Abstract: The method and system of the present invention is designed to minimize exergy consumption consistent with a given level of product purity. For example, in a distillation system, the design employs a plurality of thermostatted trays which are maintained at a sequence of temperatures specified by finding the optimal control for an irreversible thermodynamic process. The specified temperatures at each tray are achieved with the help of a tandem heat pump which works over the range of required temperatures and which delivers the specified heat demands.