A Physics Problem About Cooling Iced Tea
September 9, 2019 4:54 PM   Subscribe

I make iced tea in a 2-quart saucepan then pour it into a gallon jug half-filled with cold water. It recently occurred to me that I could have colder tea more quickly if I put the water in the freezer while the tea is steeping. So...

What quantity of water should I pour in the jug to most efficiently cool the hot tea? If I had time, I’d let the water freeze and pour the tea over the ice. But I do not have time. The more water I put in the jug, the less cool that water will be when I pull it out of the freezer. You see where I’m going with this. Assume that I’m putting the jug into the freezer at the same time I put the water on to boil, so the total time the jug is in the freezer is about 22 minutes. Assume the temperature of the tea after having steeped the requisite 15 minutes is around 170°F-180°F. Assume the temperature of my tap water is roughly 77°F at this time of year. I’m looking for an optimal solution that produces the coldest tea in the minimum time. Thank you, math and physics whizzes!
posted by BitterOldPunk to Food & Drink (36 answers total) 3 users marked this as a favorite
How about using pre-made ice? Put an appropriate quantity of ice cubes in the jug, add cool water if necessary to get the right volume, and pour the hot tea over. That way there's no time pressure (you can refill the ice cube tray and it'll freeze while you aren't around).
posted by Lexica at 5:12 PM on September 9, 2019 [1 favorite]

My ice trays create cubes that are too large to fit in the mouth of the tea jug, unfortunately. Plus that would use all our ice.
posted by BitterOldPunk at 5:13 PM on September 9, 2019

I think you should put all of the water you plan to add in the freezer, not just some of it. The temperature of the larger quantity might drop somewhat more slowly, depending on the container, but not enough to outweigh the effect of using a smaller volume of chilled water.
posted by jkent at 5:15 PM on September 9, 2019

Your freezer is going to only cool the water at its surface/perimeter so instead of putting a large quantity of water in one jug put it in many containers, ideally really wide-and-short or tall-and-narrow ones (ie with the greatest ratio of surface area to volume) and then pour it all back into the large jug when you add the tea in.
posted by any portmanteau in a storm at 5:18 PM on September 9, 2019 [7 favorites]

22 minutes isn’t enough to chill something more than a few degrees in the freezer.

This is recommended for chilling ice cream custard, but I don’t see why it wouldn’t work for iced tea: an ice bath. Fill the sink with a few inches of cold water, dump in a bunch of ice, then put your saucepan in the ice bath. The wider surface area and the water will chill the pan faster than the freezer, plus you won’t heat up your frozen food by putting a warm thing in there.

You’ll still use up ice, but you wouldn’t have to try putting it in the jug. If this is something you wind up doing frequently, maybe invest a couple bucks in another ice cube tray or two.
posted by Autumnheart at 5:20 PM on September 9, 2019 [4 favorites]

Prep cold-brew tea the night before.
posted by bunderful at 5:29 PM on September 9, 2019 [5 favorites]

2nding cold brew tea.
posted by gnutron at 5:38 PM on September 9, 2019 [1 favorite]

It's been a long time since I was any good at all at physics, but I'd say put the larger quantity of water in the freezer, for two reasons: More surface area, and temperature differential. You're trying to remove as much heat as possible from the final result, right? So expose as much of it as possible to the cold. And the temperature differential refers to the fact that the larger the differential between the cooler and the cooled, the faster the cooling happens, i.e., it's not linear, the rate of cooling slows down as the temperature of the cooled approaches that of the cooler.

All that said, putting a pitcher of water in the freezer for 22 minutes is probably not going to make a noticeable difference in your lack of instant gratification.
posted by bricoleur at 5:42 PM on September 9, 2019 [1 favorite]

I keep a container of the appropriate amount of water in the fridge at all times; it gets refilled immediately after being used so it's ready and cool at the moment I need it. I usually put some ice into the just-steeped tea to drop it some as well, but a handful or two, not a ton.
posted by Lyn Never at 5:45 PM on September 9, 2019 [4 favorites]

Get a BIG gel ice pack and a large plastic tupperware. Concentrate the boiled portion of tea. Place tupperware on ice pack, pour tea to a shallow level into tupperware. Shallow + Ice Pack under means more surface area reaching cold and cooler temps and less "core" that can hold onto heat. Water that is added should be already pre-refrigerated, you can just put it in the pitcher you plan to add tea to the night before. (Otherwise, yes cold brewer.)
posted by Crystalinne at 5:45 PM on September 9, 2019 [1 favorite]

I'm going to second Autumnheart's ice bath suggestion and raise it with: salt. By adding a whole bunch of salt to your ice bath (say, up to a 1:3 ratio of salt to ice and water by weight), you will be able to drop your temp below freezing. And the mass of the water touching the sides of the saucepan should be pretty effective at pulling out the heat.
posted by mhum at 5:47 PM on September 9, 2019

I should have added you can use a metal baking pan too (I just used a tupperware because I did that process with rice for rapid cooling storage in the fridge.)
posted by Crystalinne at 5:51 PM on September 9, 2019 [2 favorites]

For maximum surface area, how about the correct amount of water in a zip lock bag in the freezer. You can also put the jug in the freezer too to cool it off while your tea is steeping.

As others have suggested, if you can start with refrigerated water in the zip lock bag instead of tap water, it will be colder still.
posted by bruinfan at 5:51 PM on September 9, 2019

I feel like the answer here is going to be related to the potential energy thing that describes why frozen food burns more readily than thawed.
posted by rhizome at 5:59 PM on September 9, 2019 [1 favorite]

One of water's defining characteristics is its high heat capacity, so 22 minutes in the freezer isn't going to do much for it, unfortunately. Agree that cold crashing it (putting the water/hot tea in a salted ice bath) in a container with large surface area is going to be your best shot as it takes advantage of the latent heat/enthalpy of fusion of ice. But that is an enormous amount of pissing around (not to mention ice production) for what you want to achieve. It would be better to add ice directly to the water but it seems like that is not an option for you? Better yet, as others have suggested, would be chilling it overnight somehow.

There are definitely calculations to figure out how long a mass of water needs to go from one temp to another in a freezer etc. but you need to know stuff like the heat transfer coefficient of your freezer, the thermal conductivity of water (not hard to find to be fair) etc.
posted by BeeJiddy at 6:22 PM on September 9, 2019

The phase transition of ice to water also uses up more heat than just the change in its temperature. If you want to cool your iced tea quickly, add ice to the steeped pot of tea before combining it with the cold water in the jug.

But are you trying to optimize the amount of water in the jug as a thought experiment for the fun of it itself, or are you looking for a pragmatic solution to cool the tea as fast as possible?
posted by pykrete jungle at 6:56 PM on September 9, 2019

I'm bad at physics, but (according to the internet, I haven't tried this) you can chill a wine bottle in about 22 minutes if you wrap it in a wet dishtowel and throw it in the freezer. Could you do something similar to quickly chill the water you want to add to the tea?
posted by 23skidoo at 7:07 PM on September 9, 2019

On Mythbusters, they wrapped the container of liquid (a beer, I believe) in wet paper towels to maximize cooling. Pycrete jungle's suggestion to add ice to the hot tea is a good one.

I would put a plastic (it deals with thermal shock better) container of water in the freezer on its side, (maximize ice surface, minimize damage to container from expanding water) the night before. Then add tea to the container of ice, shake well (maximize temp distribution).
posted by theora55 at 7:12 PM on September 9, 2019

Do you have the fridge and counter/cabinet space to rethink your iced tea game? Because the soonest you can have your tea ready is immediately if you still have a little tea left over from the last batch.

If you can't do that, then I'd second putting all the non-tea water you'd need for a batch into a ziploc in the freezer, and then doing it again. Then you can just replace the water and always have a frozen one ready to go. If you're really hitting the tea hard, freeze three or four ziplocs. 120, 220, whatever it takes.
posted by GCU Sweet and Full of Grace at 7:25 PM on September 9, 2019

Are you trying to minimize the time to cool the entire jug of iced tea, or the first cup?

Pour the hot tea back and forth between two pots, letting it fall through the air in as long and narrow a stream as possible. You can get it pretty close to room temperature this way. Then pour half a cup of tea over an equal volume of ice in a cup, stir to equilibrate, and mix the rest of the tea separately.
posted by meaty shoe puppet at 7:46 PM on September 9, 2019 [3 favorites]

Ok, if the meta-question is how to make the coldest iced tea as quickly as possible with zero planning, here are some tips:

1) brew the tea in as little water as possible
2) cool the tea without diluting it. I would fill the sink with an inch of cool water, and place the hot saucepan into the sink right after brewing. Within 5 minutes, the tea will be much cooler and the water much warmer. Drain water and repeat.
3) use a large saucepan. It has more area to come in contact with the cool water in the sink.
4) once the tea is close to room temperature, THEN you add the chilled water/ice or whatever else (and as previously noted, 32F ice is WAY better than 32F water)
5) forget about salt. Compared to other tips, it does almost nothing for cooling. It will help you get something you would have cooled with ice to 32F down to 31 or 30, but nothing further. Salt is not cold. It does not make cold from nothing. It does not transfer heat (cold) more efficiently.
posted by Maxwell_Smart at 8:07 PM on September 9, 2019

If you're trying to cool something quickly - make sure that the container isn't prone to cracking/ exploding.

Practically, I'd put the requisite amount of diluent in a container of suitable max volume to house the concentrated hot tea - ensuring that it can deal with the rapid temperature differential.

Freeze the diluent water, pour hot concentrated tea into the vessel. Swirl until ice is dissolved.

For maximum speed, I'd buy a bunch of ice cube trays that make small enough ice cubes to fit into the vessel rather than having one large frozen mass. You can pre-fill the vessel days in advance; the ice might not remain loose, but will still maintain a lot more surface area:volume than a single mass and will quickly break up into discrete units.

You don't have to do the mixing in your final/ ultimate tea vessel; you can cool it in another, then transfer.

Another approach could be to bubble liquid nitrogen through your hot tea preparation.

A crazy pants approach would be to rig a coil system out of thin copper piping, rig that to the nozzle of a fire extinguisher, lower coil into container full of hot tea, then run the extinguisher propellent through the coil. Make sure to point the exhaust end somewhere safe. The rapidly expanding gasses will act as a refrigerant.

Personally, I make ice tea from straight brew; no dilution. I just need foresight/ patience to make it ahead of time (I do it in a french press with a slight excess of tea; successive rounds of steeping are for longer. For a quick tea fix, I fill half a mug from the first steep, and top it off with the last steep - the rest cools on the counter until cool enough to put into the fridge.

You can also make ice cubes from tea; adding those won't dilute your drink.
posted by porpoise at 8:48 PM on September 9, 2019 [3 favorites]

Seconding iced-tea ice cubes. Get another tray just for iced-tea ice cubes and then you can always have some on hand.
posted by limeonaire at 9:36 PM on September 9, 2019

What quantity of water should I pour in the jug to most efficiently cool the hot tea? If I had time, I’d let the water freeze and pour the tea over the ice. But I do not have time. The more water I put in the jug, the less cool that water will be when I pull it out of the freezer. You see where I’m going with this. Assume that I’m putting the jug into the freezer at the same time I put the water on to boil

OK, so taking all these constraints seriously instead of telling you about all the ways you could do this better, here's my analysis:

If you have two vessels, one with a mass of water M1 at temperature T1, and the other with mass M2 at temperature T2, and you mix them together, the temperature of the resulting mixture TM will be the weighted average of the initial temperatures: TM = (T1 * M1 + T2 * M2) / (M1 + M2).

So although you're quite right that the temperature of a large mass of water put into the freezer for any fixed amount of time will be higher than that of a smaller mass, that won't necessarily translate to a lesser final cooling effect because mass, as well as temperature, matters.

And in fact your freezer will pull more heat energy out of a large mass of water put inside it for any given amount of time than it will from a smaller mass, exactly because the larger mass's temperature won't drop so quickly. The rate of energy removal on cooling is proportional to temperature difference between the mass being cooled and the environment doing the cooling, so if that mass's temperature wants to stay high because it's big, the freezer will more easily keep finding heat to remove.

The temperature of the final mixture is going to depend on how the total amount of energy you add to the hot part compares to the total amount you remove from the cold part. To get the lowest final temperature, you want to add as little energy as possible and remove as much as possible. That means making your hot part as small as you possibly can, so as to get as much temperature rise out of it as possible given the minimal energy you add, while also exposing as much water to your freezer's interior as possible.

In short, your best strategy for achieving the coolest final product will be to minimize the mass of water you heat, and maximize the mass you cool, within the constraints imposed by desired total final volume and steeping effectiveness.
posted by flabdablet at 10:54 PM on September 9, 2019 [4 favorites]

and maximize the mass you cool

Do you mean "and maximize the mass with which to cool" the bollus?

But yes, you dug straight into the crux of the matter - what I struggle with is "does that make the best ice tea?"
posted by porpoise at 12:14 AM on September 10, 2019 [1 favorite]

I'd probably go the gelpack route. Keep the gelpack in the freezer. Then put the gelpack in the pitcher of water. The gelpack is a mass at a temperature below freezing that has a lower temperature of the melting / latent heat. This will keep the temperature difference between hot and cold greater than water ice would.

If you're crafty, you can make a form of gelpack by making a water + salt brine and putting it in a ziplock bag. Or water and alcohol.

On that front, from my experience, cans of beer freeze solid without bursting and make damn good ice cubes. They'll frost over and freeze moisture out of the air.

In the regular just cooling a jug of water in the freezer... The more surface area of the jug that you can get into contact with the cold bottom (maybe frost covered) bit of the freezer the better. The heat will transfer faster through that bit of solid connection than it will through the cold air. It's better if the jug is wide open at the top, if it's closed the whole top surface is basically under a blanket. You want to gently agitate the jug every few minutes or so because the cold water will settle on the bottom and the hot on the top. You want to keep them mixed. This again is to keep the temperature differential high to maximize the cooling rate.

Your optimum would be to have the flat space to put something like a roasting pan that held enough water. The thinner the better, preferably metal. This maximizes the bottom greater cooling surface and leaves the top open to the maximum amount for what cold air cooling will happen. Give it a stir every few minutes to even out the temperature layering.

This is just the same thin and shallow, maximize surface contact with cold, use ice cubes or even better non-ice cubes that are actually colder than ice cubes.
posted by zengargoyle at 12:22 AM on September 10, 2019 [1 favorite]

Do you mean "and maximize the mass with which to cool" the bollus?

No, I mean maximize the amount of water that's put in the jug in the freezer.

The procedure as described involves splitting the final volume of iced tea into a steeping portion and a chilling portion that both start as tap water, then putting the chilling portion in a jug in the freezer and the steeping portion on to boil, allowing seven minutes for boiling and fifteen for steeping, then mixing the two portions together.

As others have noted above, it's possible to do quite a lot to optimize the amount of chilling that the freezer delivers to the chilling portion in the restricted time available, but that's not what the question is about. The question is specifically about how much water to chill, not about the best way to chill it or about the best way to make iced tea.

Regardless of freezer effectiveness, the coldest result you'll get from this method happens when you allocate as little water as possible to the steeping portion and as much as possible to the chilling portion.

what I struggle with is "does that make the best ice tea?"

I'm sure there are people who would prefer the taste of a very concentrated steeping subsequently watered down. But that's not a physics problem amenable to analysis without experiment.

Also, the airplane will take off without issue and you should always switch doors.
posted by flabdablet at 2:35 AM on September 10, 2019 [3 favorites]

porpoise has it.

make sure that the container isn't prone to cracking/ exploding.
x10 - this is an easy way to get glass shards.

Of course unless you plan on drinking all the tea immediately, the fastest way to make a single cold cup is to overbrew the tea and add just an ounce or so to a cocktail shaker full of ice, then shake it until it isn't ice anymore.
posted by aspersioncast at 5:16 AM on September 10, 2019

Don't forget the Mpemba Effect -- a process in which hot water can freeze faster than cold water. (Previously)
posted by Kiwi at 5:37 AM on September 10, 2019

A friend of mine attempting to solve the same problem would pour his hot tea into multiple 13 × 9 aluminum baking pans, on top of wire cooling racks I think.
posted by XMLicious at 6:22 AM on September 10, 2019 [1 favorite]

Crush the ice. (Both to fit it in the tea pitcher and to transfer its cold faster.) Use it up. Make more ice.
posted by whuppy at 10:11 AM on September 10, 2019

I have a long-winded explanation of thermodynamics. flabdablet has the basic answer: the least amount of hot and the most amount of cold that you can manage and make good tea.

meaty shoe puppet and taking a minute to pour the hot back and forth between containers has a good point.

Temperature is roughly the average speed of molecules. Fast molecules are hot, slow molecules are cold.

The difference comes in the method of reducing the average speed of the molecules in you solution (the tea).

There are roughly three methods, which only two probably really count. Evaporation and Kinetic Energy Transfer (the third would be radiation, all photons and stuff, not going to really matter when making tea).

Evaporation and KE both work on the surface area principle in slightly different ways. Evaporation is when due to random collisions and transfers of KE some molecules manage to make the escape velocity of the system. This is evaporative cooling. This is when an occasional molecule of high KE manages to break free and float away. That means that the remaining bits not have a lower average KE and thus a lower temperature. This is why pouring the hot from one container to another will cool it down. You're both mixing up molecules and allowing the high KE ones to maybe escape and lower the temperature of the whole.

Evaporation is loss of high energy molecules from the system.

The other KE transfer bits are a high energy KE molecule bumping into some other molecule and transfering the KE. Like billiard balls or such. Give up that KE in the collision to some other molecule. This is the cold of the freezer. One way or another some fast moving molecule bumps into a slow moving one. The fast one gets slower, the slow one gets faster. It's the freezer that sucks up this extra energy.

For maximum KE transfer you want a fast molecule to either leave or hit the slowest possible molecule. Faster molecules also have a greater chance of interaction within a time. You want the greatest difference in temperature (average KE) at the boundary to maximize the KE transfer.

Pouring hot between pots will cool because the atmosphere is at a lower temperature than the hot and you're maximizing surface area for evaporation and mixing to allow even distribution of hot/cold molecules. This is like blowing on your food to cool it down.

In the freezer the evaporative cooling also happens, but to a lesser extent. The main thing is a high KE molecule bumping into a molecule of the container and transferring KE. And the container being more dense tends to transfer that KE around itself, and that the outside of that container is something that is already cold.

All of the answers so far basically boil down to best way to remove KE from your tea. The greater the surface and colder the thing you're dumping heat into, the faster your tea will be cold.

In the end, it is that TM = (T1 * M1 + T2 * M2) / (M1 + M2) equation and a bit of how much do you want to do to make those T's as low as possible in the time you have and what temperature difference and work you want to throw at the problem.
posted by zengargoyle at 11:52 AM on September 10, 2019 [1 favorite]

Every night, pop all the cubes out of the trays and refill the trays. In the morning, as the tea brews, crush the ice. Put ice into hot tea as soon as you turn off the heat. As in, put it in the brewing container, not your other day-to-day container.

You might also use some tap water and a heat exchanger to get the hot tea down to tap temperature, then ice it the rest of the way.
posted by notsnot at 12:25 PM on September 10, 2019 [1 favorite]

So you can probably write up a model of each possible method and grind on them and get an approximate answer that will be as good as all your estimated values (conductivity of plastic container, evaporation, efficiency of cooler in refrigerator, volume of water, etc. ad infinitum). And keep in mind that most of the time you get a complicated differential equation to solve, too, and there’s convection and ... stuff. Ugh.

Or you can try as many of the approaches as you like and record the temperatures. And get exact results.
posted by Gilgamesh's Chauffeur at 6:56 PM on September 10, 2019

Agreed. This is a job for empiricism. And lots and lots of (crushed) ice.
posted by whuppy at 5:29 AM on September 11, 2019

I could have colder tea more quickly if I put the water in the freezer while the tea is steeping

This, and a fair bit of ideas given above go against the grain of creating, well, tea. Sure you can make tea with less steeping water and/or cool it faster but that's not the tea you're currently drinking. So, well, those answers don't jive for me.

Your question as to when to add things and how much could be as complex as fairly intermediate level Differential Equations (a common example is mixing liquids of different, varying, temperatures) and physics (to include the ice surface area and specific heat content aspects) along with Heat Transfer questions to address your containers and any exterior influences via conduction, convection, and radiation.

So, yea, if you really want this answered, in an optimal fashion, you're looking at a fairly detailed analysis by a competent upperclassman in Mechanical, Chemical, or Aerospace Engineering if you ask me. A physicist could do it too I'm sure but the practical aspects are probably best found in the engineering field if you want to see how things are really interacting. I'm sorry but my Mech Engineering skills are just too rusty to do this problem justice.

But not of this matters if you aren't getting your tea steeped the way you want it to be in the first place!
posted by RolandOfEld at 11:39 AM on September 11, 2019 [1 favorite]

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