1. (35 pts.) A 0.5-m internal diameter spherical tank 10 mm thick stainless steel (k = 15W/m K) is used to store liquid nitrogen at 77 K. Tank is insulated with silica powder (k = 0.0017 W/m-K) and the insulation is 25 mm thick. Temperature of the outer surface of the tank was measured as 299K and it is exposed to ambient air of 300 K. The outer surface of the tank is painted white and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. The convection coefficient is known to be 20 W/m2-K. The latent heat of vaporization and the density of liquid nitrogen are 2x10$ J/kg and 804 kg/m?, respectively. (Neglect the resistance to heat transfer from the container wall to the liquid nitrogen.) a. What is the rate of heat transfer to the liquid nitrogen? b. What is the rate of liquid boil-off (L/day)? Vent Insulation Air T-300 K Liquid nitrogen Stainless steel Figure 1.