# The generalization of charged AdS black hole specific volume and number density

## TL;DR

This paper introduces a generalized specific volume for charged AdS black holes, extending the understanding of their thermodynamic phase transitions and number density in higher dimensions, with most previous results remaining valid.

## Contribution

It proposes a generalized specific volume and ratio for charged AdS black holes, broadening the scope of thermodynamic analysis and interpretation in higher-dimensional cases.

## Key findings

- Most previous conclusions are generalized without change.
- The ratio rac{3 rac{rac{ ilde{
ho}_c}{16}} in the general case.
- The necessity of the new assumption for higher-dimensional black holes.

## Abstract

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.