The Nernst theorem and the entropy of the Reissner-Nordstrom black hole

We calculate the free energy and the entropy of a scalar field in terms of the brick-wall method on the background of the Reissner-Nordstrom black hol e. We obtain the entropy of a scalar held is not only related to the locati on of an outer horizon but also is the function of the location of an inner horizon. In the approximation, the entropy is only proportional to the are a of an outer horizon. The entropy expressed by location parameter of outer and inner horizon approaches zero, when the radiation temperature of a bla ck hole approaches absolute zero. It satisfies the Nernst theorem.