The states of matter

The following is a thought experiment. Nothing written here should be construed as instructions for practical action. This is not a homework problem.

You go to your freezer, take out an ice cube, and put it in an experimental fluid of your choice. Some of the choicest fluids for this experiment are made along the banks of glens in Scotland. A scientist often feels compelled to repeat an experiment many times to be sure that the results are dependable. If you do so in this case, you might not be able to remember the results.

Here is what you observe. The fluid starts out at room temperature. The ice is initially at the temperature of the freezer, say, 260 K or -13°C. At first the ice warms up, cooling the fluid. But then, when its temperature reaches 273 K or 0°C something happens that is both extraordinary and dramatic. The ice refuses to get any warmer. Whereas just before it had no difficulty raising its temperature as it absorbed heat, it now absolutely refuses to warm the slightest bit more. Instead it undergoes a catastrophic change in its microscopic state. As it absorbs more heat from its surroundings, the molecules separate from their solid crystal structure. The ice melts into water. The whole profound transformation takes place without permitting any change in temperature until it is completely finished. If that were not the case, you wouldn’t cool your drinks with ice. You might as well throw cold rocks in them.

The thermodynamic variables

In Chapter 1 we made a truly remarkable simplification of nature. For a body of a given U, N and V it's not necessary to know what each of its atoms is doing. If we allow the body to come to equilibrium, all the microscopic information necessary to specify its macroscopic state is contained in the value of a single variable, the entropy. In this chapter we shall explore some of the consequences of that profound insight.

If we know explicitly the equation U = U(S, V, N), then we have enough information to find anything we want. For this reason S, V and N are said to be the proper variables of the energy U. We have already had some examples of how information can be extracted from this equation, and we shall have some more (Problems 2.5 and 2.7). In reality the equation is hardly ever known explicitly for any real system, but the fact that it exists in principle – which was the point of the first chapter – is what we wish to exploit.

There are seven thermodynamic variables, and these can be grouped into classes in various ways. One way is to assemble them into conjugate pairs. Each pair, when multiplied together, has the units of energy. They can also be classified as either extensive or intensive. Both are shown in Table 2.1.

The origin and meaning of the first and second laws

Of all the tales in the repertory of human folklore, one of the best may be one that is hardly ever told. It is the epic saga of the second law of thermodynamics. The second law was born in an attempt to improve the steam engine, and it went on to predict the ultimate fate of the Universe. It captured the popular imagination, defined the meaning of time, and led to the discovery of quantum mechanics. It was born, like some mythical beast, before its putative mother, the first law of thermodynamics.

Before we get swept away by the mighty tide of these powerful laws, let us remind ourselves that we already know everything there is to know about what they say and why they are true. The first law expresses, in a special way, the conservation of energy. We examined it at some length earlier. The second law says essentially that the entropy of an isolated system increases until it can get no larger. We’ve already seen that that’s true. What we have to say here is therefore mere elaboration.

Before the middle of the nineteenth century, it was believed that heat was a fluid, called caloric, which could flow fromone body to another. That view differed from our present understanding in that each body was thought to possess a definite amount of caloric, which, being a fluid, could neither be created nor be destroyed. It was a successful theory, but it wasn’t quite right.