Wizard
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July 3rd, 2017 at 8:47:59 PM permalink
A refrigerator is kept at a constant temperature of 5 degrees.

A can of beer is placed in it with initial temperature of 25 degrees.

In one hour it cools to 15 degrees.

Assume that that the penguin that lives in the refrigerator not only turns the light on and off when you open the door but shakes the beer so that it maintains a constant temperature (and explodes in your face when you open it).

Hint: The rate of heat transfer is proportional to the difference between the temperature of object to the ambient temperature.

How long will it take to cool the beer to 10 degrees from the time it is placed inside the refrigerator?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ChesterDog
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July 3rd, 2017 at 9:16:05 PM permalink
2 hours
rsactuary
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July 3rd, 2017 at 9:24:58 PM permalink
^^ I'm not sure what the answer is... but pretty sure that's the one answer it isn't.
Ibeatyouraces
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July 3rd, 2017 at 9:39:27 PM permalink
At those temperatures, the beer will freeze before you know it.

http://www.homebrewtalk.com/showthread.php?t=176193
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BlueEagle
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July 3rd, 2017 at 10:32:16 PM permalink
My guess is around 1:15
CrystalMath
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July 3rd, 2017 at 10:49:23 PM permalink
I agree with ChesterDog.
I heart Crystal Math.
Ibeatyouraces
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July 3rd, 2017 at 11:01:39 PM permalink
Unless the question is in Celsius, most beers are already frozen at 25°.
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pacomartin
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July 4th, 2017 at 12:53:24 AM permalink
Quote: Ibeatyouraces

Unless the question is in Celsius, most beers are already frozen at 25°.



I think we have to assume Celsius, as 5°C=41°F which is a normal refrigerator temperature. The warm beer is 25°C=77°F.



It's a simple differential equation dH/dt= ω H , when t=0, H=25-5=20, when t=1, H= 15-5=10. H is exponentially related to t.

H=H0 * exp( ω t) so H0=20 is the original heat differential,
10=20 * exp( ω ) given the second condition so ω = - ln(2)

So solve for time t= τ when H = 5
5=20 * exp( - ln(2) * τ )
1/4 = exp( - ln(2) * τ ) so τ =2 hours

Wizard
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July 4th, 2017 at 5:34:26 AM permalink
First, ChesterDog is the winner with the first correct answer. I owe you a cold beer.

Second, the temperatures are given in Celsius.

Third, I apologize for that one being too easy. How long will it take to cool the beer to 5.1 degrees?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ChesterDog
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July 4th, 2017 at 7:18:18 AM permalink
Quote: Wizard

First, ChesterDog is the winner with the first correct answer. I owe you a cold beer.

Second, the temperatures are given in Celsius.

Third, I apologize for that one being too easy. How long will it take to cool the beer to 5.1 degrees?



I get t = log [ ( 25 - 5 ) / ( 5.1 - 5 ) ] / log(2) = log(200) / log(2) = 7 hours 39 minutes.
Wizard
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July 4th, 2017 at 8:37:02 AM permalink
Quote: ChesterDog

I get t = log [ ( 25 - 5 ) / ( 5.1 - 5 ) ] / log(2) = log(200) / log(2) = 7 hours 39 minutes.



Correct! You get a liter of beer for the extra credit.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
OnceDear
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July 4th, 2017 at 9:07:50 AM permalink
Quote: Wizard

Quote: ChesterDog

I get t = log [ ( 25 - 5 ) / ( 5.1 - 5 ) ] / log(2) = log(200) / log(2) = 7 hours 39 minutes.



Correct! You get a liter of beer for the extra credit.


Dammit. I didn't know there was a prize going begging, and I knew the answer :o)
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Ibeatyouraces
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July 4th, 2017 at 9:11:30 AM permalink
Beer is disgusting. Being rewarded with it would be punishment.
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FleaStiff
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July 4th, 2017 at 10:30:46 AM permalink
Math? Thermodynamics?
How many of you if confronte with this problem would simply open the refrigerator and drink the can of beer rather than whipping out a slide rule?
Wizard
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July 4th, 2017 at 10:56:16 AM permalink
Quote: FleaStiff

Math? Thermodynamics?
How many of you if confronte with this problem would simply open the refrigerator and drink the can of beer rather than whipping out a slide rule?



I'll choose the slide rule.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Canyonero
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July 4th, 2017 at 11:17:22 AM permalink
Huh, interesting. I had to solve that problem when I was 14 as part of a competition called "physics olympics". It wasn't a beer though. I passed that round.

I failed the next round when I had to calculate the tides on Earth relative to the position of the moon. (Assuming the Earth was homogenously covered in water with no landmass. [Insert physicist assuming something absurd joke here.]) To this day I don't know how to do this.
Wizard
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July 4th, 2017 at 1:44:54 PM permalink
Quote: Canyonero

Huh, interesting. I had to solve that problem when I was 14 as part of a competition called "physics olympics". It wasn't a beer though. I passed that round.



That is quite a problem for 14. Glad to have another genius on the forum!
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ontariodealer
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July 4th, 2017 at 11:18:45 PM permalink
are we talking real beer or American beer??
get second you pig
Wizard
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July 5th, 2017 at 6:11:37 AM permalink
Quote: ontariodealer

are we talking real beer or American beer??



Winners choice between Lucky Lager, Burgie, and Miller.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Ibeatyouraces
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July 5th, 2017 at 6:53:17 AM permalink
Quote: Wizard

Winners choice between Lucky Lager, Burgie, and Miller.


Be the AP that you are and get them Olde English. 😎
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Wizard
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July 5th, 2017 at 8:59:44 AM permalink
Quote: Ibeatyouraces

Be the AP that you are and get them Olde English. 😎



I prefer Old Milwaukee. In part because they aren't so pretentious as to put an e after the "Old."
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
wudged
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July 6th, 2017 at 5:27:05 AM permalink
Quote: Wizard

I prefer Old Milwaukee. In part because they aren't so pretentious as to put an e after the "Old."



It's not meant to be pretentious; it's shtick about old vs. modern English. "ye olde brewery"

( and apparently "ye olde" is incorrect also https://en.wikipedia.org/wiki/Ye_olde )
boymimbo
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July 6th, 2017 at 9:32:18 AM permalink
Quote: Wizard

I prefer Old Milwaukee. In part because they aren't so pretentious as to put an e after the "Old."



Yikes. There is lots of good beer out there!
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Ibeatyouraces
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July 6th, 2017 at 9:35:30 AM permalink
Apparently, you guys didn't get my joke. OE is about the cheapest, if not THE cheapest beer there is.
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charliepatrick
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July 6th, 2017 at 10:08:33 AM permalink
Beer: Probably off topic but I'm a fan of Real Ale rather than gaseous stuff that some pubs sell. There's an organization called CAMRA which promotes it. Thus, if you look, there's some very good pubs around - these are two near me...
https://whatpub.com/pubs/HAS/00842/bookshop-alehouse-southampton
https://whatpub.com/pubs/HAS/00470/guide-dog-southampton
pacomartin
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July 6th, 2017 at 9:53:40 PM permalink
Quote: Wizard

In part because they aren't so pretentious as to put an e after the "Old."

It's a fake spelling that was started as a mock antiquity. The "Ye Olde _____" construction was being made fun of by 1896. So your disdain is well placed.
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