This study was performed with the intention of giving a deeper insight about the thermodynamic effectiveness of a thermal system. In this study, a fired heater (or furnace) existing in a petrochemical plant located in Aliağa, İzmir, Turkey were investigated from both first and second law point of view to identify the true magnitude of thermodynamic inefficiencies and reveal the true potential improvements for the system components. Hence, apart from the classical energy analysis, both conventional and advanced exergy analysis were applied to the system. The major source of inefficiencies within the system was enlightened by determining the exergy destructions and recommendation for possible modifications for improving thermodynamic efficiencies were stated. For each system component, amount of exergy destructions were determined and exergy efficiencies were calculated as 40.9% and 39.3% for fired heater (FH) and air preheater(APH), respectively in conventional exergy analysis. Besides, applying the advanced exergy analysis method it was seen that exergy efficiencies can be increased up to 52.4% and 85.8%, respectively.