  We use the recently derived density of states for a particle confined to a
spherical well in three dimensional fuzzy space to compute the thermodynamics
of a gas of non-interacting fermions confined to such a well. Special emphasis
is placed on non-commutative effects and in particular non-commutative
corrections to the thermodynamics at low densities and temperatures are
computed where the non-relativistic approximation used here is valid.
Non-commutative effects at high densities are also identified, the most
prominent being the existence of a minimal volume at which the gas becomes
incompressible. The latter is closely related to a low/high density duality
exhibited by these systems, which in turn is a manifestation of an
infra-red/ultra violet duality in the single particle spectrum. Both
non-rotating and slowly rotating gasses are studied. Approximations are
benchmarked against exact numerical computations for the non-rotating case and
several other properties of the gas are demonstrated with numerical
computations. Finally, a non-commutative gas confined by gravity is studied and
several novel features regarding the mass-radius relation, density and entropy
are highlighted.
