Interpretation of Wind Chill Derivative

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Mabeuf

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I have a homework question that states the following:

(Chemistry: Wind Chill) At 0? the heat loss H (in kilocalories per square meter per hour) from a person’s body can be modeled by
H = 33(10?v - v + 10.45)
where v is the wind speed (in meters per second).

(a) Find dH/dv and interpret its meaning.

I am pretty confident the derivative is 33(5/?v - 1), my problem is what is the interpretation? Doing the math is the easy part, what does it mean? Any help?
 
Mabeuf said:
I have a homework question that states the following:

(Chemistry: Wind Chill) At 0? the heat loss H (in kilocalories per square meter per hour) from a person’s body can be modeled by
H = 33(10?v - v + 10.45)
where v is the wind speed (in meters per second).

(a) Find dH/dv and interpret its meaning.

I am pretty confident the derivative is 33(5/?v - 1), my problem is what is the interpretation? Doing the math is the easy part, what does it mean? Any help?
Click to expand...

What does derivative mean?

Do a google search - tell us what you found.
 
Without doing and internet search, a derivative is the slope a tangent line to a curve at a given point or the rate of the change of a function in relation to an independent variable.

I still don't understand what 33(5/?v - 1) means even in relationship to H = 33(10?v - v + 10.45)

I know H = Heat Loss, v = wind speed in meters per second.

So if I plug in a speed of 30mps I could solve the first equation as H = 33(10?30 - 30 + 10.45) = 33(10*5.47722558 - 30 + 10.45) = 33 (35.2222558) = 1,162.33444 or in other words 1,162.33 Kilocalories per square meter per hour in heat are lost at 0? if the wind is 30mps.

So if I use the 30mps in the derivative equation, I get 33(5/5.47722558 -1) = 33(-0.0871290716) = -2.87525936

Based on this I guess the change in H as it relates to v feels like a temperature change of -2.875?
 
Since the unit of H is KCal and the unit of 'v' is mps - the unit of 'dH/dv' is KCal/mps.

So then dH/dv = - 2.875 at v = 30 mps means,

at v = 30 mps, each 1 mps change (increase or decrease) of v will change H (decrease or increase) by 2.875 KCal.
 
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