  Comparing with an ordinary thermodynamic system, we investigate the possible
microscopic structure of a charged anti-de Sitter black hole completely from
the thermodynamic viewpoint. The number density of the black hole molecules is
introduced to measure the microscopic degrees of freedom of the black hole. We
found that the number density suffers a sudden change accompanied by a latent
heat when the black hole system crosses the small-large black hole coexistence
curve, while when the system passes the critical point, it encounters a
second-order phase transition with a vanishing latent heat due to the
continuous change of the number density. Moreover, the thermodynamic scalar
curvature suggests that there is a weak attractive interaction between two
black hole molecules. These phenomena might cast new insight into the
underlying microscopic structure of a charged anti-de Sitter black hole.
