Answered: SA (mg/L) 16 12+ 8+ 4 16 24 32 40 T(°C)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The quantity of oxygen that can dissolve in water depends
on the temperature of the water. (So thermal pollution influences
the oxygen content of water.) The graph shows how
oxygen solubility varies as a function of the water temperature T
.
(a) What is the meaning of the derivative S'(T) ? What are
its units?
(b) Estimate the value of S'(16) and interpret it.

Expert Solution

Step 1

The quantity of oxygen that can dissolve in water depends on the temperature of the water.

The graph shows how oxygen solubility varies as a function of the water temperature $T$ .

We have to find the meaning of the derivative $S' (T)$ and estimate the value of $s' (16)$ .

Step 2

The instantaneous rate of change is denoted as $S' (T)$ .

$S' (T) = \lim_{∆ x \to 0} \frac{∆ y}{∆ x}$ .

Here $y = S (T)$ measured in milligrams per liter and $x = T$ measured in centigrade.

The derivative $S' (T)$ is the rate of change of the quantity of oxygen solubility with respect to water temperature $T$ .

The units are milligrams per liter per centigrade $(\frac{m g}{L}) / ° C$ .

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