Ducts whose cross sectional area varies axially and which sustain a subsonic mean flow and temperature gradients are found in engineering applications which include combustors, automotive exhaust systems, and boilers. Non- isentropic flow conditions arise when there is significant heat transfer from the duct. The axially varying flow conditions affect the acoustic energy balance of the system and are significant for understanding thermo-acoustic oscillations. For example, the acoustic energy absorbed or generated depends on the mean entropy loss, which can be controlled by the amount of heat transfer from the duct. The objective of this work is to investigate the axial acoustic energy change by considering the acoustic energy absorption coefficient, Δ, in a varying area duct with a non-isentropic mean flow and temperature gradient. The response of the duct?s acoustic field to acoustic forcing is determined using a semi-analytical solution of linearized Euler equations, with the acoustic-entropy coupling neglected. A parametric analysis is performed to investigate the effect of mean flow gradients on the axial change in the acoustic energy for a given geometry of the duct. The dependence of Δ on the mean temperature ratio and acoustic reflection coefficient at the inlet, R1, is investigated for both low and high values of duct flow Mach number. This allows conclusions to be drawn on when acoustic energy is generated or absorbed.