I am most grateful to the Syndics of the Cambridge University Press for inviting me to prepare a third edition of Gases, Liquids and Solids. The basic structure is unchanged. The main theme is that the three primary states of matter are the result of a competition between thermal energy and intermolecular forces. The second motif is that a whole range of properties e.g. the specific heat capacity of solids, the thermal conductivity of nonmetals, the elastic modulus of rubber, thermal expansion, surface tension, the viscosity of gases and liquids, osmotic pressure, the adiabaticity of sound waves in air, the dielectric properties of gases, liquids and solids, van der Waals forces between solid bodies, the hardness of metals, may be understood in terms of simple models and unsophisticated mathematics.

Few changes have been made in the early chapters on the properties of gases. In dealing with solids I have added short sections on the structure of surfaces and the phenomenon of surface melting and have extended the treatment of the elastic properties of crystalline solids and of rubber. In liquids there are further elaborations of the theory of viscosity and its application to the behaviour of lubricating oils.

But the main change in the book is the recognition that there are other states of matter which are of great scientific interest and which impinge on many aspects of everyday life.

The subdivision of physics into mechanics; heat, light and sound; magnetism and electricity; properties of matter; and kinetic theory, goes back to the early days of classical physics. During the last twenty or thirty years there has been a discernible trend towards a regrouping of subjects, partly to allow for new knowledge and partly to allow for new methods of approach. Few of the areas have received such an impulse as those which, in classical days, were grouped together as kinetic theory and properties of matter. The new approach is to emphasize the atomic structure of matter and to show that, by assuming the existence of attractive and repulsive forces between atoms and molecules and the presence of thermal energy, it is possible to explain nearly all the bulk properties of gases, liquids and solids in terms of relatively simple models.

This book, which attempts to do this, is based on the lecture course given to first-year students at Cambridge. Its treatment is relatively simple and contains very little quantum physics or wave mechanics. It represents an attempt to bridge the gap between sixth-form physics and physical chemistry, and the more advanced courses which follow in later years of specialization. If it has any merit at all this is largely due to the devotion of many generations of Cavendish teachers who have hammered out the type of treatment and approach I have given here.

The three primary states of matter are the result of a competition between thermal energy and intermolecular forces. In this book we show that many of the bulk properties of a given substance in its gaseous, liquid and solid state may be correlated in terms of intermolecular forces thus emphasizing the fact that the three states are linked by a common property. Simple models are introduced and the mathematics is generally straightforward and unsophisticated.

Chapter 1 is a simple account of the nature of atoms and molecules and the forces between them, and includes a rather more detailed explanation of van der Waals forces. The second chapter deals with temperature and the concept of heat. These are the introductory chapters.

The next three chapters describe the properties of gases. This is a well-worn area where the molecular approach has long been used to describe the bulk behaviour. Chapter 3 gives the simple kinetic theory of ideal gases, while Chapter 4 deals with a more sophisticated treatment which includes a simplified approach to the Boltzmann distribution, and a discussion of the equipartition of energy. Chapter 5 deals with imperfect gases where perfect gas behaviour is modifled to allow for the finite size of the molecules and for the forces between them.

We turn at once from gases to solids. In gases the molecules are virtually free, in solids they are bound to particular sites and their main thermal exercise consists in vibrating about their equilibrium positions.

In this chapter we describe briefly some of the main features of the colloidal state. The colloidal state is very widespread in biological systems and in many practical situations. Basically a colloid consists of two distinct phases, a continuous phase (the dispersion medium) and a particulate phase, where the particles generally have dimensions ranging between 20 and 2000 Å (2 and 200 nm). The two phases can be liquidin- liquid (milk), solid-in-liquid (paint), liquid-in-gas (aerosol) and other combinations. The basic problem with colloidal systems is their stability. Clearly the particles must not be too large otherwise gravity will produce ready sedimentation. However, if the density of the two phases is similar this tendency will be reduced. The other important factor is the attractive force between the particles: if this is too large the particles will cling together and separate as a cluster from the dispersion. To prevent this, various techniques are employed to reduce the attractive forces or to introduce repulsive forces.

van der Waals forces between macroscopic bodies

Before we approach the problem of colloid stability we need to know the van der Waals forces between the particles and how these are affected by the presence of a continuous phase (e.g. a liquid) between them.

The van der Waals force between macroscopic materials was quoted in Chapter 1 (equations (1.21) and (1.22)) in order to demonstrate the difference between normal and retarded forces. Here we indicate a simple derivation.

In this chapter we consider briefly some of the basic concepts of heat and temperature. The treatment is simple and restricted to those aspects which will be of use in later parts of the book.

Temperature

The concept of temperature

The concept of temperature originally arose from a sensory feeling of hot or cold. Probably all physical concepts arise in a similar way; the next step is to turn the idea into something more general and, in particular, more objective. One such approach is as follows. It is found that a given mass of gas is completely specified by its volume V and its pressure P. Suppose we start with 1 kg of a gas and subject it to any changes we wish, whether by compressing it, cooling it, allowing it to expand, heating it; we then take another 1 kg specimen of the same gas and carry out a completely different series of operations. If we end up with the same values of V and P for the two samples, the final states will be found identical in every way – colour, warmth, viscosity, and every objective and subjective test to which we can subject the sample.

If we end up with different P, V values there is something different about the samples and if they are placed in contact changes take place until they reach identical P, V values (see section 2.1.3 below).

In this chapter we shall discuss the flow properties of liquids, and derive or state some of the more standard equations of flow. However, our main attention will be directed to a molecular model of viscous flow; this follows closely the theory proposed by Eyring.

Flow in ideal liquids: Bernoulli's equation

As with gases we can assume the existence of ideal liquids in which internal forces play a trivial part, so that they have negligible surface tension or viscosity. Their flow properties are determined solely by their density. Of course, no liquids can have zero internal forces, they would not be liquid if this were so, but they can often behave as ideal liquids in flow if the inertial forces dominate.

Consider the flow of such an idealized liquid and let us follow the path of any particle in it. If it moves in a continuous steady state we may draw a line such that the tangent at any point gives the direction of flow of the particle. Such lines are called streamlines. They are smooth continuous lines throughout the liquid and can never intersect – no fluid particles can flow across from one streamline to another. Let AB represent an imaginary tube in the liquid bounded by streamlines (figure 11.1 (a)). At A the liquid is at height h1 above a reference level, the pressure acting at that point is p1, the cross-sectional area of the tube is α1, and the liquid flow velocity is v1; at B the corresponding quantities are h2, p2, α2, v2. Consider the energy balance during a short time interval dt.

Atoms and molecules

The evidence for atoms and molecules

Matter is not a continuum of uniform density, but consists of discrete particles or, if one wishes to be more up to date, of localized regions of very high density separated by regions of almost zero density. The particulate nature of matter has been known to us since the time of the Greeks and the idea of atoms (units which could not be further cut or divided) is generally attributed to Democritus (c. 460–370 bc). Many of his concepts have a surprisingly modern ring and constitute a tribute to the immense power, as well as the originality, of the Greek approach to logical inference and abstract reasoning. Much of his work was, indeed, the result of thought rather than of direct experiment. One must not, however, read too much modern science into these early ideas. For example in a passage quoted by Theophrastus, De Sensu, 61–2, Democritus states, ‘Hard is what is dense, and soft what is rare … Hard and soft as well as heavy and light are differentiated by the position and arrangement of the voids. Therefore iron is harder and lead heavier.’ But it would be wrong from this to attribute to Democritus a knowledge of dislocations and point defects.

The first real attempt to get to grips with the basic ‘atoms’ of matter had to wait until more quantitative measurements and generalizations had been made.

We pass at once from gases to solids. In gases the atoms and/or molecules are almost completely free; in solids they are almost completely lacking in mobility. Indeed in a solid the thermal motion is so greatly reduced that individual atoms can move from their fixed positions only with the greatest difficulty. It is this which imparts to solids their most characteristic macroscopic property – they maintain whatever shape they are given, they have appreciable stiffness. Although the atoms are in fixed locations they possess some thermal energy – in some cases individual atoms can diffuse through the solid but in general the process is extremely slow. Their main thermal exercise consists in vibrating about an equilibrium position.

Types of solids

There are three main types of solids: crystalline, amorphous and polymeric. The first part of this chapter will deal with crystalline solids; amorphous solids will be described briefly at the end while a separate chapter (Chapter 13) will be devoted to polymers.

Crystalline solids

The main feature here is long-range order. The molecules or atoms are in regular array over extended regions within each individual grain or crystal. With large single crystals the regular array may extend over an enormous number of atoms or molecules. For example with a single crystal of copper of side 1 cm, along any one direction there will be 30 000 000 copper atoms in regular array, the arrangement of the last few being (in the ideal case) in perfect step with the first.

Introduction

We know that there are certain metallic bodies which attract one another and which, if suitably suspended will tend to point in the north-south direction. These materials are magnetic. We also know that if a current is passed through a coil of wire, the coil itself behaves like a magnet and will attract a bar magnet or another similar coil. If we insert certain ‘magnetic’ materials into the coils the interaction between the coils will be changed. The coil also possesses a certain self-inductance and if we insert similar ‘magnetic’ materials into the coil its self-inductance will be increased.

These are some of the basic observations involved in magnetism and the purpose of this chapter is to discuss the magnetic properties of matter in terms of atomic and electronic mechanisms. There are many resemblances to dielectric effects the main differences being that

1. (a) there is no such thing as an isolated magnetic pole;

2. (b) there is no magnetic equivalent of a condenser;

3. (c) there is no dielectric analogue of a solenoid.

The most fundamental approach to magnetism is due to Einstein. He considered the electric field generated by a moving charge and the force it would exert on another charge moving parallel to it with the same velocity. Because of relativity effects the space ahead of the moving charge is crowded and this compression of space in which the electric field operates produces an additional force on the other charge over and above that calculated from the classical coulombic law.

In this chapter we shall first describe a rather more sophisticated kinetic theory of perfect gases. Part of the exercise is purely computational and, although it looks more impressive, adds little to our physical understanding. There are, however, a number of points which emerge which are interesting and useful and which shed new light on some of the assumptions made in the simpler forms of the kinetic theory. We shall also discuss the velocity distribution in a gas and the thermal energy of its molecules.

A better kinetic theory

Assumptions

First we recapitulate our basic assumptions. Let us assume that we are dealing with a very large number of molecules uniformly distributed in density; that they have complete randomness of direction and velocity; that the collisions are perfectly elastic; that there are no intermolecular forces; and finally that the molecules have zero volume.

We now consider a way of describing their distribution in space. Thus to each molecule we attach a vector representing its velocity in magnitude and direction (figure 4.1 (a)). We then transfer these vectors (not the molecules) to a common origin (figure 4.1 (b)) and construct a sphere of arbitrary radius r, allowing the vectors to cut the sphere (if necessary by extending their length). Then the velocity vectors intersect the sphere in as many points as there are molecules.

If we postulate randomness of molecular motion all directions are equally probable, so that these points will be uniformly distributed over the surface of the sphere.