Pure carbon dioxide, at one atmosphere pressure, is blown into a bath of liquid
ID: 1056535 • Letter: P
Question
Pure carbon dioxide, at one atmosphere pressure, is blown into a bath of liquid steel through a solid steel tube set in a refractory brick, which forms part of the refractory lining of tire furnace bottom. Above it is a 1 metre deep bath of liquid steel, containing 0.1 wt% dissolved carbon. The endothermic reaction associated with the reaction; CO_2(g) + C_liquid steel = 2CO_(g) Delta H degree = +41.2 Kcal/mole results in heat being sucked out of the liquid steel at the place where this chemical reaction takes place. Since this occurs at the moment the CO_2 gas comes into contact with the melt, the cooling is sufficient to cause the liquid steel to freeze locally. At steady state conditions, a frozen hemispherical mushroom of solidified steel forms. This shell will protect the refractory nozzle from any erosion by high velocity localized flows of liquid steel. MUSHROOMS (thermal accretions) formed by bottom jetting of CO_2 through liquid steel (CO_2 + C = 2CO) (picture courtesy of Kawasaki Steel). This photo is a top view of a hemispherical "mushroom" or sponge-like porous hemisphere of solid steel that was formed on top of a refractory brick containing a 1/4 inch I.D. nozzle, set m the bottom of a steelmaking furnace of 250 tonne capacity. Use the oxide free energy diagram to estimate the (endothermic) enthalpy change, Delta H degree for this reaction, under standard conditions, and confirm the Delta H degree data provided in the equation. Given the inlet CO_2 gas enters at 0.15 Nm^3/min, estimate the size (i.e. diameter, cm.) of the "mushroom" (or "thermal accretion") that will form. Data: Melting point of pure (low carbon) steel, T_alpha, rho = 1540 degree C. Steel bath temperature, T_bath =1600 degree C Heat transfer coefficient from liquid steel to 'mushroom', h = 10 kW m^-2 K^-1.Explanation / Answer
1. I have caculated the enthalapy changes from Ellingham diagrams. the plot have been plotted between gibbs free energy (Kj/mol) and the temperature in K . Our reaction temperature was nearly about 1600oC. from the ellingham diagram slope gives entropy valve of curve and its y intercept gives the value of change in enthalpy . from that y intercept is calculated as 10.14 kj/mol. which was valid with data given in the equation
2.For find out the thickness of the mushroom we have to calculate the q value . so formula for finding q is
q = m cp dt = 69.44 * 0.49 * 60 = 2041 kW
then h = 10 Kw/m2 k , dt = 60 k
q = h Am dt = 2041 = 10 * Am * 60
then Area of the mushroom is = 3.402 m
area of the sphere = 4*3.14*R2 = 3.402
R = 0.512 m or 51.23 cm
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