In all of the Physics
courses which you have taken up to now, you were eventually
able to formulate some
*exact*, or nearly exact, set of equations
which governed the system under
investigation. For instance, Newton's equations of
motion, or Maxwell's equations for electromagnetic fields.
You were then able to analyze
the system by solving
these equations, either exactly or approximately.

In thermodynamics we have no problem formulating the governing
equations. The motions of atoms and molecules are described *exactly*
by the
laws of quantum mechanics. In many cases, they are also described to a
reasonable approximation by the much simpler
laws of classical mechanics. We shall not be
dealing with systems sufficiently energetic for atomic nuclei to be
disrupted, so we can forget about nuclear forces. Also, in general,
the gravitational forces between atoms and molecules are completely
negligible. This means that the forces between atoms and molecules are
predominantly electromagnetic in origin, and
are, therefore, very well understood. So, in principle, we could write down
the exact laws of motion for a thermodynamical system, including all of
the inter-atomic
forces. The problem is the sheer complexity of this type of
system. In one mole of
a substance (*e.g.*, in twelve grams of carbon, or eighteen grams
of water) there are
Avagadro's number of atoms or molecules. That is, about

particles, which is a

The method adopted in this subject area is essentially dictated by the
enormous complexity of thermodynamic systems. We start with some
statistical information about the motions of the constituent atoms or molecules,
such as their average
kinetic energy,
but we possess virtually
no information about the motions of individual particles. We then try
to deduce some other properties of the system
from a statistical treatment of the governing equations.
If fact, our approach
*has* to be statistical in nature, because we lack most of the
information required to specify the internal state of the system. The best we
can do is to provide a few overall constraints, such as the average volume and
the
average energy.

Thermodynamic systems are ideally suited to a statistical approach because of
the enormous numbers of particles they contain. As you probably know
already,
statistical arguments actually
get *more exact* as the numbers involved get larger.
For instance, whenever I see an opinion poll published
in a newspaper, I immediately
look at the small print at the bottom where it says how many people
were interviewed. I know that even if the polling was done without bias,
which is extremely unlikely,
the laws of statistics say that there is a intrinsic error of order
one over the square root of the number of people questioned.
It follows that
if a
thousand people were interviewed, which is a typical number,
then the error is at least three percent. Hence, if the headline
says that so and so
is ahead by one percentage point, and only a thousand people were
polled, then I know the result is statistically meaningless.
We can easily
appreciate that if we do statistics on a thermodynamic system containing
particles then we are going to obtain results which are valid to
incredible accuracy. In fact, in most situations we can forget that the
results are statistical at all, and treat them as exact laws of Physics.
For instance, the familiar equation of state of an ideal gas,

is actually a statistical result. In other words, it relates the