Ehrenfest scheme for the extended phase space of f(R) black holes

In this letter, the original expressions of Erhenfest equations have been introduced directly into the black-hole research by treating the cosmological constant and its conjugate quantity as thermodynamic pressure and volume, respectively. The nature of phase transition at the critical point of P-V criticality of AdS black holes in f(R) gravity has been investigated as an example. The specific heat at constant pressure CP, the volume expansion coefficient a and the isothermal compressibility coefficient.T are found to diverge at the critical point. An analytical check of Ehrenfest equations has been carried out and it has been proved that both Ehrenfest equations are satisfied. So AdS black holes in f(R) gravity undergo a second-order phase transition at the critical point. This result is consistent with the nature of liquid-gas phase transition at the critical point and would help deepen the understanding of the relations between AdS black holes and liquid-gas system. Moreover, the influences of f(R) correction on the thermodynamics and the phase transition of AdS black holes in f(R) gravity have also been shown in this letter.Copyright (c) EPLA, 2014