Liquid nitrogen loaded into an insulated tank at 1 atm absolute pressure is kept at the boiling point by allowing a small amount of it to gradually evaporate and flow out of the tank. In order to keep a constant temperature, the rate at which nitrogen vapor is vented from the tank must be such that the latent heat of vaporization exactly balances the rate of heat transfer through the tank wall. A thin-walled liquid nitrogen cylinder, 40 cm in diameter and 1.5 m tall, is covered with 4 cm of an insulating material with k = 0.0020 W/m K. The external heat transfer coefficient is h = 20 W/m² K and the external air temperature is 22°C.

(a) Determine the steady rate of heat transfer into the tank.

(b) Determine the rate at which nitrogen vapor needs to be vented from the tank in kg/s.

(c) Determine how long the tank will last if it is initially completely filled with liquid nitrogen.