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DM
Numerade Educator

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Problem 57 Hard Difficulty

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 $ S $ 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.

Answer

a) oxygen solubility ,
per liter per degree Celsius.
b. -0.25 milligrams

Discussion

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DG

David Base G.

October 26, 2020

Finally, now I'm done with my homework

CA

Catherine A.

October 27, 2020

CA

Catherine A.

October 27, 2020

That was not easy, glad this was able to help

Video Transcript

So in this problem were given the soluble bility of oxygen in water and it is a various with temperature we were given a graph T. In degrees C. And yeah, sigh ability? S in milligrams per leader. And we have a graph that looks something like this, right? Or this is 16 up here and on down. Okay. And the first question we're asked is, what does S prime at T. Was the meaning of the derivative. And what are its units? Well, this property means the rate at which the oxygen, sorry, ability yeah, changes with respect two temperature, specifically the temperature of water in this case. Okay. And the units will be milligrams for leader degrees C. Okay, then, the next thing we're asked to do is to estimate the value Value of s. prime at 16 and interpret it. All right part. So from the graph we can see that? S prime at 16. Yeah. Is s of 16 S. Of a. Yeah, over 16 minus eight. Which coming off the graph Is approximately 10 -12 over eight, which is going to be -2/8. Or negative 0.25. Okay. So what does that mean? That means is the temperature temperature past 16 degrees C. Yeah, the oxygen, sorry, ability is decreasing ah a rate 0.25 milligrams for leader degrees C.