Exergy represents a measure of quality of energy and because exergy is destroyed due to process irreversibilities within a system to produce entropy, the exergy expressions and analysis developed in this work could be used to operate the intrinsically unsteady-state lyophilisation processes more efficiently. It is shown that the time optimal control operation of a freeze dryer with respect to heat input to the trays and total pressure in the drying chamber, reduces the duration times of the primary and secondary drying stages by 42.43% and 41.17%, respectively, and this leads to a reduction of 38.19% in the magnitude of the total exergy losses of the lyophilisation system studied in this work. Also, the potential for reducing further the exergy losses when organic co-solvents and water forming non-ideal mixtures of solvents with positive deviations from Raoult's law are used in a lyophilisation system operated under time optimal control, is discussed.