  We consider the energy density of a spin polarized $\nu=1/2$ system for low
temperatures. We show that due to the elimination of the magnetic field and the
field of the positive background charge in the calculation of the grand
canonical potential of Chern-Simons systems through a mean field formalism one
gets corrections to the well known equations which determine the chemical
potential and the energy from the grand canonical potential. We use these
corrected equations to calculate the chemical potential and the energy of the
$\nu=1/2$ system at low temperatures in two different approximations.
