Pontooning this weekend we had two different twelve ounce beer cans. Which stays cold the longest?
Disregard (or not) the slight difference in specific gravity.
Assuming they’re in the same environment, and that that environment is at warmer than appropriate beer temperatures? The short one. The rate of change of an object’s temperature is the product of four factors: The difference between its temperature and the environment, a factor for how good the insulation is, a factor depending on the specific heat, and the surface area. The first three factors are the same for both, so the one with higher surface area will heat up faster. For any given volume, the lowest surface area is a sphere, so the can that’s closer to sphere-shaped will have less surface area.
Yeah! That was what I thought. Several boaters disagreed, for a variety of spurious reasons.
The tall narrow one will stay cold longer the white iPA will warm quickly in my stomach.
Assuming volumes are constant
pi x r[sub]1[/sub][sup]2[/sup] x h[sub]1[/sub] = pi x r[sub]2[/sub][sup]2[/sup] x h[sub]2[/sub]
Surface area:
2 x pi x r[sub]1[/sub] x h[sub]1[/sub] + 2 pi x r[sub]1[/sub][sup]2[/sup] vs 2 x pi x r[sub]2[/sub] x h[sub]2[/sub] + 2 pi x r[sub]2[/sub][sup]2[/sup]
Let’s simplify
r[sub]1[/sub][sup]2[/sup] x h[sub]1[/sub] = r[sub]2[/sub][sup]2[/sup] x h[sub]2[/sub]
and
r[sub]1[/sub] x h[sub]1[/sub] + r[sub]1[/sub][sup]2[/sup] vs r[sub]2[/sub] x h[sub]2[/sub] + r[sub]2[/sub][sup]2[/sup]
so r[sub]1[/sub][sup]2[/sup] = r[sub]2[/sub][sup]2[/sup] x h[sub]2[/sub]/h[sub]1[/sub]
the first part of the surface area comparison is now
sqrt(r[sub]2[/sub][sup]2[/sup] x h[sub]2[/sub]/h[sub]1[/sub]) x h[sub]1[/sub] + r[sub]2[/sub][sup]2[/sup] x h[sub]2[/sub]/h[sub]1[/sub] = r[sub]2[/sub] x sqrt(h[sub]1[/sub]h[sub]2[/sub]) + r[sub]2[/sub][sup]2[/sup] x h[sub]2[/sub]/h[sub]1[/sub]
Why have we done all of this? Because if two masses are the same, the one with the larger surface area will heat up faster. So when is
r[sub]2[/sub] x sqrt(h[sub]1[/sub]h[sub]2[/sub]) + r[sub]2[/sub][sup]2[/sup] x h[sub]2[/sub]/h[sub]1[/sub] > r[sub]2[/sub] x h[sub]2[/sub] + r[sub]2[/sub][sup]2[/sup]?
Dividing by r[sub]2[/sub]
sqrt(h[sub]1[/sub]h[sub]2[/sub]) + r[sub]2[/sub] x h[sub]2[/sub]/h[sub]1[/sub] > h[sub]2[/sub] + r[sub]2[/sub]
While I agree with Chronos from a thermodynamics standpoint, I have to disagree that the other three factors are the same. I drink the real beer (even an IPA), rapidly warming it up to 98 F in my stomach. The Bud Light Lime gets chucked overboard and stays cool in the lake. 
I agree with you and Chronos. It’s pretty basic physics. I’m sure the other boaters mean well, but they’re wrong.
running coach and dracoi have added new conditions which change the nature of the problem. They are obviously not to be trusted near my beer cooler.
And of course who can argue with Saint Cad’s assessment? For that matter, who can understand Saint Cad’s assessment?
The only question was which stays colder. No other conditions were specified. 
That was my eyeball analysis as well but St Cad did the real analysis. FWIW the taller can should have a greater air convection cooling/heating effect which adds to its heat gain setting in free air.
Note that I did specify “assuming that they’re in the same environment”.
As a licensed beer-snob from Oregon, I can state that the beer on the left, tall and narrow, should be drank first, the less you taste it the better. The one on the right, short and squat, should be allowed to warm a little, best drank at around 45º - 55ºF. That depends on the quality of the IPA. It’s brewed in Vermont so and I’m not sure they know how. Perhaps running coach has the right of it drinking that dog first and dumping the Butt-Wipe for the fishes.
The only beer that’s helped by lime is Corona; hell, motor oil would help the taste of Corona …
Chronos, I’m agreeing with you. You have radiation, conduction, and convection. All point to the fat can staying cold longer.
I don’t like many wheat beers, but Fresh Slice is an exceptional beer for boating. Anyone know about the “In A Pinch?” on the can?
That was dracoi.
I would not sully my hands touching that stuff.
If circumstances simply require drinking the inferior beer (instead of chucking it overboard) always drink the good stuff first. That way the taste of the good stuff is unsullied. With luck you can anaesthetize your taste buds sufficiently to not notice the flavor (or lack thereof) in the swill. Admittedly this technique works better if you have several of each, not just one of each.
And under these experimental conditions the tall skinny one stays cooler longer unless it’s sitting in the direct sunlight. In the direct sun it *might *warm up faster than the one already in your gut.
Note that even the Bible endorses this technique.
How much of a factor would conduction through the base be?
That’s often a good strategy. But given that they’re starting ice- cold and warming up, and you’re looking at one of each, I agree with watchwolf: guzzle (or even shotgun, if that’s your thing) the piss-beer while it’s still too cold to taste. Then slowly savor the good stuff as it warms up.
Depends on the composition (primarily heat capacity) and temperature of what it’s sitting on.
If you ever get a chance, put a room temperature can (beer or soda) on a block of ice. It’s fascinating to see 1) how quickly it sinks into the ice as it melts and 2) how you get an absolutely perfect impression of the can’s bottom in the ice. The experiment works well in snow too, but we expect snow to compact whereas watching the can sink into ice makes it clear that you’re only seeing the result of melting ice.
Of course, that’s about a maximum conduction scenario. Certainly a faster heat transfer than the beer sitting on a table or being held in the air.