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HomeworkSolutions_C12 - Homework Set 12 Shell mass/molar...

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Homework Set # 12: Shell mass/molar balance for components in a multi- component system Problem #1: Recall the example of evaporation of component A contained in a test tube in the lecture note (or see section 18.2, 2 nd edition, 17.2, 1 st edition). (a) By neglecting the convective flux of component A, show that this leads to ( ) ( ) 1 1 2 2 1 A A z z cD N x z z = = A x (b) What error is made in the determination of D in the example 18.2-2 (or 17.2-2, 1 st edition) if the result in (a) is used? Answer: a. Without the convection term, the total molar flux of A is equal to the diffusion flux of A. For steady state . A A dx N cD const dz = − = Since c and D are constant, thus ( ) ( ) 1 2 2 1 . A A A x x dx const dz z z = = − Therefore, ( ) ( ) 1 1 2 2 1 A A z z cD N x z z = = A x b. Error in the determination of D in the example 18.2-2 To get the solution of Example 18.2-2 by using the result in (a), we make the following calculation with the help of the equation of state for an ideal gas.
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