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

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Ion4

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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.
 
Ion4 said:
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.
Click to expand...

Which law of heat-transfer are you planning to use?

Please enlighten us with your thoughts/work, so that we may know where to begin to help you.
 
Correct.

Now please state the law and start using it...
 
61 degrees is drinking temperature for beer?. Where is this considered drinking temperature for beer?. Goofyland.

Anyway,
Try starting with \(\displaystyle \frac{dT}{dt}=k(T-44)\)

The beer is taken from 72 degrees into 44 degrees and allowed to cool to 61 degrees.

This takes 1/2 an hour. Thus, an initial condition is T(1/2)=61 and T(0)=72

Use this to find C and k.

Next, the beer has to be kept in this fridge until it cools to \(\displaystyle T_{low}\). \(\displaystyle T_{low}\) is the temperature to find so that when it is set out at 72 degrees, it takes 1/2 an hour to warm up to 61 degrees.
 
galactus said:
61 degrees is drinking temperature for beer?. Where is this considered drinking temperature for beer?. Goofyland.

I suppose that is Eng-land.

Anyway,
Try starting with \(\displaystyle \frac{dT}{dt}=k(T-44)\)

The beer is taken from 72 degrees into 44 degrees and allowed to cool to 61 degrees.

This takes 1/2 an hour. Thus, an initial condition is T(1/2)=61 and T(0)=72

Use this to find C and k.

Next, the beer has to be kept in this fridge until it cools to \(\displaystyle T_{low}\). \(\displaystyle T_{low}\) is the temperature to find so that when it is set out at 72 degrees, it takes 1/2 an hour to warm up to 61 degrees.
Click to expand...

.
 
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