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Countercurrent condensation loop

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I will be attempting to make liquid nitrogen from air. Part of the process involves passing air compressed to 200 atm through a coil and rapidly expanding it. The expanded air that does not form liquid from the rapid cooling will pass back over the condensor coils in a counter-current fashion to precool the compressed air. Of course, this countercurrent system will be insulated from the surroundings.

My question is this: how long should should I make the countercurrent coil for it to be effective? I know I will transfer more heat with a longer coil, but there has to be a point of diminsishing returns. There are many variables so I think this comes down to experience. Does anyone have any idea?

I am planning on something between 8-16 feet for the coil.

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