A 2.5 cm diameter cylindrical refractory crucible for melting lead is to be built for thermocouple calibration. An electrical heater immersed in the metal is shut off at some temperature above the melting point. The fusion-cooling curve is obtained by observing the thermocouple emf as a function of time. Neglecting heat losses through the wall of the crucible, estimate the cooling rate (W) for the molten lead surface (melting point 327.3?C, surface emissivity 0.8) if the crucible depth above the lead surface is(a) 2.5 cm,(b) 17 cm. Assume that the emissivity of the refractory surface is unity and the surroundings are at 21?C.(c) Noting that the crucible would hold about 0.09 kg of lead for which the heat of fusion is 23,260 J/kg, comment on the suitability of the crucible for the purpose intended.GIVENA cylindrical refractory crucible filled with molten leadCylinder diameter (D) = 2.5 cmMelting point of lead (T1) = 327.2?C = 600.3 KSurface emissivity of lead (ε1) = 0.8Mass of lead in crucible (m) ?? 0.09Heat of fusion of lead (hfg) = 23,260 J/kgASSUMPTIONSHeat loss through the wall of the crucible is negligibleThe emissivity of the refractory surface (crucible wall above the lead) is unity (ε2 = 1)The surroundings behave as a blackbody enclosureThe temperature of the refractory surface is uniform atTR

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Az: e = 1 T2 = T. T.= 294 K Refractory Sureface : AR, TR Lead Surface : A, T- 645.3 K. Lead M= 0.09 Kg D=7.5 cm