Can a gas be cooled well below its boiling point by expansion?

Let's say I have an air compressor compressing a pure nitrogen gas stream to several bar. After being compressed the stream is cooled to a saturated vapor. The stream then runs through an expansion valve to atmospheric pressure.

Will liquid nitrogen come flowing out?

• What has the atmospheric boiling point got to do with any of this? Sep 8, 2019 at 1:47
• Posting this as a comment because I'm not sure if it's relevant to your question: For a typical fluid, the liquid and vapor "phases" are continuously connected. You can go smoothly from one to the other by evolving the system along a path in the temperature-pressure plane that goes around the phase-transition line, because the phase-transition line ends at a critical point. Sep 8, 2019 at 2:33
• @ChetMiller I edited to clarify I wasn't talking about boiling point at atmospheric pressure but at whatever pressure it is compressed to—to become a saturated vapor Sep 8, 2019 at 19:13

If done correctly, the compressed gas exiting the expansion nozzle will almost immediately condense into liquid. Repeating this process over and over again is how "liquid air" was first prepared over 100 years ago and is the basic principle upon which all gas-cycle refrigerators operate.

• I edited to clarify it's a saturated vapor just before decompression. Does this affect your answer? Sep 8, 2019 at 19:14
• no, it will not. Sep 8, 2019 at 23:15

tl;dr - To my understanding, no, liquid nitrogen will not come pouring out. It will still be gaseous.

Here's how I understand this:

Temperature is defined as the average kinetic energy of an object, or of the particles in an object.

Your proposal is to, in essence, decompress a gas in order to see whether or not its temperature will decrease - and the answer is, in some senses, yes and no.

Yes, because if you stick a thermometer into the decompressed gas, it will likely show a lower temperature due to the fact that less particles with the same energy as before are hitting it, causing the thermometer to register a lower temperature.

But if you're simply measuring the average kinetic energy of the particles, decompression itself doesn't really have a noticeable effect on the gas's temperature in that sense.

There's an example of this in the real world - the thermosphere, which is very, very warm compared to ambient temperatures on Earth. The thing is, the air is so thin there that we would barely feel any heat due to the lack of particles hitting our skin to transfer heat energy. Read more here:

• I edited to clarify it's a saturated vapor just before decompression. Does this affect your answer? Sep 8, 2019 at 19:15

From the open system, control volume version of the first law of thermodynamics, the change in enthalpy per unit mass of the nitrogen passing through the valve will be zero. If you check a pressure-enthalpy diagram for nitrogen, you will see immediately that if the upstream pressure is less than about 20 bars, none of the nitrogen will condense. It will all emerge superheated at a lower temperature.