8 - Disorder, entropy, energy, and temperature

Summary

Let me count the ways

Elizabeth Barrett Browning

The most subtle of the concepts that surfaced in the last chapter is equilibrium. Although the word suggests something unchanging in time, the molecular viewpoint has offered a closer look and shown temperature to be the average effect of molecular agitation. At first sight, it seems hard to say anything, let alone anything quantitative, about such chaotic motions. Yet, paradoxically, their very disorder provides a foundation upon which to build a microscopic theory of heat.

How does a dilute gas reach equilibrium? Contemplate a system in a thermally insulating rigid container, so that there is no transfer of energy or matter between the inside and the outside. As time passes, the energy the gas started with is being exchanged between the molecules in the system through random collisions. Finally, a state is reached which is unchanging as far as macroscopic observations are concerned. In this (equilibrium) state each molecule is still engaged in a complicated dance. To calculate the motion of any one molecule, one would eventually need to calculate the motion of all the molecules, because collisions between more and more of them, in addition to collisions with container walls, are the cause of the random motion of any one. Such a calculation, in addition to being impossible, even for the largest modern computer, would be futile: the details of the motion depend on the precise positions and velocities of all the molecules at some earlier time, and we lack this richness of knowledge.