The boiling temperature of nitrogen at atmospheric pressure at sea level (1 atm pressure)...

The boiling temperature of nitrogen at atmospheric pressure at sea level (1 atm pressure) is - 196°C. Therefore, nitrogen is commonly used in low-temperature scientific studies, since the temperature of liquid nitrogen in a tank open to the atmosphere will remain constant at - 196°C until it is depleted. Any heat transfer to the tank will result in the evaporation of some liquid nitrogen, which has a heat of vaporization of 198 kJ/kg and a density of 810 kg/m3 at 1 atm.

Consider a 4-m-diameter spherical tank that is initially filled with liquid nitrogen at 1 atm and ‒196°C. The tank is exposed to 20°C ambient air and 40 km/h winds. The temperature of the thin-shelled spherical tank is observed to be almost the same as the temperature of the nitrogen inside. Disregarding any radiation heat exchange, determine the rate of evaporation of the liquid nitrogen in the tank as a result of heat transfer from the ambient air if the tank is (a) not insulated. (b) insulated with 5-cm-thick fiberglass insulation (k = 0.035 W/m · °C), and (c) insulated with 2-cm-thick superinsulation that has an effective thermal conductivity of 0.00005 W/m · °C.