  It is shown that the classical entropy of the extremal black hole depends on
two different limits procedures. If we first take the extremal limit and then
the boundary limit, the entropy is zero; if we do it the other way round, we
get the Bekenstein-Hawking entropy. By means of the brick wall model, the
quantum entropy of scalar field in the extremal black hole background has been
calculated for the above two different limits procedures. A possible
explanation which considers the quantum effect for the clash of black hole
entropy in the extremal limit is given.
