Originally Posted by Epitope
Ironically a heat pipe is probably the closest thing to what you are imagining. A heat pipe uses the phase change of liquid to vapor to absorb heat much like liquid nitrogen cooling. However, the vapor is condensed and recycled inside the tube and wicked back to the heat source to continue the cycle.
You are basically describing a liquid nitrogen heat pipe... I doubt a LN2 heat pipe would work very well because liquid nitrogen doesn't have surface tension and self attraction like water does. I doubt it would wick nearly as well as water. Nor does it have the heat absorbing properties of water. Water is one of the most efficient substances known to man when it comes to absorbing heat. It takes more energy to raise a given amount of water 1 degree C than almost any other material.
Liquid nitrogen heat pipe is impossible. In order to condense nitrogen needs not only to be at a high pressure, but also at least -147c. Not to mention, heat pipes work at a constant pressure throughout the system (in other words if we cooled the hot side to -147c the lowest temperature we could have on the cold side is -147c). To have different pressures in the system would require an active cooling system, thus defeating the purpose of the heat pipe. In the ideal world we would have the cold side of the heat pipe be a low pressure while the hot side is a very high pressure. This way we could achieve ~-205c on the cold side and only need ~-155c on the hot side.
Wait! I have an idea, lets get a phase change to cool the cold side of the heat pipe to -147c. And thus the cascade was born.
Im being sarcastic here, basically we are talking about refrigeration. All of this is impossible without a system of coolers that constantly cycle through their refrigerants cooling the next stage. With nitrogen we would need like 5 or 6 stages.