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Chem. - Heat and Mass Transfer I - Spring 2010 Assignment 1 Due: Monday May 31st at 4: A gas mixture at a total pressure of 1.5 x 105 Pa and 295 K...


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Dep. Chem. Eng. – Heat and Mass Transfer I – Spring 2010 Assignment 1 Due: Monday May 31 st at 4:00 p.m. 1. A gas mixture at a total pressure of 1.5 x 10 5 Pa and 295 K contains 20% H 2 , 40% O 2 , and 40% H 2 O by volume. The absolute velocities of each species are -10 m/s, -2 m/s and 12 m/s, respectively, all in the direction of the z-axis. (10%) a) Calculate the mass average velocity and the molar average velocity for the mixture. b) Determine the four fluxes: j O2,z , n O2,z , J O2,z , N O2,z 2. Knowing that 0 . = - + A A A r t n ρ , prove that 0 . = - + A A A r j Dt Dw ρ , where D stands for substantial derivative (total derivative). (20%) + - = n w D n A A AB A ρ Hint: 0 . = + t v ρ ρ 3. A 0.15-m-long, 0.015-m-diameter test tube containing ethanol is left open in the laboratory. The level of ethanol is initially 0.1 m below the top. The temperature in the laboratory is 26°C and the atmospheric pressure is 0.987 atm. The vapour pressure of ethanol is 0.08 atm. If the concentration of ethanol in the air outside the test tube is negligible and the concentration of ethanol near the liquid surface can be calculated using Dalton’s law, determine: (25%) a) An expression for the concentration profile of ethanol in air inside the test tube if the liquid level is held constant. b) An expression for the instantaneous molar flux of ethanol. c) The time required for the level of ethanol to decrease by 0.005 m if the evaporation rate does not change with time. Remember that the decrease in ethanol level will be equal to its rate of transfer to the gas phase: dt dz C v C N liq A A liq A A , , interface = = Data: density of ethanol: 784 kg/m 3 . Answer to (c) = 52 h 4. A 0.20-m-long test tube was used to study the diffusion process in which liquid A diffuses into gas B . In one study the level of liquid A was initially 0.1 m below the top of the tube. The temperature was 25°C and the total pressure was maintained at 1 atm. The molar flux of component A at the top of the test tube was found to be 1.6x10 -3 kgmol/m 2 .h. Find the diffusion coefficient for A into gas B . Assume that gas B is insoluble in liquid A . The partial pressure of A at the surface of the liquid was 0.06 atm. Answer = 0.063 m 2 /h (20%) 5. Gas A diffuses through two immiscible liquids contained in a capillary tube as shown below. The concentration of A at the bottom of the capillary tube is maintained at a constant value. The partial pressure of A in the gas is 0.05 atm. The equilibrium relationships for A in the two liquids are: (25%) 1
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Dep. Chem. Eng. – Heat and Mass Transfer I – Spring 2010 Assignment 1 Due: Monday May 31 st at 4:00 p.m. C A,I = 200 P A C A,I = 2 C A,II where P A has units of atm and C A has units of kgmol/m 3 . The concentration of A at Z 2 is 3.0 kgmol/m 3 . The diffusivities of A in liquids I and II are 1.5 x 10 -9 m 2 /s and 7.5 x 10 -9 m 2 /s, respectively. The thickness of the liquid I layer ( Z 0 Z 1 ) is 0.02 m and of the liquid II layer ( Z 1 Z 2 ) is 0.05 m. Assume that convective effects at the bottom of the capillary tube are negligible and that liquid I has a very low vapour pressure. Calculate the molar flux of A dissolving into liquid II and plot the concentration of A in liquids I and II as a function of Z . Answer = 1.5 x 10 -7 kgmol/m 2 .s 2 Liquid II Liquid I Gas A Z 2 Z 1 Z 0
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