As a student engineer, this seems a good time to consult your Heat Transfer textbook if you have had that course. I recommend you go through the calculations yourself and set up your own spreadsheet for your problem. While there may be quicker ways to find a "canned" answer, doing it yourself will help you truly understand it and will put you on the road to being an expert in heat transfer.
First you must determine the mass flow rate and the relief temperature at several discrete time intervals. If you are lucky, the relief temperature will be above -20F at each time step because vapor to vapor heat transfer through a bare pipe is not very efficient. You can calculate the cooling duty rate required at each time step by multiplying together the vapor mass flow & the heat capacity & the temperature difference required. Now you have the heat flow (Q). Look to fill in the other parameters in the equation Q=U*A*LMTD. Calculate the LMTD assuming the air is constant temperature. You can calculate an overall heat transfer coefficient (U) or pick a reasonable value guided by experience. Now you can solve for the heat transfer area required. Since you know the pipe diameter, you can solve for the length needed. Do this for each time step and find the maximum length required. Add some extra length to cover the simplifying assumptions in your calculations.
Chris Haslego offers a useful spreadsheet in the files section of cheresources:
http://www.cheresour...ure-prediction/
The formulas are viewable and you can use his spreadsheet as a sanity check for your calculations. Use that spreadsheet also to investigate the effects of pipe wall thickness and insulation.