Cooling and Freezing

We are always ignorant about the detailed microscopic state of a macroscopic lump of matter. What we know about it is generally of a statistical nature. Statements about its temperature, pressure, magnetism and so on, are statements about average properties. The entropy is defined as a measure of our ignorance. All this was explained in Chapter 2.

There is one exception. If we could get the lump of matter to the absolute zero of temperature, it would (in principle) be in a single quantum state: the state of minimum energy. The entropy (as well as the temperature) would be zero. This would be very interesting, because we would be studying the quantum theory of macroscopic things, not just of atoms. It is very difficult to get near enough to the absolute zero of temperature to achieve this single quantum state. But fortunately nature does provide us with many examples of interesting large-scale quantum effects that occur when bodies are made cold enough. Some of these have always been familiar; others were total surprises when they were discovered in the twentieth century.

When water is cooled, ice crystals form. This happens at a welldefined temperature (for a given pressure). There is a qualitative difference between water and ice. In a crystal, the molecules are arranged in a regular array, held in place by the forces between them. Knowledge about the positions of molecules at one point tells us something about their positions at macroscopic distances away (say, millimetres).