kulrblind

Here's one for you math/physics types. This is a question I've wondered about for a while now, but haven't had any luck figuring out the answer.

Problem: You've got 12 beer (cans, or bottles, you choose), and you want to put them in the 'fridge and get them out when they're cold. You don't want to leave them in any longer than you possibly have to, so you want to know:

"at which point are the beers (beer, for the noncanadians) the coldest they're going to get in the refrigerator?"

Some obvious items to be specified:
1. starting temp of beer in question
2. cans or bottles ( i hear cans chill faster )
3. type/size/power of refrigerator, and coolness setting
4. the rate of heat loss of beer (similar to that of water?)


So, assume what you will. Personally, i'd assume the beer at room temp (22c/72F), assume a standard fridge with other food in it already (not a big empty fridge), and a setting that will bring food to about 4C or 39F.

You can also assume one can/bottle if it makes it any easier (i.e. no co-chilling going on).

edit: It should be clear that this is not a "how to you get beer the coldest, fastest" question.

Let's hear your ideas, folks!

goddfather40

This may help, though some of the variables you mention cannot be represented. It is about Newton's Law of Cooling.

http://www.sosmath.com/diffeq/first/...on/newton.html

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Bigwahzoo

The main variable that you are missing in order to do this problem is the combined convection/radiation heat transfer coefficient between the can and the surrounding air. This is not going to be a constant instead the heat transfer coefficient will decrease as the temp of the can reaches the air temperature. So in other words the can will initially cool quickly and then the cooling rate will slow down as it approaches the air temp.

That said I think a reasonable number for the heat transfer coefficient would be about 10 w/m^2*C

Also the dimensions of the can are needed. I would estimate the dimensions of a can to be 12.5 cm tall with a diameter of 6 cm. I think with all of the above information the problem is now solvable.

Bigwahzoo

Here is my procedure for doing this problem and lets see what happens:

First we must find the area over which the can will be cooled. I will ignore the top and bottom areas since they will most likely be stacked so therefore natural convection will not occur.

A=pi*D*L=3.14*.06*.125 = .02355 m^2

We can now find the thermal resistances:
I am ignoring the thermal resistance of the can since it is very thin and made of aluminum so it will cool much faster than the beer.
R from convection = 1/h*A 1/ [10 w/m^2*C * .02355 m^2] = 4.246 C/W

We can now calculate the steady rate of heat transfer to the beer
Q = T2 –T1 / R = 22-4 /4.246 = 4.239 W or J/s

Now it is time for some more assumptions. I am going to assume that beer has the same thermal properties as water.

Density = 998kg / m^3
Specific Heat = 4182 J/kg * C


Density * Volume gives a mass of .3527 Kg
Finally the amount of energy dissipated by cooling the can 18 C will be 26549 J


26549/ 4.239 = 6263 Seconds = 104 minutes = 1.74 Hours



My final answer for the cooling of the beer cans is 1.74 hours. Does that sound like a reasonable answer?

kulrblind

Bigwahzoo: that sounds entirely reasonable. Originally, I thought people could simplify it as much as they needed/wished to. When I first thought of the problem, I considered only the starting and ending temperature of the beer (aka water, it's major component) and the rate of heat loss (4.2kJ/kg*C).. it was at that point that I knew my liberal arts education was being stretched to its limits.

So, in short... I like it! 105 minutes seems like it could be a feasible answer.

Everyone agree?

edit: I think there should be some experiments this Friday to check your math, Bigwahzoo.

Redlemon

1. Get a room-temperature can of beer

2. Open beer

3. Stick a Polder remote thermometer into the beer, and seal the hole with Silly Putty or similar.

4. Put beer back in fridge, stick Polder display to outside of fridge, close door.

5. Start timer on Polder, and watch temperature fall.

/Alton Brown fan

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orphen

Does it matter? lol

goddfather40

Should there be a coefficient of drunkenness too? I tell you what when someone has to make a beer run and you've already pounded some back, the ideal temperature gets higher and higher.

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Tophat665

Bigwazoo, I'm too long out of E-School to remeber how this would effect the thermal properties, if at all, but an American light lager, such as a Budweiser, is going to have a specific gravity between 1.010 and 1.005.

1 hour and 45 minutes seems about right though. I put beer in the beer keeper to get it cold, though (my wife calls it the crisper).

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kulrblind

I guess it depends how badly you want the first (or first two) beer


We put it in the freezer and set the beer-timer (i.e. oven timer) for 35-40 minutes. That way, unless you're completely hammered, you don't get beercicles in the freezer.

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asudevil83

COLD BEER

well, if your doing it this way, then it'll take you about 15 minutes to cool 12 beers, as this one does 4 beer in 5 min....but if not then my GUESS would be 1.574 hours.

lonster

I find it easier to buy cold beer from the shop. If in doubt get a lift with a friend so you can start on the cold ones on the way home, then put six in the freezer then the rest at the back of the fridge.

Bossnass

I would just like to go on the record to clarify that 'beers' is not an acceptable term. At least with the company I keep, as a Canadian, drinking Canadian beer. We long ago determined that 'beers' was slang that orginiated with the strange folk from Saskatchewan and Manitoba that drink Pilsner.

The working theory is that perhaps, if you are hovering near that 'white trash' line and you are drinking large-ish quantities (>9 each) of lower quality beer, 'beers' is the right term for you.

No offense, of course, 'beers' is one of my pet peeves.

Tophat665

You're at least half wrong - Whether or not it is the correct plural for multiple containers of beer, Beers are different kinds of beer - stouts and ales and pilsners and Oud Bruins are beers.

However, what is the proper plural of beer when you have mre than one unit thereof? You can't have 12 beer, or is that acceptable Canadian usage? I think you may have beer and deer confused. Let me clear it up: you drink the one without antlers. Either that or there are foxen in the henhice.

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Bossnass

Oh, I'm pretty sure that 'beers' is technically the correct usage.
I agree, stouts and ales and pilsners and Oud Bruins are beers, but in my personal jarogn, I would phrase it as 'differnt types of beer.

Tonight I have consumed four beer while my girlfriend has drunk three glasses of wine. All fo ur of my beer were of the same type, although there are two types of beer in my fridge.

Semantically correct? Doesn't really bother me. It would seem that 'beers' is a more effcient and accepted term. But my girlfriend did not have four wines. Moose aren't meese, and indeed several deer are several deer. And I will stand by my refusal to use the term beers, in particular when I have had a few beer. Languages and dialects evolve (devolve?), and I think 'beers' is long overdue for extinction.

kulrblind

Having been born in Manitoba, and spent my early drinking years in Alberta, I can say that I grew up sayign "beers", though not influenced by anyone from Manitoba. It's more goddamn fun to say beers.

Example:
What did you do last night?
I went out with Friend X for some beers.

If I'd claimed I went out with Friend X for beer, one might think we went to pick up a case. In this case, "beer" is akin to "drink", and becomes pluralized (pluralised?) when consumed in copious quantities.

Bah.. whatever.

Jephree

Till it's cold

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mrsandman

Same, except microwave timer and 45-50 minutes.

Icy cold and delicious!

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madhatter

Ahhh... I love a it when a tranport phenomena problem pops up.

However, I would want to drink a cold beer while I am working the problem. I can cool a beer(12 oz. aluminum can) from room temperature to 40 degrees celsius in 30 second or less. This just happens to be a popular problem in transport phenomena classes.

The trick is to put the beer in a container full of ice with some water. Now you spin the beer about its vertical axis in the ice. (spinning on the vertical access will prevent the beer from exploding when you open it) Poof! 30 second cold beer. Try it at a party sometime.

For the chemists reading this, you can add salt to the ice to lower the temperature of the ice bath to futher speed up the beer cooling process.

kulrblind

Okay, guys and girls. Who's gonna go out on a limb and host the first "beer cooling" party? It'll be a BYOT (bring your own theory) event.
Please bring your favourite micro-brewed beer, too.

Bigt6909

I'm a big fan of putting in the fridge for an hour and then drinking it... or where i live, place the beer outside in a 10 inch snowbank and wait about 15 min and it's cold as ever

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