We study the excess entropy and the corresponding non-gravitational feedback energy ( E _ { feedback } ) in the intra-cluster medium ( ICM ) by considering a sample of 38 galaxy clusters using Chandra X-ray and NRAO VLA Sky Survey ( NVSS ) /Giant Metrewave Radio Telescope ( GMRT ) radio observations .
We find moderate correlation of the feedback energy and brightest cluster galaxy ( BCG ) radio luminosity ( L _ { R } ) with the various cluster thermal properties .
We show conclusively that the active galactic nucleus ( AGN ) is more effective in transferring feedback energy to the ICM in less massive clusters .
We find that within 0.3 r _ { 500 } , the feedback energy correlates with cluster temperature as E _ { feedback } \propto T _ { obs } ^ { 0.98 \pm 0.37 } .
Moreover , for radio detected BCG sample we find that BCG radio luminosity at 1.4 GHz scales with gas mass as L _ { R } \propto m _ { g,obs } ^ { 1.76 \pm 0.71 } and with X-ray luminosity as L _ { R } \propto L _ { X,obs } ^ { 0.94 \pm 0.35 } .
Finally , we discuss the implications of our results with regard to feedback in clusters .