From thermodynamics point of view, in this era of aiming at energy conservation and sustainability, we need to develop more accurate ways to design thermal power, cooling and heat pump cycles. It has been the general practice in thermodynamic analysis of cycles to use the Carnot efficiency and Carnot coefficient of performance (COP) which are the highest upper bound to efficiency and COP of cycles. In the present report through the application of the 2nd law of thermodynamics for irreversible processes, which results in the general inequality relation for the entropy production, we have introduce new upper- and lower-bounds to the efficiency of thermal power cycles and COP of cooling and heat pump cycles. The resulting upper- and lower-bounds are closer to the actual efficiency and COP of cycles. That allows us a more precise design of cycles and the choice of cycles’ working fluids.