Abstract: By using the method of quantum statistics,we directly derive the partition functions of the bosonic field and fermionic field in the Sen black hole with an axial symmetry.Then via the improved brick-wall method and the membrane model,we calculate the entropies for the bosonic field and fermionic feld.We derive the entropy of the black hole which is not only related to the area of the outer horizon but also the function of the area of the inner horizon.In our results, there are no logarithmic divergent terms and left terms.There does not exist the question why the entropy of the scalar field or Dirac field outside the horizon is the entropy of the black hole.The influence of the spinning degeneracy of particles on the entropy of a black hole is studied.When the radiation temperature of the black hole approaches absolute zero,the entropy determined by the area of the inner and outer horizons also approaches zero.This satisfies the Nernst theorem.It can be taken as the Planck absolute entropy of a black hole.

Keywords: 
• membrance model /
• entropy of a black hole /
• Nernst theorem