hw7 - Homework 7 PHZ 5156 Due Tuesday, November 2, 2009 1....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework 7 PHZ 5156 Due Tuesday, November 2, 2009 1. In class, we discussed the diffusion equation and also a bit about Boltzmann statistics. In this problem, we will explore diffusion in the presence of an external field. We saw in class that the mass current J z of diffusing particles is given in terms of the diffusion constant D and local density n ( z,t ) as J z =- D n z (in one dimension). Consider now an external field acting so that the diffusing particles feel an external force with z-component F z =- dU dz , where U ( z ) is the potential energy of a particle at z . If the force F z = F (i.e. a constant force independent of z), then the potential energy is (up to a constant) U ( z ) =- F z . With this added force, the mass current is taken to be J z =- D u z + nF where is the mobility . a) Consider the case where J z = 0 (i.e. equilibrium). Recall first that in equilibrium, based on our discussion of Boltzmann statistics, that at temperature T we have n ( z ) = n e- U ( z ) /k B T . Next, show that there is a relationship between and D , = D k B T b) Use the continuity equation n t + J z z = 0 to obtain the one-dimensional Smolu- chowski equation, n...
View Full Document

This note was uploaded on 08/08/2011 for the course PHZ 5156 taught by Professor Johnson,m during the Fall '08 term at University of Central Florida.

Page1 / 3

hw7 - Homework 7 PHZ 5156 Due Tuesday, November 2, 2009 1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online