For the Fermi gas filling the space inside the spherical cavity of arbitrary radius and with an arbitrary, including small, number of particles, the thermodynamic characteristics are calculated in the general form, namely: entropy, energy, thermodynamic potential, constituent elements of equation of state, heat capacities, and compressibilities. The size effects relating to the discrete structure of levels are investigated. On the example of the two- and three-level models, there is traced both the sequence of level filling with increasing temperature and the temperature dependence of the chemical potential. As shown, at temperatures, at which the filling of a new level begins, the heat capacity undergoes jumps.