What the Pythy one is talking about is the critical point, which is another combination of pressure and temperature of a phase diagram (just like the "normal" boiling and melting points of a substance... "normal" being the temp at 1 atmosphere). Most materials have one. It is a temperature at or above which it becomes physically impossible to cause liquification. For nitrogen it's the aforementioned -146.96C. At any temperature above that, nitrogen will not change phase to a liquid regardless of pressure -
not at any pressure, add all the 0's you want. So to generate liquid nitrogen, the temp
must be below -146.96C. You need ~300 psi at around -160C to liquify nitrogen, less than -196C to liquify it at atmospheric pressure (14.69595 psi) - which is just below it's boiling point of -195.80C at 1 atmosphere.
There is also a triple point - where a substance can exist in all 3 phases (solid, liquid, gas) at the same time. For nitrogen it's -210 C and 1.807602 psi.
The commercial LN2 generators I pointed you to before use a stirling cycle.
Here's a linky that shows in general how it works. This is the section of the overall generator that you put the thumbnail up for.
Peace :toast: