II Statistical Physics
2 Classical gases
So far, we have been doing statistical physics starting from quantum mechanics.
But statistical mechanics was invented before quantum mechanics. So we should
be able to do statistical mechanics classically, and we will apply it to the case of
classical gases. This classical theory agree quite well with experiment, except
for a few small things that went wrong, and it turns out we have to solve these
problems by going quantum.
To do statistical physics classically, the idea is to figure out what the classical
version of the partition function should be. We can then use this to derive the
different thermodynamic quantities, as we have previously managed to express
them in terms of the partition function.
After figuring out the partition function, we are going to study three types
of classical gases. We begin by looking at monoatomic ideal gases, which is the
simplest type of gases one can think of. They do not have internal structure and
do not interact with each other.
After understanding monoatomic ideal gases, we will move on to consider
two possible modifications. The first is the case of a diatomic (ideal) gas, where
the gases now have some internal structure, and hence kinetic energy is not the
only possible kind of energy. It turns out the theory works out pretty similarly
to the monoatomic case, except that the average energy of each particle is higher
than the ideal gas version.
Finally, we will consider what happens if we have gas molecules that do inter-
act with each other, and we will do so perturbatively, assuming the interactions
are small (which they are).