In this paper, we extend the phase space of black holes enclosed by a spherical cavity of radius rB to include $$ V=4\pi {r}_B^3/3 $$
V
=
4
π
r
B
3
/
3
as a thermodynamic volume. The thermodynamic behavior of Schwarzschild and Reissner-Nordstrom (RN) black holes is then investigated in the extended phase space. In a canonical ensemble at constant pressure, we find that the aforementioned thermodynamic behavior is remarkably similar to that of the anti-de Sitter (AdS) counterparts with the cosmological constant being interpreted as a pressure. Specifically, a first-order Hawking-Page-like phase transition occurs for a Schwarzschild black hole in a cavity. The phase structure of a RN black hole in a cavity shows a strong resemblance to that of the van der Waals fluid. We also display that the Smarr relation has the same expression in both AdS and cavity cases. Our results may provide a new perspective for the extended thermodynamics of AdS black holes by analogy with black holes in a cavity.
In this paper, the Joule-Thomson expansion of Born-Infeld AdS black holes is studied in the extended phase space, where the cosmological constant is identified with the pressure. The Joule-Thomson coefficient, the inversion curves and the isenthalpic curves are discussed in detail using a 4-dimensional black hole. The critical point of a Born-Infeld black hole is depicted with varying parameter
and the charge Q. In
plane, the inversion temperature curves and isenthalpic curves are obtained with different parameter
and charge Q. We find that the missing negative slope is still conserved in Born-Infeld black holes. We also extend our discussion to arbitrary dimension higher than 4. The critical temperature and the minimum of inversion temperature are compared. The ratio is asymptotically
as Q increases or
with
, and reproduces previous results at higher dimensions.
In this paper, the Joule-Thomson expansion of Born-Infeld AdS black holes is studied in the extended phase space, where the cosmological constant is identified with the pressure. The Joule-Thomson coefficient, the inversion curves and the isenthalpic curves are discussed in detail by 4-dimensional black hole. The critical point of Born-Infeld black hole is depicted with varying parament β and the charge Q. In T − P plane, the inversion temperature curves and isenthalpic curves are obtained with different parament β and the charge Q. It shows that feature of the missing negative slope is still conserved in Born-Infeld black hole. The critical temperature and the minimum of inversion temperature are compared, the ratio is asymptotically 1/2 as Q increases or β → ∞ .
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