# Pressure in a sealed cylinder half-filled with liquid nitrogen, allowed to rise to room temperature?

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?

• I've edited the title. Please try to give titles that describe the topic as specifically as possible. In general, questions on stackexchange are supposed to be of interest to other people than the person posting them. Can you give some motivation for this question? Why 200 degrees F and not some other temperature?
– user4552
Feb 1, 2019 at 5:26
• Ben, I have always been intrigued with the pressures that liquid nitrogen can create when changing to supercritical fluid state in a sealed vessel. I have never been able to get data on these pressures and also the effect of starting the sequence with different levels of the gas in a liquid state in the vessel. Ex. 1/4, 1/2, 3/4 full. I know that if starting with the vessel full you have hydro static pressures that are extremely high. I want to research these different conditions for future reference. Any help would be greatly appreciated. Thanks, Harold Feb 1, 2019 at 17:25

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.

• Thanks for your response! I am thinking the higher the level of liquid in the vessel when it is sealed and allowed to reach room temperature the higher the pressure will be. Am I correct? Example, 1/4, 1/2, 3/4 full. Also the higher the super critical fluid temperature the higher the internal pressure. Is this a correct statement? I am amazed at the pressures that can be created under these conditions. Would like to know just how high they really are. Feb 1, 2019 at 17:35
• Yes. Just like sticking more gas in a gas cylinder raises the pressure. I'm relying on the calculations from that page. High temperature supercritical fluids can be approximated by ideal gas equation in some cases, but I don't know where that breaks down for nitrogen. Feb 1, 2019 at 18:50
• Would you be available for hire to consult for my start up company, Lotus Systems? Feb 1, 2019 at 20:06

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

• David, Thanks for the response. I tried using the link but had trouble putting in values to get the desired result. I'm still working with it and maybe I can figure it out in time. It would be a great resource for me. I want to use it to find different internal pressure in the sealed vessel with different levels of liquid Nitrogen in the vessel. I want to see how these different levels effect the internal pressure. Feb 1, 2019 at 17:48
• The pressure in the container that is filled only with liquid and vapor nitrogen will depend only on the temperature of the container, based on the vapor pressure of nitrogen. For details, see info regarding the Antoine equation:en.wikipedia.org/wiki/Antoine_equation. For temperatures above the critical temperature, a good first start would be the modified ideal gas law, which is $PV=znRT$, where z can be found from the law of corresponding states:en.wikipedia.org/wiki/Theorem_of_corresponding_states Feb 1, 2019 at 17:54
• David, My math skills are weak so I'm not able to take advantage of the links. One thing I was surprised about is the final pressure is the same with a 1/4 full starting level as with a 1/2 full vessel when reaching room temperature. I want thinking the more molecules in the tank the higher the pressure would be? Feb 1, 2019 at 18:24
• I suspect that your conclusion regarding equal pressure is incorrect. My math skills are not so weak, and I have the time, so I'll take a look at your problem and get back to you. Also, I'm curious ... why do you want to know such information? Feb 1, 2019 at 18:37
• We are looking at using this and other gases in research for green energy projects. We want to know the properties in several respects. Also I have always been amazed at the pressures these gases can create but have never known exactly what they are under certain conditions. I would never do this experiment as I am well aware of the hazard potential. We are looking for someone to consult with in the near future for hire on a regular basis. Use cell phone and PayPal. Feb 1, 2019 at 20:16