The function of the second law

The first law of thermodynamics is a generalization of the principle of conservation of energy to include heat. It places a restriction on the changes of a system which are energetically possible. Not all such changes occur, however, and we have already acknowledged this fact in discussing thermal equilibrium and hotness. If two bodies are placed in thermal contact it would be energetically possible for their temperatures to diverge; it would not violate the first law. However, we know that this does not happen. The temperatures converge and eventually thermal equilibrium is established. Thus there is an essential irreversibility of nature, a natural direction for change, which we need to take into account in trying to describe thermal processes. The first function of the second law is to express this irreversibility.

Secondly, although we know that work may be converted into heat by a suitable dissipative mechanism (Joule's paddle wheels, or a resistor), we have not examined the conversion of heat into work. The first law emphasized the equivalence of heat and work as forms of energy, but it tells us nothing about the conversion from one form to the other; and, in particular, it tells us nothing about the efficiency with which heat may be converted into work, a matter of enormous practical importance.

Liquid state physics no longer has the luxury status of an intellectual plaything – a kind of purgatory between gas and solid, a statistical mechanical jungle populated only by the foolhardy and/or academics. Pressing demands are increasingly being made upon the subject by adjacent branches of physics, and many people are being unwittingly drawn into the field from more conventional and immediately rewarding routes in physics. A subject which has not, as yet, satisfactorily accounted for the solid-fluid transition, nor which has yielded more than three further hard sphere virial coefficients in the 75 years since Boltzmann's original calculations, is evidently beset with problems: but there lies the source of the fascination.

This book is meant to be a guide to the uninitiated, and perhaps to broaden the outlook of those already there. It represents a very personal account of my own journey into the subject, and in consequence the content and approach might be considered in some respects somewhat idiosyncratic. I have made some attempt to present the material objectively, although inevitably one's own particular interests and viewpoints should and do assert themselves. Nonetheless, I felt the time was ripe to include separate chapters on the liquid surface and on the machine simulation methods, and to expand the by now routine statistical mechanical developments of the pair distribution associated with the names of Kirkwood, Born and coworkers, Bogolyubov, Percus and Yevick, and others. Of necessity some selection is inevitable, and I have arbitrarily restricted the discussion to the non-critical domain of the so-called ‘simple’ liquids, including the quantum liquids to a certain extent, although liquid water does receive a brief mention.