Liquefying Nitrogen: Problem w/ Latent Heat at 280.6K

[gfd43tg]

Sorry for the template not being present, when I use my phone it doesn't show up. I am trying the problem about liquefying liquid nitrogen, and I am having my first problem finding the latent heat of vaporization at 280.6 K. I try using trouton's rule, and I get a domain error because the inside is negative with a power of 0.38.


I can't really tell if my drawing is right, I am assuming that the order in which it enters the system is a throttle valve, then a heat exchanger. Some vapor leaves the system, which is the combined throttle valve and heat exchanger, before entering the heat exchanger. Then, the rest goes through the heat exchanger.

 

[gfd43tg]

Here is a new attempt, this time I made the inlet condition the reference. I am still stuck about the vaporization enthalpy using troutons rule and getting a negative number due to the reduced temperature being greater than unity