Sharing Out the Energy - Molecular Modelling - page 95

7

Sharing Out the Energy

The structure of matter can be thought about on two different levels. On the one hand, there is
the macroscopic view where we focus on equations such as the perfect gas equation of state

pV = nRT (7.1)

This approach deals with large chunks of matter and involves ideas like temperature, heat
capacity and pressure that are familiar from everyday life. It is based on measurements
taken with thermometers, pressure gauges and other instruments that are familiar in an
ordinary science laboratory.
On the other hand there is the microscopic approach where we focus on individual atoms
and molecules. This approach involves rather abstract ideas and tends to be based on theory
rather than experiment. Atoms and molecules can be studied directly by spectroscopic
techniques, but they bring their own problems because we usually have to understand
quantum mechanical principles before we can interpret the experimental findings.
Another problem is that there are typically 10 23 particles in a macroscopic sample, a
number that beggars understanding.
Then again, the concept of temperature does not appear from Newton's equations, nor
does it appear in the Schrödinger equation. It is actually a measure of the way that energy
is shared out between available quantum states, but more of this shortly.
There must be a link between the two approaches, but what can it be? To be positive,
things are not as bad as they might seem. What matters in a macroscopic sample are not
the individual properties of the constituent atoms and molecules, rather their statistical
properties. It does not matter whether we know which individual particle of 10 23 collides
with the wall of a container when we want to understand the pressure; what does matter is
the average behaviour of the 10 23 particles present.
The two great pioneers of this subject were Ludwig Boltzmann (1844-1906) and Josiah
Willard Gibbs (1839-1903). In fact they worked independently. Boltzmann's tomb car-
ries his famous equation relating a thermodynamic property (entropy, S ) to a statistical