Extended phase space thermodynamics and P - V criticality of charged black holes in Brans-Dicke theory

Motivated by conformal relation between dilaton gravity and Brans-Dicke theory, in this paper, we are taking into account extended phase space thermodynamics to investigate phase transition of charged black holes. We regard spherically symmetric charged black hole solutions in the presence of a scalar field in both Einstein and Jordan frames and calculate related conserved and thermodynamic quantities. Then, we study the analogy of the black hole solution with the Van der Waals liquid-gas system in the extended phase space by considering the cosmological constant proportional to thermodynamical pressure. We obtain critical values of thermodynamic coordinates and plot P - V and G - T diagrams to study the phase transition points and compare the results of dilaton gravity and Brans-Dicke theory.