[KorematsuFredt]

Is compressed air in itself source of energy ? Or does it depend on the external air pressure as well ? For example I compress air in a canister and move it to outer space or deep underwater, does the energy we can exploit out of it goes up or down ?

[jmolinski]

Yes, if you take such a container into space, the gauge pressure (pressure relative to ambient atmospheric pressure) goes up. A cold gas thruster is a type of rocket engine that is basically a pressurized tank of gas with a valve connected to a propelling nozzle. The nozzle takes a high-pressure, low-velocity gas and converts it to a low-pressure, high-velocity gas, and directs its output generating thrust (which is a reaction force - Newton's 3rd law). The lower the ambient pressure, the higher the expansion ratio of the nozzle can be, which results in a higher output velocity of the gas, which directly increases the thrust. It would give you a higher specific impulse, which is a measure of fuel efficiency for reaction (thrust) engines.