3. A sphere of pure carbon, 12 mm in diameter, burns in a flowing stream of oxygen gas. The sphere is surrounded by a stagnant film of gas of an estimated thickness of 3mm. The average temperature of the gas-film is 1300C and the total pressure is 1 atmosphere. The product of combustion is assumed to be CO2 only and its partial pressure in the bulk gas is 0.2 atm. Calculate: a. The initial rate of combustion b. The time required for the size of the carbon sphere to get reduced to 8 mm. The diffusivity of CO2 in O2 at the given conditions is 3.4 cm/s, the density of the carbon sphere is 900 kg/m3. Assume that the thickness of the stagnant gas-film remains unchanged even when the size of the carbon sphere decreases