“Cooling TWO six packs of beer in a small refrigerator” Your dorm room has a tem
ID: 884835 • Letter: #
Question
“Cooling TWO six packs of beer in a small refrigerator”
Your dorm room has a temperature of 72 oF, and you have two six packs of (nonalcoholic) beer you want to get ready to a drinking temperature of 61 oF for dinner.
Your fridge has a temperature of 44 oF, 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 Tlow , 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. to get to drinking temperature from room temperature takes a lowering by 11 degrees.
a) [1] Why is it that Tlow is NOT 50 oF (as one might naively assume)?
b) [3] Determine Tlow , and calculate the total time required to cool both six packs with this strategy.
[Hint: you should work out both the function Tcool (t), which describes the “cooling regimen”, as well as Twarm (t), which describes the “warming” regimen. Draw graphs of both of these functions , and describe carefully (geometrically) what is going on here….]
Explanation / Answer
dT = kt
where, dT = Tf-Ti
t = time (min)
For Temperature of 44 oF to 61 oF we have,
61-44 = k x 30
k = 0.57 oF/min
Now, going from 72 oF to 61 oF
72-61 = 0,57 x t
t = 19.30 min
So it would take 19.30 min for fridge to cool a six pack beer from 72 oF to 61 oF
a) Tlow is not 50 oF : Cooling takes longer time then heating. A 50 oF will bring the temperature too close to 61 oF the required temperature for drinking. The liquid would be at much higher temperature by the time one drinks in the time given for colling the second six pack beer.
b) Tlow = 44 oF. So it would take enough time for six pack to cool from 72 oF to 61 oF and warmng up six pack from 44 oF to 61 oF for drinking at same time.
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