Chapter 24, Problem 4P

Integration provides a means to compute how much mass enters or leaves a reactor over a specified time period, as in

$M={\int }_{t_1}^{t_2}Qcdt$

Where $t_1\text{ and }{t}_2=$ the initial and final times, respectively. This formula makes intuitive sense if you recall the analogy between integration and summation. Thus, the integral represents the summation of the product of flow times concentration to give the total mass entering or leaving from $t_1\text{ to }{t}_2$. If the flow rate is constant, Q can be moved outside the integral:

$M=Q{\int }_{t_1}^{t_2}cdt\left(\text{P24}\text{.4}\text{.1}\right)$

Use numerical integration to evaluate this equation for the data listed below. Note that $Q=4{\text{m}}^3/\text{min}$.

$t_{}$min	0	10	20	30	35	40	45	50
$c,\text{mg}/{\text{m}}^3$	10	35	55	52	40	37	32	34