EBK NUMERICAL METHODS FOR ENGINEERS
EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 1, Problem 7P

The amount of a uniformly distributed radioactive contaminant contained in a closed reactor is measured by its concentration c (becquerel/liter or Bq/L). The contaminant decreases at a decay rate proportional to its concentration-that is,

decay rate = k c

where k is a constant with units of day day 1 . Therefore, according to Eq. (1.13), a mass balance for the reactor can be written as

d c d t = k c ( change in mass ) = ( decrease by decay )

(a) Use Euler's method to solve this equation from t = 0 to 1  d with k = 0.175 d 1 Employ a step size of Δ t = 0.1 . The concentration at t = 0 is 100 Bq/L.

(b) Plot the solution on a semilog graph (i.e., ln c versus t) and determine the slope. Interpret your results.

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EBK NUMERICAL METHODS FOR ENGINEERS

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