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 $=kc$

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

$\begin{array}{l}\frac{dc}{dt}=-kc\\ \left(\text{change in mass}\right)=\left(\text{decrease by decay}\right)\end{array}$

(a) Use Euler's method to solve this equation from $t=0$ to $1\text{ d}$ with $k=0.175d^{-1}$ Employ a step size of $\Delta t=0.1$. 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.