Monday, February 06, 2006

Ideal amount of ice in a coke

My little brother spent too much time in Europe, and now drinks his cokes without ice--as long as it's not too warm to start with.

For the rest of us, uncorrupted, how much ice should there be in a cup of coke? Too much, and you're wasting coke space. Too little, and the ice is completely gone by the time you've finished, and your coke warms up. (Horrors!)

The solution involves balancing the heat loss with the melting of the ice, and making lots of assumptions. I've assumed a perfectly-insulating right circular cylinder open at one end, so the area of heat exchange is constant, I've used a simple model of what the heat exchange area between the melting ice and the coke is, the ice is assumed to exchange heat only with the coke, equilibration of liquid temperature is taken to be instantaneous, and also I've neglected a lot of small details about the final minutes, when a lot of these approximations break down. (For example, the ice starts to exchange heat with the air, too.) I've decided that I can't even tolerate a fraction of a Kelvin temperature rise in my coke, so when the last ice disappears, so should the coke.

Plugging in some simple numbers (for example, I drink my 16 oz. coke at a constant linear rate over 20 min.), I get about 10% ice as ideal.

Experiments will be conducted tomorrow. Conjectures and refutations!


Blogger Bob Hemm said...

Sean, I think your decision to assume that the right-circular cylinder is perfectly insulating will likely have disastrous consequences for the efficacy of your computations. Especially when one takes into account the empirical observation that by minute 7 or so, a properly chilled container of coke begins to form condensation on its external surface (leading to the dreaded ring-shaped water stains on wooded surfaces), it seems unacceptable to ignore the extensive exchange of heat that is being conducted through the wall of the container.

Furthermore, when using a lid (assuming the lid to be at least somewhat effective in preventing free circulation of air), you must remember that as you drain the cup, the volume of air with which the open surface of the container will be exchanging heat increases, and that the air being imported will warmer than the air inside the cup. This will require a nesting of variables and thus frustrate the normal formulas that are generally used in lieu of the calculus from which they are derived.

I know these are details that you meant to factor out for the sake of simplicity, but I believe they will have substantial effects on the optimal level of ice. This, when these factors are included, I would estimate the necessary percentage of ice to be closer to 25-30%. Plus I like my Coke ever so slightly watered down.

1:33 AM  

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