NOVELTY - The method involves cooling a to-be-treated fluid (40) through heat transfer without change of state of the fluid, and cooling a portion of another to-be-treated fluid (42) in an enclosure (111) so as to obtain a solid (62) comprising carbon dioxide and low carbon dioxide gas. Liquefaction of a portion of the solid is carried out by introducing the portion of the solid into a molten bath (121) for obtaining primary carbon dioxide rich fluids. The former cooling process is carried out by reheating a portion of the primary carbon dioxide rich fluids and a portion of the low carbon dioxide gas.    USE - Method for producing low carbon dioxide gas and primary carbon dioxide rich fluids from a to-be-treated fluid comprising a carbon dioxide and volatile compound such as methane, oxygen, argon, nitrogen, carbon monoxide, helium and hydrogen, more volatile than carbon dioxide, for a production unit that is utilized for producing electricity and vapor from industrial fumes (claimed). Can also be used for producing electricity and vapor from carbonaceous fuels such as coal, hydrocarbons e.g. natural gas, fuel and oil residues, household waste, biomass, gases of refineries, chemical factory, iron and steel plants or cement factories, fumes from boilers utilized for heating buildings, and exhaust fumes from freight vehicles.    ADVANTAGE - The method permits capturing of carbon dioxide from the to-be-treated fluid including carbon dioxide and more volatile compound in efficient manner. The cold fluids resulting from a separation process are heated, while the to-be-treated fluid is cooled, thus reducing the quantity of energy necessary for the separation and compression of carbon dioxide, and making the electricity and vapor producing unit adaptable to different operation constraints such as pressure at which carbon dioxide is obtained, availability and costs of negative kilocalories required for separation of carbon dioxide by cryo-condensation.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of a carbon dioxide capture unit implementing a process of producing low carbon dioxide gas and primary carbon dioxide rich fluids from a to-be-treated fluid comprising a carbon dioxide and volatile compound more volatile than carbon dioxide.    To-be-treated fluids (40, 42)    Solid (62)    Exchanger (109)    Enclosure (111)    Molten bath (121)