How Much Ice Do You Need For Your Drinks?

The Navy has an ice command, and I assume its members always bring ice to parties simply because the partygoers assume they will, and would be angry if they didn’t. Self-fulfillment. Aka a feedback loop.

Anyway, Rhett does the calculation of how much ice it takes to cool a drink down if you own an ideal cooler, and find that a 12 oz (355ml) can of water is cooled to 0ºC with just 100g of ice. Being a responsible physicist, he does a reasonability check:

[I]f I have a 6 pack of drinks, I would need 600 grams of ice, a 12 pack would need 1.2 kg of ice. Yes, that seems small. Remember this is the ideal case.

I like to look at this another way. This tidbit stems from a NOVA show on getting things cold (Absolute Zero, which aired just before I started blogging — which explains why I can’t find a blog post on it) they explained how people used to ship ice to the tropics and made a big profit on it, and this was made possible because the amount of energy to melt a certain mass of ice was equal to the energy to subsequently heat it up to ~80ºC. We can check this by dividing the latent heat of fusion (334 J/g) by the specific heat (4.18 J/g-K) and we get that answer. Which means that freezing/melting ice involves a LOT of energy compared to changing its temperature by a few degrees. If 80ºC requires an equal mass, cooling by a quarter of that should require a quarter of the ice, plus a little for cooling the aluminum. Which gives you the 100g/can ideal case. (I guess the true “ideal case” would then be 2.4 kg of ice)