Liquid nitrogen for cooling the high-purity germanium detectors, maintained at a temperature of 78 K, is stored in a dewar made from two concentric cylinders. The area between the cylinders is evacuated, so no conduction or convection can occur. The inner cylinder has an outside diameter of 0.6 m and an outside height of 1.5 m. There is a 0.1 m gap between the inside and outside cylinders. The surfaces of both cylinders are gray, with emissivity of 0.2. The outer surface of the outer cylinder has emissivity of 0.8 and loses heat by radiation to surroundings at 300 K.

a. Find the total heat rate into the liquid nitrogen.
b. If the heat of vaporization of the nitrogen is 2 x10^5 J/kg, estimate the boil-off rate (in kg/s).