2Classical gases

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).