the point of the nitrogen is that it needs to evaporate on by the heat of the cpu. look at it as boiling water on a chip the chip will be stuck at 100°c as long as there is water. but if you want to use a closed loop than you need to find a way to compress it and condense it back and than let it re loop to the cpu.
witch would require a lot of energy.

if the nitrogen is a gas like in your case it would react as an heat insulator (the air around you is 70% nitrogen or so it would react as normal air cooling).

or do you mean something like a heat pipe or a vapour chamber.

Like a heat pipe or vapor chamber; becoming gas after it boils from the CPU heat or the simple heat of case lights. Then becoming liquid again as it reaches the cool part where the heat is dispensed.

You are looking at some intense equipment to do this. Most LN coolers are passive, just pouring the cold stuff onto the CPU with no maintenance of the nitrogen's temps. It evaporates out of the system in a short period of time.

http://www.ln2cooling.com/index.php?main_page=product_info&cPath=33&products_id=85&zenid=9nip56fh660631ugu7pmh4bi55

There ARE liquid nitrogen systems that include the cooler system to preserve the LN2 temperatures. But you are talking at 10's if not 100's of thousands of dollars. The Cray3 XMP was cooled with an LN2 contact submersion system.

Look into phase change systems. They keep the chips sub zero, and run about the $3k mark

I'm just glad to know these exist, I knew about the other way which was just powering it into a funnel looking thing and it sits there while evaporating.

Is there any videos showing such a loop?

these loops will be made to withstand high pressure. a simple and cheaper example of these kind of loops is at the backside of your fridge . the difference will be that you will have a larger cooler(mayeb whit fans) and more compressing stages.

Yea just someone who copied and paste but this thread is dead; I received my answers.