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32_562ln08 - MIT OpenCourseWare http/ocw.mit.edu 5.62...

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MIT OpenCourseWare http://ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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5.62 Spring 2007 Lecture #32 Page 1 Kinetic Theory of Gases – Transport Coefficients We begin by considering the important case of diffusion . Diffusion is a very important transport property for chemists because it describes the mass transport necessary to bring molecules into sufficiently close proximity for chemical reactions to occur. Imagine a one component gas in a fixed volume at fixed T and p but with possible (slight) variation in the density ρ (z,t) in the z-direction at time t. ! " ( z + # z ) " ( z ) " ( z # z ) We imagine 3 planes at some position z separated by the mean free path and enquire about the simplest description of j z m the net flux of particles in the z- direction. The flux has units of mass per unit area per unit time. At the microscopic level, over a distance on the order λ , a particle trajectory is likely to be interrupted by a single collision that deflects its path to a different height z, which is in a re ! j z m (z,t) gion of different density. We make the assumption that the microscopic flux, denoted , has the form of local effusion flux determined in Lecture #31: ! j z m (z,t) = j angle ( ! ,t) = v 4 " cos #$ (z,t) With this form of the flux, we can determine the net flux of particles at the average z- position moving in the positive z-direction: j z m (z,t) = ! ! j z m (z + " z ,t) + ! j z m (z ! " z ,t) = ! v 4 # cos $ % (z + " z ,t) !% (z ! " z ,t) [ ] up from below down from above The mean free path λ z may be considered small so we expand the density around the middle position: 4/24/08 11:08 AM
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5.62 Spring 2007 Lecture #32 Page 2 ! (z ± " z ,t) # ! (z,t) ± " z $! $ z
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