Some years ago from now I've seem some basic details about what was then called "kinetic theory of gases" where the study of property of gases was made by statistical considerations about the momentum of the molecules and so on. One interesting thing about this is that this allowed one to view temperature as a mean of kinetic energy of the molecules.
Now last year I've studied Thermodynamics which was concerned with just macroscopic matter and right now I'm taking a course on Statistical Mechanics. When I studied Thermodynamics I thought Statistical Mechanics was all about that ideas from kinetic theory of gases but generalized to arbitrary systems.
Up to now the course just treated about the so called "microcanonical ensemble" which basically proceeded as follows: we consider a certain system and some macroscopic state described by some parameters with energy among them. Then we consider the number of microscopic states compatible with a given macroscopic energy with constant energy, that is, we give $\Omega(E)$.
From that we write down the entropy as $S(E) = k_B \ln \Omega (E)$. From this point forward, everything works like Thermdynamics, the difference is that by a counting of states we got the entropy, which on Thermodynamics was not possible to derive from anything.
Now, I don't see any relationship whatsoever between this and the kinetic theory and this made me wonder whether or not there exists a relationship between those subjects.
My point is that kinetic theory seems to provide a more detailed description based on mechanics. We have for example the Maxwell distribution of velocities telling how the velocities of the molecules distribute. On the other hand, although Statistical Mechanics as presented in the course up to now considers microscopic details of the system, it still provides just the same things Thermodynamics does, which are not so detailed on how the system behaves (for example, we know the pressure and things like that, but there's no idea whatsoever about what the molecules are doing, there are no means of dynamical quantities and so on).
So what is the true relationship between the two subjects? Are they related or they are two completely different things?
Best Answer
Based on a quick read of the Wikipedia article on the kinetic theory of gases, it looks like you would need statistical mechanics to derive any of the results in the kinetic theory of gases. For example, the Maxwell distribution of velocities is typically derived using the canonical ensemble. However, the equilibrium velocity distribution is not a dynamical quantity. If you want to get dynamical quantities like the viscosity you would have to use nonequilibrium stat mech. This is typically not taught in an intro stat mech class. If you are interested in getting dynamics from stat mech, one place to look would be Statistical Mechanics by McQuarrie. There are several chapters in that book on time correlation functions and linear response theory. It might be a bit advanced, but I think getting dynamics from stat mech is a more advanced topic than simply getting thermodynamics.