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Cooling two six packs of beer in a small refrigerator...

by Protocol2.0
Tags: calculus, law of cooling, temperature
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Protocol2.0
#1
Feb22-12, 02:33 PM
P: 1
Your dorm room has a temperature of 72 F, and you have two six packs of beer that you want to get ready to a drinking temperature of 61 F for dinner. Your fridge has a temperature of 44 F, and experience has shown that a room-temperature six pack, placed in the fridge, will be at drinking temperature after 30 minutes.
Unfortunately, your fridge can only take one six pack at a time...
You devise the following strategy of having both six packs cool by dinner time:

Cool the first six pack to a temperature of [T][/low], which is suitably BELOW drinking temperature, so that when you take six pack #1 out, it will come up to drinking temperature in exactly the time required to cool six pack #2.

1.) To get to drinking temperature from room temperature takes a lowering by 11 degrees. Why is it that [T][/low] is NOT 50 F (as one might naively assume)?

2.) Determine [T][/low], and the total time required to cool both six packs with this strategy.
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kai_sikorski
#2
Feb22-12, 03:17 PM
PF Gold
kai_sikorski's Avatar
P: 162
First of all.. best homework question ever

Second of all: you need to show some attempt at a solution before we can help you.


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