Systematic approach to the exergy determination, organized on exact thermodynamic basis, shows that the familiar Petela equation [1] is valid only for the exergy of radiation closed in a resting volume ("exergy of enclosed radiation"). The thermodynamics of heat pumps, separators and energy converters driven by the, solar and thermal energy has been analyzed focused on the energy limits for transformation or consumption of solar energy and applications in which an essential role is played by optimization and the optimal control theory. As an example, dynamic programming minimization of total work supplied to a two-stage drying system driven by heat pumps is described and analyzed.