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01-22-2015 06:03 AM  3 years agoPost 1
TheHud

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Ellsworth, ME - USA

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Working toward my Electrical Engineering degree. Taking Differential Equations course. Had a problem today, not sure I did it right, would like input.

Place a cup of water in a fridge that is set at 35 degrees.
T(5)=70 degrees (Water Temp after 5 min in fridge = 70)
T(8)=60 degrees (Water Temp after 8 min in fridge = 60)

Find original temp of water when placed in fridge: T(0)=?

Using Newtons law of cooling, I came out with water starting temp at just over 96 degrees.

Am I close? I am not looking for an exact answer from anyone, just want to know if I am close.

Gun control is like fighting drunk driving by making it harder for sober people to buy cars.

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01-29-2015 07:37 PM  3 years agoPost 2
AirWolfRC

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Calculus will get exact but some mental gymnastics will do here.

==Establish the gradient using the two reference points

10º drop in 3 minutes
. . . with an average difference to target (35º) of 30º (65-35)

That's 10º per 3 min per 30º average difference to target
That's 0.111º per min per degree diff. to target

==Extrapolate to answer

(T(0) - 70) / 5 / ((T0 + 70) / 2) - 35) = 0.111

solve for T(0)

T0 = 96.9

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01-29-2015 08:04 PM  3 years agoPost 3
jackp332

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Claremont, Nh USA

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Holy Mathemagician!

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01-29-2015 08:41 PM  3 years agoPost 4
don s

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Chesapeake, VA

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...

E820, Raptor G4N, X50F/E, E620, Forza 450, and some planks.

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01-30-2015 01:35 AM  3 years agoPost 5
TheHud

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Ellsworth, ME - USA

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Thanks AirWolfRC. I had given up on anyone answering. I ended up with about 96.4 when I worked it out, so at least I was in the ballpark.

Gun control is like fighting drunk driving by making it harder for sober people to buy cars.

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01-30-2015 01:38 AM  3 years agoPost 6
Flying Brian

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St. Clairsville, Ohio

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I really just don't even know!!!!

How the hell do you have time for that kinda MATH, and building helis? WOW

"I just don't Listen" "

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01-30-2015 03:33 AM  3 years agoPost 7
GREYEAGLE

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Flat Land's

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Don't you want Boyel's law ? Just asking -

Theirs a Couple that apply to Delta T- depending if it's a gas or a Solid

Newton played with Falling apples

Then theirs Planick's law on Radiation or Light Shift / Green or Red or Hot or Cold and the Difference : The To or Fro " Coming or Going

Whole bunch of Funn Stuff you can toss at it.

We can even Jazz it with Micro Wave and get excited without boiling it and SLAP IT for the Poof ! Gives Up a Pile of Energy

Note " The Temp of the Fridge is going to change ALSO on the Second cup What happen to that ??

P.S. Water and ELECTRICITY Do - Not Mix

Get Nutty : Start with Ice Cube's

YOU WILL GET a MATHEMATICAL ANSWER TOO !! Some are Negative Numbers or Positive Number's

greyeagle

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01-30-2015 03:47 AM  3 years agoPost 8
drdot

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So. California, Orange County.

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fwiw..

SLAP it for the poof!....haven't done that in years!......

John.

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01-30-2015 03:56 AM  3 years agoPost 9
RM3

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Killeen, Texas - USA

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How the hell do you have time for that kinda MATH, and building helis? WOW
Yeah you'll be surprized with the range of peoples professional abilities that enjoy this hobby.

others on this site are full blown experts that work for high end aerospace companies, others are actual Heli pilots, I knew two that flew BlackHawks here at Ft. Hood TX. then others are everyday Joes that have construction jobs... this hobby really has no stereo type when it comes to who is a RC aircraft pilot...

for example I do computer programming for embedded systems and Industrial controls, but you would never have guessed that by looking at my gallery.

showing a preference will only get you into trouble, 90% of everything is crap...

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01-30-2015 09:02 AM  3 years agoPost 10
EEngineer

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TX

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(T(0) - 70) / 5 / ((T0 + 70) / 2) - 35) = 0.111
Just curious....Where did the "/5" factor come from?

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01-30-2015 03:05 PM  3 years agoPost 11
AirWolfRC

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That's the time from T(0) to T(5) . . . minutes
the 0.111 is a per minute change

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01-31-2015 01:12 AM  3 years agoPost 12
EEngineer

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TX

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==Establish the gradient using the two reference points
10º drop in 3 minutes
. . . with an average difference to target (35º) of 30º (65-35)
That's 10º per 3 min per 30º average difference to target
That's 0.111º per min per degree diff. to target
==Extrapolate to answer
(T(0) - 70) / 5 / ((T0 + 70) / 2) - 35) = 0.111
solve for T(0)
Would have thought 10 deg. per 3 min per 25 deg. (60 - 35)

Which is 0.1333 deg. per minute per deg. diff to target....

So,

(T(0) - 60) / 8 / ((T(0) + 60) / 2) - 35) = 0.1333

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01-31-2015 02:31 AM  3 years agoPost 13
AirWolfRC

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Close but no cigar.

The drop of 70º to 60º drop needs to be taked from the middle of that drop (65º) because the lapse rate at 5 minutes is not the same as the rate at 8 minutes.

So without using calculus (asymptotic limits and all that stuff), I took a linear interpolation between the two points. This is not completely accurate, as I originally mentioned, but will do.

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01-31-2015 04:12 AM  3 years agoPost 14
EEngineer

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TX

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Good...

Let's see if his professor agrees....

Hope he reports back....

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01-31-2015 02:19 PM  3 years agoPost 15
TheHud

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Ellsworth, ME - USA

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I will report back, but my professor is...well, think of a slightly better dressed version of Tommy Chong, with a brilliant mind for mathematics. It may be a while before I get it back.

Gun control is like fighting drunk driving by making it harder for sober people to buy cars.

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02-04-2015 03:18 AM  3 years agoPost 16
TheHud

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Ellsworth, ME - USA

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UPDATE:

Got it back, I had it right....what I did:

Tf=35 degrees= temp of refrigerator, T5 min=70 degrees, T8 min=60 degrees, Find T0 min =original temp of liquid when placed in fridge.
t=time, t 5 min = .083333 hours, t 8 min=.133333 hours
C is a constant, k is proportionality constant

Temp of water=Tf+Ce^(-kt)
70=35+Ce^(-k*.083333)
35=Ce^(-k*.083333)
35e^(k*.083333)=C

60=35+Ce^(-k*.133333)
25=Ce^(-k*.133333)
Substitute in C from above
25=35e^(k*.083333) * e^(-k*.133333)
25=35e^(k*(.083333-.133333))
25/35=e^(-k*.05)
.714286=e^(-k*.05)
ln(.714286)=-k*.05
-k=-6.72944

From first calculations above:
35=Ce^(-k*.083333)
35=Ce^(-6.72944*.083333)
C=61.32

Therefore :
T at 0 min=35+61.32e^(-6.72944*0)=96.32 degrees which was the correct answer.

The professor did it differently, with fewer steps, but this is the way I figured it out. I see now I did not need to convert minutes to decimal...but still worked out.

Gun control is like fighting drunk driving by making it harder for sober people to buy cars.

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02-04-2015 03:38 AM  3 years agoPost 17
GREYEAGLE

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Flat Land's

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Cool ! VERY GOOD - I HATED IT - No EXCITEMENT > Forced into Forgetting IT

Now where would you apply It ?? for purpose ? and WHY ?

Slowing something Down ? That's Water : Solid / Gas / or Liquid ?

COOL ! More work in Typing it Out - Yer Nutt's !!

I like em when you crack the top the ICE Instantly Float's Up ! like magic - The effect of AC-hole to mess with the conversion.

What 's that got to do with Electrical Engineering ? Playing with Liquid Helium ? and Them Big Coil's in a Hospital ?

Hint: Don't Mix Water and Electricity : Ole Einstein NEVER Could Figure it Out Still working on it TOO !!!

greyeagle

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02-04-2015 06:05 AM  3 years agoPost 18
EEngineer

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TX

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Cool...good job all the way around....

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