  In this paper, by proposing a generalized $specific~volume$, we restudy the
$P-V$ criticality of charged AdS black holes in the extended phase space. The
results show that most of the previous conclusions can be generalized without
change, but the ratio $\tilde{\rho}_c$ should be $3 \tilde{\alpha}/16$ in
general case. Further research on the thermodynamical phase transition of black
hole leads us to a natural interpretation of our assumption, and more black
hole properties can be generalized. Finally, we study the number density for
charged AdS black hole in higher dimensions, the results show the necessity of
our assumption.
