  For the ideal Fermi gas that fills a quantum well confined by two parallel
planes, there are calculated the thermodynamic characteristics in general form
for arbitrary temperatures, namely: the thermodynamic potential, energy,
entropy, equations of state, heat capacities and compressibilities. The
distance between planes is considered as an additional thermodynamic variable.
Owing to the anisotropy, the pressure of the Fermi gas along and transverse to
the planes is different, so that the system is characterized by two equations
of state and a set of different heat capacities. Limiting cases of low and high
temperatures are considered. The temperature dependencies of the entropy and
heat capacities at low temperatures remain linear, just as in the volume case,
and their dependencies on the chemical potential and density undergo jumps at
the beginning of the filling of new discrete levels. It is shown that the
behavior of thermodynamic quantities with the distance between plates can be
either oscillating or monotonic, depending on what quantity is assumed to be
fixed: the volume or surface density. For high temperatures the corrections to
thermodynamic quantities are obtained, which are proportional to the ratio of
the thermal de Broglie wavelength to the distance between planes.
