2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35984It is shown that that the area law for the entropy of a quantum field in the Schwarzschild black hole is due to the quantum statistics. The entropies for one particle, a Boltzmann gas, a quantum mechanical gas obeying Bose-Einstein or Fermi-Dirac statistics, and a quantum field in the Schwarzschild black hole are calculated using the microcanonical ensemble approach and the brick wall method. The area law holds only when the effect of quantum statistics is dominated.4 pages, revtexGeneral Relativity and Quantum Cosmologytext