Chemistry Challenge?

Physical chemistry( challenge question) please help!!?

• Cryogenic liquids (liquid N2, He, etc) are typically stored in Dewar flasks (fancy thermos bottles) that consist of mirrored glass walls (to reduce radiative heating) separated by vacuum (a cylinder within a cylinder). How long would a liter sample of liquid argon last in a flat bottomed cylindrical Dewar with an inner radius of 5cm and height of 20cm and an outer radius of 10cm and height of 25 cm assuming that the only energy transfer that occurs is radiative between the walls of the Dewar (the top surface does not receive any radiation). The emissivity of silvered glass is 0.02 over all wavelengths, the outer surface of the Dewar is at 300K, the temperature of liquid Argon is 87 K, the density of liquid argon is 1.40 g cm3 , and the latent heat of vaporization is 1200 J/g. , The latent heat of vaporization is a measure of how much “extra” energy is required to vaporize a substance at its boiling point (the boiling point of argon is 87K). (Assume that all of the energy impinging on the inner cylinder is used to vaporize the Argon). I have an idea on how to proceed with this problem we need to account for the absorbtion and emmissivity. we can use the same formula for both of them P*= (boltzman constant)*(emmisivity)*(temperature)^4*a... then, we can find the net absorbtion of energy followed by the time but i am confused about the area i have to choose in each case ( absorbtion,emmision) !!! in other words, Do i have to include top surface area in both cases?

• Answer:

  This gets ugly [but it IS P-Chem, after all] because the reflected radiation bounces around until absorbed. Use the Radiosity method http://en.wikipedia.org/wiki/Radiosity_%28heat_transfer%29#Radiosity_Method Which equation looks really imposing until you see that N= 2. For the equation you will need a view factor from here http://www.engr.uky.edu/rtl/Catalog/sectionc/C-95.html