# Liquid Nitrogen Expansion to Desired Temperature

I want to take liquid nitrogen in a pressurized container and spray it through a hose onto objects in a room.

The container has a pressure regulator so I can adjust pressure as desired. The requirement is that a particular temperature is reached on exit from the hose.

I understand that the final temperature will of course be room temperature but that is after reaching equilibrium. I desire a temperature above liquid but still very cold no where near room temp upon exiting the hose (T_desired or T_3).

There would be a phase change from liquid to gas, and then a gaseous expansion to the desired temperature that can be achieved by regulating the pressure valve.

What are the equations for this process, particularly if I want to know the volume of nitrogen gas emitted from the hose at the desired temperature?

Note: This is for a practical application so the answer can contain simplifying assumptions, but please list them if used. Ex. Constant volume as liquid.

Edit: If temp cannot be regulated by the pressure valve alone, then I would like to know what temp it is at, as well as the volume.

This container is a good example: princetoncryo.com/cylinder/cryo-cyl/cryo-cyl-35l-lp.html

• If you want to heat up the gas to a certain temperature, you need to add a heat source. What and where is that heat source supposed to be? Aug 16, 2014 at 2:32
• It is flowing from a thermos-like container through a hose that is exposed to room temperature. The change from liquid to gas will surely generate a change in temp, no?
– BAR
Aug 16, 2014 at 2:34
• So you are pressurizing liquid nitrogen with e.g. helium? And then you let the liquid expand into a lower external pressure? That will, at most, reduce the temperature of the liquid further. If the resulting temperature is above the temperature of liquid nitrogen at room temperature, some of the liquid will boil off, until you reach the boiling point, at which you will have a thermodynamic equilibrium. I thought the problem was to generate gas at a given temperature rather than the boiling temperature? At this point I have to assume I misunderstand what you are trying to do. Aug 16, 2014 at 2:47
• The LN2 is pressurized when filled at a provider facility. It is a real container with known volume, temp, and a pressure gauge. The first sentence [in Original Post] is exactly what I want to do.
– BAR
Aug 16, 2014 at 2:57
• If you want a certain temperature for the gas, you need to have a heat source. Now, that heat source could be the heat conduction of the surrounding air trough the hose, but I would strongly advise against that. Liquid nitrogen has a lower temperature than liquid oxygen, and if you chose your flow parameters poorly, there may be liquid oxygen collecting on your hose, which, in case of improperly chosen materials is a serious hazard. There will also be plenty of condensation and ice buildup, which are considered additional hazards. The proper way is a gas heater. Aug 16, 2014 at 3:02

This problem has certainly been solved in practice in a number of applications - cryosurgery, cryogenic treatment of metals, and cryogenic cooling of x-ray crystallography samples, but the approach will depend on the application.

The flow of liquid nitrogen is always always unstable and fluctuating, because it is usually impossible to prevent small amounts of boiling from generating unpredictable amounts of gas. If this is unacceptable, you will need to boil the liquid first in a vessel or phase separator, and then pass it through the nozzle.

If you intend for the liquid to be boiled in the hose by external heating or contact with ambient air, you may be disappointed. Droplets of liquid will remain in the stream because of the Leidenfrost effect - poor thermal contact between the droplets and the wall of the hose. The result will be a spray of droplets mixed with gas.

You might therefore need a proper heat exchanger - using a long thin pipe or perhaps a metal mesh, to ensure the liquid is fully boiled. Ambient heat can be quite adequate, and is routinely used in boil-off heat exchangers, provided you don't mind large amounts of ice and water condensing on the outside. I wouldn't worry about condensation of oxygen - as long as this occurs in an open environment the oxygen will not build up in dangerous amounts. Oxygen buildup can certainly be dangerous if it occurs inside an enclosed container.

If you need a controlled temperature, then I agree that a heater and temperature sensor are required. A pipe exposed to the environment will gradually cool down as it becomes insulated by ice.

The dewar will have two outlets - one for liquid (unpredictable as I explained above) and one for gas. The gas outlet is very useful, but is not fully insulated, so there will be a minimum temperature below which it will not go. You say that the container has a pressure regulator - but you need to clarify this. Does it have a built-in boiloff device to maintain the pressure? If not, you will find that extracting liquid or gas depressurises the dewar.

Before you do any of that, however, you need to say how big a room you are going to be doing this in, what size of dewar you are using, and what rate of flow you are hoping to use. I would like to carry on discussing with a StackExchanger who is still breathing air with at least a bit of oxygen in it.

Sorry if this answer is disappointingly unmathematical - you need to define the physical regime first, before equations can be usefully applied.

• Good info +1, but I am looking for equations. What more physical properties are you looking for? Equations are generalized with variables after all..
– BAR
Aug 17, 2014 at 4:02
• And its ok that the output is a mix of gas and liquid. I am thinking of simply using a rated pressure building device and running it through a cryo hose.
– BAR
Aug 17, 2014 at 4:10

The usual way to "spray" things with cold nitrogen vapor is to transfer the nitrogen to a one- or two-gallon dewar with an open top, and pour liquid on them. If you want to spray them with vapor, do the same thing but stand on a ladder so that the liquid doesn't quite reach the object.

The usual way to control temperatures using liquid nitrogen is cooling to 77 K by immersion, with a heater element and temperature readback on the sample if a temperature above 77 K is desired.

You will find that cold nitrogen vapor is much less efficient at cooling your "objects in the room" than the liquid. The heat capacity per unit mass of nitrogen vapor is comparable to that for nitrogen liquid, but the liquid is roughly a thousand times more dense than the vapor and also can remove the latent heat of vaporization.

If you are interested in using a vapor hose plus pressure regulator already attached to your dewar for this project, it should be a simple experiment to have the first thing you spray be a thermometer and to make your own table of gas temperature vs. regulator pressure. Your hose will probably form water ice on the outside, which will insulate it from the room, so you may want to do a few temperature-vs-pressure curves for different frost thicknesses.

If you are interested in attaching your own hose to the vapor outlet on a dewar, be warned that frost inside the hose could block the outlet and seal up your dewar. Make sure you understand the relief system on the dewar before you do this! An accidentally sealed container of liquid nitrogen will absorb lots of energy from the room and then explode. You do not want this.