The main objective of this book is to analyze the cogeneration system coupled with external heat reservoir of finite heat capacity and including both external irreversibility due to the finite-rate heat transfer between the working fluid and heat reservoirs and internal irreversibility due to the heat dissipation of working fluid. Internal irreversibility and External irreversibility is included in the analysis by introducing an internal irreversible parameter, defined by second law of thermodynamics and variation of temperature of the heat reservoir. The presence of both the irreversibility parameters shows that a cogeneration power plant with irreversibilities delivers less energy output and has a lower efficiency than those of the reversible and endoreversible cycles. The model presented here is of more use when compared to those obtained by earlier researchers. The effect of the heat consumer temperature parameter ( ) & extreme temperature ratio ( ) on the maximum total exergy rate & the corresponding exergy efficiency are analyzed. The result has been plotted graphically considering various parameters.