Damghan University Press Iranian Journal of Astronomy and Astrophysics 2322-4924 6 1 2019 04 01 The phase transition of corrected black hole with f(R) gravity انتقال فاز سیاه چاله تعمیم یافته با گرانش( f(R 1 8 152 10.22128/ijaa.2019.342.1055 EN Mohammad Rostami Department of Physics&amp;lrm;, &amp;lrm;North Tehran Branch&amp;lrm;, &amp;lrm;Islamic Azad University&amp;lrm;, &amp;lrm;Tehran&amp;lrm;, &amp;lrm;Iran. Jafar Sadeghi Department of Physics, University of Mazandaran Sedigheh Mirabotalebi Department of Physics, North Tehran Branch, Islamic Azad University, Tehran, Iran. Amir Ali Masoudi Department of Physics, Alzahra University, Tehran, Iran. Journal Article 2019 10 30 In this letter, we consider static black hole in f(R) gravity.<br />We take advantage from corrected entropy and temperature and investigate such black hole. Finally, we study the $ P - V $ critically and phase transition of corrected black hole with respect to entropy and temperature. Here also, we obtain the heat capacity for the static black hole in $ f(R) $ gravity. This calculation help us to investigate some singularity.<br />We have shown that the corrections exist for any black hole, but they are important for a small black holes and negligible for the large black holes. The advantage of a static black hole in $ f(R) $ gravity is its holographic picture, which is a van der Waals fluid. Then, We have shown that in the presence of corrections there is still a van der Waals fluid as a dual picture.<br />The critical values of event horizon radius for phase transitions are shown due to the corrections of entropy and temperature.<br />We have some figures which show the phase transition and $ P - V $ critically. https://ijaa.du.ac.ir/article_152_e26cb129b4163749762fc63251538928.pdf