Show transcribed image text Tpi of Siffusion CHAPTERT'.I IC and Mass Transfer Between Phases 553 , (a What is the effective thickness of the gas film for the evaporation rin a 2-in.-diameter wetted-wall column at a Reynolds number of 10,000 wat of Wmperature o intoef 40 C? (b) Repeat the calculation for the evaporation of ethanol At 1 atm the diffusivities are 0.288 cm'/s for water in air and 0145 em'/s for ethanol in air. Solution. For air at 40°C 273.16 = 1,129 × ρ- -1.129 x 10-3 g/cm? μ=0.0186 cP (App. 8) μ 1.86×10-4 ρ 1.129 x10-3 = 0.165 cm 2/s 22,410 313.16 (o) For the air-water system, 0.165 Sc = 0.288 0.573 From Eq. (17.70), Sh = 0.023 ( 10.000)0.81 (0.573)044-31 .3 4D/D , 2.0 In the film theory, kc-D,/Br and since Sh Sh = B7 =-= 0.064 in. BT (b) For the air-ethanol system. Sc = 0.165/0.145 = 1 14: Sh = 0.023(10,000)0.81 (1.14)044-42.3 423=0.047 in y Eo power of the diffusivity instead of the 1.0 power implied by the film 3in, 66) were used, the corresponding values of B, would ess B becomes smaller as the diffusivity decreases because k, varies with only the 0.56 theory. If Eq. (17 053 in. These somevw 3 is used instead of Du.50 Is S ese are somewhat closer to each other because D