If a cylinder could withstand any pressure how high would the pressure rise if the vessel was filled half full of liquid nitrogen then sealed and then allowed to warm to room temperature? What if allowed to warm to 200 degrees F. Also, what state would the nitrogen be in during this period, liquid/vapor, vapor only, other?
Above the critical temperature and pressure (126K), nitrogen is a supercritical fluid (has properties of both a gas and a liquid).
If it started half full of liquid, then you're asking at what pressure is the density half of liquid nitrogen. That's about 800 kg/m^3. Using http://www.peacesoftware.de/einigewerte/stickstoff_e.html it appears that 450 bar at 15 degrees C will be sufficient. You can play around with finding similar at other temperatures.
The nitrogen is above its critical temperature when it is at room temperature. It doesn't contain the standard liquid or vapor phases at that point. It would be only one phase, which would be a supercritical fluid. See https://en.wikipedia.org/wiki/Supercritical_fluid