  We use the brick wall model to calculate the free energy of quantum scalar
field in a curved spacetime (D +1) dimensions. We find the thermodynamics
properties of quantum scalar field in several scenaries: Minkowski spacetime,
Schwarzschild spacetime and BTZ spacetime. For the cases analysed, the
thermodynamical properties of quantum scalar field is exactly with the
reported. It was found that the entropy of the gas is proportional to the
horizon area in a gravity field strong, which is consistent with the
holographic principle.
