A sufficiently robust pressure vessel (much stronger than the gas cylinders you are thinking of) could theoretically be used in the system you describe, but would have several notable safety hazards.
1. After the tank reaches room temperature, in order to cool it off again you would need to vent some gas out to cool it off. Venting nitrogen gas into a room is an especially bad idea if you are standing in it, as it is an odorless asphyxiant. So your “simple” tank would need a dedicated ventilation system to the outside to not kill you.
2. If the tank does not have a vacuum wall to insulate the exterior surface, then when it is cold enough to get liquid nitrogen out, it is cold enough to give you frostbite from touching it.
3. Cooling the tank through venting will build up ice around the vent, potentially making it impossible to close. You also wouldn’t want a safety release valve buried in ice.
4. Pressure vessels always have a small risk of rupture or exploding. If the nitrogen is room temperature under a high pressure, then such an event will instantly fill the room choking everyone inside. If the tank is full of cold liquid nitrogen under a reasonable pressure, a rupture will not lead to an explosion, and people will likely have time to evacuate.
5. Rapid heating and cooling of a pressure vessel to cryogenic temperatures and back sounds absolutely horrible from a materials standpoint. I would absolutely not trust that vessel unless it was super-thick. And thus super heavy.
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