{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hmwk4

# hmwk4 - Department of Chemical Engineering University of...

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

Department of Chemical Engineering University of California, Santa Barbara Eng 5A Fall 2001 Instructor: David Pine Homework #4 Homework due: Wednesday, 24 October 2001 Note: Every student should work on the homework by himself or herself. It is ok to to get help from others, but the work should be your own. Reading: Chapter 8 in The Mathematica Primer discusses troubleshooting strategies. It’s useful reading. Demo 7 illustrates many of the concepts addressed in problems 2-5 on lists & matrices. 1. Consider the radioactive decay of 239 U 239 Np 239 Pu. We can model these three reactions by the ODEs d [U] dt = - k u [U] (1) d [Np] dt = k u [U] - k n [Np] (2) d [Pu] dt = k n [Np] (3) (a) Solve these ODEs using Mathematica by the following method. First solve Eq. (1) to obtain an expression for the time dependent concentration [U]( t ). Assume that 100% of the starting material is uranium (U). Then, substitute your solution for [U]( t ) into Eq. (2) and solve for [Np]( t ). Finally, use these results to obtain an expression for [Pu]( t ). Hint: [U]( t ) + [Np]( t ) + [Pu]( t ) = 1

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}