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In a cryogenic propellant the fuel and the oxidizer are in the form of very cold, liquefied gases. These liquefied gases are referred to as super cooled as they stay in liquid form even though they are at a temperature lower than the freezing point. Thus we can say that super cooled gases used as liquid fuels are called cryogenic fuels.
These propellants are gases at normal atmospheric conditions. But to store these propellants aboard a rocket is a very difficult task as they have very low densities. Hence extremely huge tanks will be required to store the propellants. Thus by cooling and compressing them into liquids, we can vastly increase their density and make it possible to store them in large quantities in smaller tanks. Normally the propellant combination used is that of liquid oxygen and liquid hydrogen, Liquid oxygen being the oxidizer and liquid hydrogen being the fuel. Liquid oxygen boils at 297oF and liquid hydrogen boils at 423oF.
As we now know the properties of cryogenic fuels, we can proceed further and see how they are employed to impart thrust to the rockets.