Question

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 3-m-diameter spherical tank that is initially filled with liquid nitrogen at 1 atm and -196°C. The tank is exposed to ambient air at 15°C, with a combined convection and radiation heat transfer coefficient of 35 W/m2.°C. The temperature of the thin-shelled spherical tank is observed to be almost the same as the temperature of the nitrogen inside. Determine the rate of evaporation of the liquid nitrogen in the tank as a result of the 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 which has an effective thermal conductivity of 0.00005 W/m °C. N, vapor T=15°C atm Liquid N -196°C Insulation

Answer 1

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A hACTT) - 35×4T>CS)スCIS+196) te bc ATb 208, 905.9 W. 208, 805. 9m x198 m1054-5 121.5 m (b) Rinsula tHon 2T K 4TTK72 7.s5-LS 0488 K/w 47TX o63Sx5a 55 Kconvout side YhA354/sg29.6/ 15+196 A o10488+9.46x70千 4241 5 W. Amx199 う1mミム42 K 1 52-1.S cc) 477 6.000oSxl.5 x1-52 ,1g 2 152 m Rinsulation 22 13.96 K/w 4. Kconvout std e W 35x 4x523 A 15+146 (3.959 84 5.11 K9 W. b ベっ(m-0.0763 k9/s Gmx198 FI8-