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## Two beers

Right!

I buy two bottles of cold beer at the bar, they're both taken out of the fridge and opened at the same time. I'm holding one in each hand. I can only down a few before my stomach gets full and the following dilemma sets in:

Asssuming I drink steadily, and assuming I prefer cold beer to warm beer, is it better to drink all of one bottle before starting the other, or to take alternate sips from each?

Ponder...! (and if you feel like it, think of fizziness too, to make it interesting).

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 Recognitions: Gold Member Science Advisor Staff Emeritus Why would you open them both ? Anyways, I'll give this a shot, in a little while. I'm hungry now...
 Recognitions: Gold Member I would probably say that you would be better off drinking all of one bottle then the other. This is because there is more liquid in the untouched bottle so will remain cooler for longer as it will take more time for your hand to warm it up. If you drank the two alternating, then as the amount of liquid decreases, they will both get warmer more quickly. This is talking from a little experience.... maybe I should test this theory.

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## Two beers

I'm not entirely convinced about jimmyp's argument.

There are so many variables here...I'm going to assume you hold the bottle by the neck and introduce very little heat into it, so that the rate of heating unheld is nearly the same as the rate of heating when held. So the beer is mostly being warmed by the ambient air. I'm also going to neglect second order effects like surface area and outgassing rates.

The temperature differential is small enough that we can use Newton's cooling law :

dT/dt = Km(t)[T - T0], where

T = beer temperature,
T0 = air temperature
t = time
m = mass of beer in bottle
K = some proportionality constant

Now, if beer is being drunk out of only one bottle for a given period, for that bottle we have

m(t) = m0[1 - t/B] and for the other bottle (which is waiting, untouched) we have

m(t) = m0, during this same period. After the first bottle is drunk, the second bottle's mass behaves like the first for the subsequent period.

If beer is being drunk from both bottles, their mass behaviors are identical, and are given by

m(t) = m0[1 - t/2B]

In the above expressions,
m0 = initial mass of beer, and
B = time taken to drink one bottle of beer.

Now we have the necessary framework. We simply plug in for m(t) in the different scenarios and get separable differential equations. These can be solved to find T(t) for each of the bottles in each of the cases (quite easily).

(For instance, when drinking one-at-a-time, for the beer that is drunk first :

T(t) = T0 - (T0 - Ti)*exp[-K*m0*t(1 - t/2B)]

I've run out of patience, and decided not to calculate the others, but they can be done just as easily.)

Now, the last step is to relate the extent of dislike to the temperatures. Let's say the extent of dislike is a linear function of the temperature. Then the objective is to determine which of the 2 cases gives the lower time integrated temperature (integrated over the times that each beer is being consumed).

Do all of these things and plug in realistic numbers to get a complete (well ???) solution.

I'm gonna go get me a beer,

Ciao !

 The algorithm :- 1>Buy two bottles 2>Drink them one after another 3>Buy two more 4>Drink them alternately 5> if no decision can be made repeat steps 1 to 4 till decision can be made 6>stop ofcourse this is an infinite loop -- AI
 Recognitions: Gold Member Science Advisor Staff Emeritus Running algorithm : 1> Bought two bottles (and opened them both : "pop, pop") 2> Drank one bottle (mmm...that was good...I love beer ); drank second bottle (mmm...a little warm ...I love bold ceer...I mean cold beer ! ) 3> Bought two more beers (bartender looks happy...the chicks look hot...opened both beers : "pop, ...'cmon ...ppppppop") 4> Start drinking from them alternately (hmmm...this beer's great...wow, so's this one..sheersh everybody ...hic...burp) continue drinking (is this beer getting warm ??...who cares ! ) last gulps (this tastes like horse p!...damn, so does this ) 5> Decision time (now which did I like better...mmm...the chicks were better on the second round...don't remember the first time too well...burp...I need another beer or two) go to step 1 (and increment number of p's before each 'pop' by 5) 6> Bartender drags your senseless body out and dumps it on the sidewalk where you enjoy a blissful slumber.
 We need to get identical twins with identical sensitivity to temperature to try this experiment. It may be that doctors have done this experiment before, but then got fired for unethical practice.

 Quote by brewnog I buy two bottles of cold beer at the bar.
one question first,

are you above the legal age for drinking in your area?

 Recognitions: Gold Member Science Advisor Well I'm 20 now (drinking age 18), but was 15 when we started going to this place, where it's so busy that it makes sense to buy in bulk at the bar. It's only 60p a bottle, so the algorithm suggested by TenaliRaman is almost always used, and after around step 4 nobody cares how cold they are anyway.
 Recognitions: Gold Member Science Advisor Staff Emeritus Thanks to Gokul for that valiant effort in gathering the preliminary data for this experiment. Clearly, we now see there is an order effect, so we need to design the experiment to cancel that out. A cross-over design seems the only way to handle this. Here's the experimental plan. Gather several drinking buddies, erm, subjects. Buy each of them 2 beers. Half of them should drink alternately from both bottles, and the other half should drink the bottles sequentially. Have them rate the two bottles of beer. Now, buy them 2 more beers. The half that drank alternately now should drink sequentially, and vice versa. Have them rate the two bottles again. Oh, drat, there still may be an inter-observer variation...this is the difficulty when relying on subjective measures. Better incorporate a repeated measures component just to be certain. Day 2, take the same group of drinking budd...sorry...subjects...and again buy them two beers. The group that started out with alternating bottles on Day 1 should start out sequentially this time, and those that started out sequentially last time should drink alternatingly this time. Otherwise, conduct the experiment for Day 2 the same as for Day 1. Expected results: A group of dedicated drinking buddies for life!

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 Quote by Gokul43201 I'm not entirely convinced about jimmyp's argument. There are so many variables here...I'm going to assume you hold the bottle by the neck and introduce very little heat into it, so that the rate of heating unheld is nearly the same as the rate of heating when held. So the beer is mostly being warmed by the ambient air. I'm also going to neglect second order effects like surface area and outgassing rates. The temperature differential is small enough that we can use Newton's cooling law : dT/dt = Km(t)[T - T0], where T = beer temperature, T0 = air temperature t = time m = mass of beer in bottle K = some proportionality constant Now, if beer is being drunk out of only one bottle for a given period, for that bottle we have m(t) = m0[1 - t/B] and for the other bottle (which is waiting, untouched) we have m(t) = m0, during this same period. After the first bottle is drunk, the second bottle's mass behaves like the first for the subsequent period. If beer is being drunk from both bottles, their mass behaviors are identical, and are given by m(t) = m0[1 - t/2B] In the above expressions, m0 = initial mass of beer, and B = time taken to drink one bottle of beer. Now we have the necessary framework. We simply plug in for m(t) in the different scenarios and get separable differential equations. These can be solved to find T(t) for each of the bottles in each of the cases (quite easily). (For instance, when drinking one-at-a-time, for the beer that is drunk first : T(t) = T0 - (T0 - Ti)*exp[-K*m0*t(1 - t/2B)] I've run out of patience, and decided not to calculate the others, but they can be done just as easily.) Now, the last step is to relate the extent of dislike to the temperatures. Let's say the extent of dislike is a linear function of the temperature. Then the objective is to determine which of the 2 cases gives the lower time integrated temperature (integrated over the times that each beer is being consumed). Do all of these things and plug in realistic numbers to get a complete (well ???) solution. I'm gonna go get me a beer, Ciao !

Oh yeah, I see, bring maths into this...

 Drink them at teh same time or have one hand in a fridge while you drink the other beer

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 Quote by jimmy p Oh yeah, I see, bring maths into this...
Don't mix well, eh ?

 Just recently I had ordered three beers which the bar tender opened and I drank all three over the period of 45 minutes. The third one felt just as cold as the first. I'd say I got to the third one after about 30 minutes... But, my point is, if the beer's in a bottle, and it's not the Sahara desert, your beer will stay cold a long time. So do what you like, but remember to keep drinking and keep making love to gorgeous middle-aged women. This is key!
 You also have to take into effect the consistency of the beer itself, A light beer i.e. Miller Light versus a thicker beer such as Guiness. The beers would have slightly different cooling effects because of the way they retain temperature. Also, you have take into effect the material the bottle is made out of and wether or not it was sitting on the counter when he wasn't drinking it. If the counter was metal and the ambient air was cool, it would cool differently than if the counter was wood. Also, are you a cold hearted bastard? Then your hands would be ice cold.

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