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

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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 Tags calculus, law of cooling, temperature