Liquid nitrogen is stored in a dewar made of two concentric spheres with the space between them evacuated. The inner sphere has an outside diameter of 1 m and the space between the two spheres is 0.1 m. The surfaces of both spheres are gray with an emissivity of 0.2. If the saturation temperature for nitrogen at atmospheric pressure is 78 K and its latent heat of vaporization is 2 x 105 J/kg, estimate its boil-off rate under the following conditions(a) The outer sphere is at 300 K.(b) The outer surface of the surrounding sphere is black and loses heat by radiation to surroundings at 300 K. Assume convection is negligible.(c) Repeat item (b) but include the effect of heat loss by natural convection.GIVENLiquid nitrogen in two concentric spheres with the space between them evacuatedInner sphere diameter (Di) = 1 mSpace between spheres (s) = 0.1 mBoth surfaces are gray with equal emissivites (ε1 = ε2) = 0.2Saturation temperature of nitrogen (Tn) = 78 KLatent heat of vaporization of nitrogen (hfg) = 2 x 105 J/kgASSUMPTIONSSteady stateThermal resistance of the sphere walls is negligibleThermal resistance between the nitrogen and the inner sphere is negligible (T1 =Tn)

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A2 T-300 K Nitrogen T,-78 K -D;- 1m S= 0.1 m