Two large vessels are connected by a truncated conical duct which is 2 ft in length and has internal diameters of 8 and 4 in., respectively at its larger and smaller ends. One vessel contains a uniform mixture of 80 mole percent nitrogen and 20 mole percent oxygen, and the other a uniform mixture of 30 mole percent nitrogen and 70 mole percent oxygen. The pressure throughout the system is 1 atm and the temperature is 32 F. The diffusivity for the nitrogen oxygen system under these conditions is 0.702 ft2/hr. Determine the rate of transfer of nitrogen between two vessels in the early stages of the process assuming the complete absence of convection and that nitrogen diffuses along the duct in the direction of decreasing diameter. Compare the result with that which would be obtained if the conical duct were replaced with circular tube of diameter equal to the average of the terminal diameters of the truncated core-that is 6 in.