4.1 Canonical phase space density:
Considering the Maxwell-Boltzmann distribution in a classical
3D fluid, show that
a) with increasing kinetic energy the density of states decreases
b) in spite of this the most probable kinetic energy is not zero.
Apply this to the general canonical phase space.
4.2 Grand canonical ensemble:
Using the grand partition function, derive the mean number of particles
in one of an ideal gas at standard conditions.