In this paper, we study Joule-Thomson effects for charged AdS black holes. We obtain inversion temperatures and curves. We investigate similarities and differences between van der Waals fluids and charged AdS black holes for the expansion. We obtain isenthalpic curves for both systems in the T -P plane and determine the cooling-heating regions.

In this paper, we study Joule-Thomson expansion for Kerr-AdS black holes in the extended phase space. A Joule-Thomson expansion formula of Kerr-AdS black holes is derived. We investigate both isenthalpic and numerical inversion curves in the T -P plane and demonstrate the cooling-heating regions for Kerr-AdS black holes. We also calculate the ratio between minimum inversion and critical temperatures for Kerr-AdS black holes.

In this letter we investigate the throttling process of the charged Anti-de Sitter (AdS) black holes in the rainbow gravity. In the extended phase space of these black holes, the cosmological constant plays the role of a varying thermodynamic pressure and the black hole mass is identified with the thermodynamic enthalpy. We derive exact expressions for the Joule-Thomson coefficient and the inversion temperature in terms of black hole parameters and constants of rainbow gravity analytically, and then perform a numerical analysis for the isenthalpic and inversion curves of charged AdS black holes. Our calculations show all quantities are sensitive to rainbow parameter η. We also discuss the isenthalpic curves for different values of the black hole mass.

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Considering the modified entropy-area relation from DSR-GUP (Doubly special relativity-Generalized uncertainity principle), we obtain the modified Friedmann equations from the first law of thermodynamics at apparent horizon. Due to the importance of GUP at Planck scale, we investigate the Friedmann equations and show the maximum energy density ρ at Planck scale. Since GUP implies a minimal length, we find a minimum apparent horizon which has a potential to remove the Big Bang singularity. Furthermore, we analyse the effects of DSR-GUP on deceleration parameter q for the equation of state p = ωρ and the flat case. Finally, we check the validity of the generalized second law (GSL) of thermodynamics and show that it is valid for all eras of the universe for any spatial curvature. 1 We use the unitsh = c = G N = l 2 P l = 1 2 We recall that the extended gravity framework arises from the necessity to extend standard general relativity in order to attempt to achieve the famous Dark Energy and Dark Matter problems [26]. In this framework, the recent starting of the gravitational wave astronomy with the famous detections of LIGO [27] could be, in principle, decisive to confirm the physical consistence of standard general relativity, or, alternatively, to endorse the framework of extended theories of gravity [28]. In fact, some differences between general relativity and alternative theories can be pointed out in the linearized theory of gravity through different interferometer response functions [28].