sujins:
There are some facts that you are not stating and another that doesn't equate to what you are stating:
1) I assume you are dealing with Liquid Nitrogen (LIN) in the saturated state; if so, then you have no case for liquid thermal expansion. What you have is is the potential for LIN vaporization once its latent heat is absorbed through the insulation. You will probably have two phase flow through the required PSV.
2) How is it that you can have LIN at +50 oC? Either you've made a major typo or you have a very exotic liquid Nitrogen. Once the LIN starts to vaporize - and it will do so very, very quickly - you will have a mixed phase within the short span of pipe. The insulation doesn't have to fail, as such. Heat will eventually leak in to vaporize the LIN that is blocked in (you haven't said this either, but the LIN has to be blocked in, right?). What you have on your hands is a heat leak calculation that will determine the rate of LIN evaporation.