Methods of separating carbon dioxide from flue gas and sequestering liquid carbon dioxide

Systems and methods to separate carbon dioxide from flue gases and sequester carbon dioxide are described here. By using the properties of carbon dioxide and the temperature in a body of water (e.g., the ocean or freshwater body of water) or the temperatures of the ambient atmosphere, gaseous carbon dioxide can be converted to a liquid and separated from other gases. Pressure used to separate carbon dioxide from other gases may also be used to sequester liquid carbon dioxide. The liquid carbon dioxide is inert and can be discharged into the ocean without dissolving in seawater and acidifying the ocean. The liquid carbon dioxide may further be densified to be denser than seawater. The liquid carbon dioxide can then sink to the bottom of the ocean or be injected into ocean sediments or sediments and rocks beneath the ocean floor, inert and sequestered for the long term.