Heat engine efficiency for four-dimensional charged AdS black holes in Rastall gravity

Abstract

In this paper, we analyze the [Formula: see text] criticality and the heat engine efficiency of two black holes, one is the four-dimensional charged AdS black hole in Rastall gravity and the other is the four-dimensional charged AdS black hole surrounded by quintessence in Rastall gravity. For the four-dimensional charged AdS black hole in Rastall gravity, the ratio [Formula: see text] is related to the Rastall parameter [Formula: see text]. When [Formula: see text] the ratio becomes [Formula: see text], which is same as the van der Waals liquid-gas system. Additionally, as the Rastall parameter [Formula: see text] increases, the heat engine efficiency [Formula: see text] of the black hole will increase. Moreover, the efficiency [Formula: see text] decreases rapidly at first and then increases with the entropy [Formula: see text]. But the efficiency ratio [Formula: see text] decreases with the Rastall parameter [Formula: see text]. For the four-dimensional charged AdS black hole surrounded by quintessence in Rastall gravity, as the charge q increases, the critical specific volume [Formula: see text] and the efficiency ratio [Formula: see text] also increase, however, the critical temperature [Formula: see text] and the critical pressure [Formula: see text] gradually decrease. Moreover, the heat engine efficiency [Formula: see text] and the efficiency ratio [Formula: see text] of the black hole are similar to the four-dimensional charged AdS black hole in Rastall gravity.