# Cooling a cup of coffee with help of a spoon

During the breakfast with my colleagues, a question popped into my head:

What is the fastest method to cool a cup of coffee, if your only available instrument is a spoon?

A qualitative answer would be nice, but if we could find a mathematical model or even better make the experiment (we don't have the means here :-s) for this it would be great! :-D

So far, the options that we have considered are (any other creative methods are also welcome):

## Stir the coffee with the spoon

Pros:

• The whirlpool has greater surface than the flat coffee, so it is better for heat exchange with the air.
• Due to the difference of speed between the liquid and the surrounding air, the Bernoulli effect should lower the pressure and that would cool it too to keep the atmospheric pressure constant.

Cons:

• Joule effect should heat the coffee.

## Leave the spoon inside the cup

As the metal is a good heat conductor (and we are not talking about a wooden spoon!), and there is some part inside the liquid and other outside, it should help with the heat transfer, right?

A side question about this is what is better, to put it like normal or reversed, with the handle inside the cup? (I think it is better reversed, as there is more surface in contact with the air, as in the CPU heat sinks).

## Insert and remove the spoon repeatedly

(I personally think it doesn't pay off the difference between keeping it always inside, as as it gets cooler, the lesser the temperature gradient and the worse for the heat transfer).

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As a side note: the Joule effect will be completely, totally, absolutely negligible. It will be effectively zero. –  kharybdis Feb 16 '11 at 20:55
A similar question on cooking.SE. –  Qmechanic Jun 17 '13 at 8:41

I did the experiment. (dipping wins)

• H2O ice bath
• canning jar
• thermometer
• pot of boiling water
• stop watch

There were four trials, each lasting 10 minutes. Boiling water was poured into the canning jar, and the spoon was taken from the ice bath and placed into the jar. A temperature reading was taken once a minute. After each trial the water was poured back into the boiling pot and the spoon was placed back into the ice bath.

 Method:                  Final Temp.
1. No Spoon              151 F
2. Spoon in, no motion   149 F
3. Spoon stirring        147 F
4. Spoon dipping         143 F


Temperature Readings have an error $\pm$ 1 F,

 Red line, no Spoon
Green line, Spoon in, no motion
Aqua line, Stirring
Blue line, Dipping


Data:

No Spoon

Min Temp (F)
0   182
1   180
2   174
3   171
4   168
5   164
6   161
7   158
8   155
9   153
10  151

Spoon, no stir, no dip

Min Temp (F)
0   180
1   175
2   172
3   168
4   165
5   162
6   160
7   156
8   153
9   151
10  149

Stirring

Min Temp (F)
0   180
1   175
2   171
3   167
4   164
5   161
6   158
7   155
8   152
9   150
10  147

Dipping

Min Temp (F)
0   180
1   177
2   173
3   168
4   164
5   160
6   156
7   152
8   149
9   146
10  143

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Haha, thanks for this. Perhaps you could do the blowing experiment as well –  Columbia Feb 20 '11 at 2:44
I accepted this answer to be fair with my own words, as I said that the experiment would be best :-) –  fortran Feb 21 '11 at 8:16
Yes, on the first run I poured boiling water into the jar, let it come up to temperature, then poured the water back into the pot, let it come back to a boil, then started. As the data shows, the three trials with the spoon had initial temperature of 180F, I didn't fudge it :) The ice cold spoon knocked two degrees off the water before the thermometer came up to temperature. –  drhodes Feb 22 '11 at 5:43
Argh. No SI units :P –  BandGap Apr 26 '13 at 14:24
Note: You've been mentioned in the latest what-if xkcd. –  Manishearth Nov 12 '13 at 12:22

Stirring will win, hands down, every time.

This is why physicists need to talk to chemists once in a while.

As Georg correctly remarks, the latent heat of vaporization of water is enormous - but he's wrong about waving the spoon; stirring is the champion here.

Why? Temperature is really the average kinetic energy of the molecules in the bulk substance, which actually have a variety of individual kinetic energies. Stirring is the fastest way to bring high-kinetic-energy outlier water molecules to the surface, where they will overcome the electrostatic bonding mechanisms that keep them in the liquid phase, and jump into the air (vapor phase). This rapid decrease in the high-energy outliers is the quickest way to cool a hot aqueous solution.

It's similar to stirring iced tea. If you just plop ice cubes into a glass of warm tea, it will take quite a while for the warmer tea to cool; if you stir it vigorously, it will reach a cold equilibrium within seconds; the latent heat of fusion absorbed by the ice melting is similarly enormous.

This kind of thing has a lot of applications to laboratory and industrial chemical processes, surface catalysis, petroleum cracking, yadda yadda. You learn a lot about it in third-year university physical chemistry, and really must master it before or during graduate work as a chemist.

If you want an even faster way to cool a cup of coffee, here's a tip from my Granddad Parker: forget the spoon and saucer your coffee. In other words, pour the top part of it from the cup into a saucer, and then back again a few times. The large and constantly changing surface area during this process will cause extremely rapid evaporation of those high-energy outliers, much faster than stirring. Saucering was very common up through the Great Depression, which is one of the reasons older coffee sets always included saucers. You also get deep-ish saucers at many restaurants as a holdover from this practice, although I doubt many people do it any more.

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This is actually a trick i've seen elderly Chinese people use. Tea too hot? pour it back and forth between two cups. –  knowtheory Feb 17 '11 at 5:26
Yep, the two-cup trick is really good for cooling, and also for making carbonated soft drinks go flat (lose their carbonation) - flat ginger ale is useful for calming nausea. If you have a couple of really big (e.g. 2-3x liquid volume) glasses and pour rapidly back and forth to generate lots of bubbles, you can make 12 oz of ginger ale go almost as flat as tap water in 20-40 seconds. That would take several minutes of stirring, or hours if just left to sit. –  Bob Murphy Feb 17 '11 at 5:38
Incidentally, latent heat of vaporization is how the ancient Egyptians used to make ice for their cocktails while building the Pyramids. They'd set out pans of water overnight, and between the low humidity and breezes, some of the water would evaporate, sucking enough kilojoules out of the remaining water to cause part of it to freeze even though the ambient temperature was definitely not below freezing. It's the same principle as the swamp coolers some folks used for air conditioning when I lived in Texas. –  Bob Murphy Feb 17 '11 at 5:49
Good explanation, but dunking the spoon will win over stirring. Dunking will not only introduce air into the liquid, absorbing heat and whisking it away as soon as the air bubbles back to the surface, but it will also stir the coffee at the same time. In other words, dunking = stirring + air bubbles. –  Michael Feb 17 '11 at 7:48
@Bob, With respect to Egyptians: You forget the temperature of the clear night sky and radiation. Temperatures below zero are common in desert areas, even without pans of water (unstirred!) –  Georg Feb 17 '11 at 11:38

How to cool a cup of coffee with the help of a spoon. Hmm...

• Empty the cup using the spoon, discarding the hot coffee.
• Strike the cup with the spoon, shattering it and forcing it to release the hot coffee.
• Drink the coffee with the spoon.
• Use the spoon to carve a cup-shaped hole in a large block of ice, put the cup in there.
• Put the spoon in the coffee, attach it to the cold side of a small thermoelectric-effect element.
• Use the spoon to catapult the cup 200km up. Measure temperature before it comes back down.
• Use the spoon to add a spoonful of liquid helium to the coffee. Slowly.

I'm sure you can come up with some good ones (edit away!)

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""Use the spoon to add a spoonful of liquid helium to the coffee. Slowly."" Funny, this is the most ineffective and the most expensive method. :=) –  Georg Feb 16 '11 at 18:49
@Chipaca--life's not fair:) you get +1 for basically stealing a variant of my answer and I get a -1 for a more subtle answer :) I am sure I could come up with a very large list of equally valuable answers... –  Gordon Feb 16 '11 at 18:55
@Gordon all lists of answers that are not the ones you wanted automatically tie in to the joke about the \$FAMOUS_PHYSICIST who answered how to measure the hight of the building using a barometer... whereas just a single not-the-answer-you-wanted makes it look like you didn't understand the question. –  Chipaca Feb 16 '11 at 18:59
@Chipaca --nah, the list is just too much of a good thing--gilding the lily. Besides, how do you measure the "hight"? –  Gordon Feb 16 '11 at 21:00
don't forget you'd need to be in an intensely-insulated room to "pour" liquid helium: it won't stay liquid in a normal atmosphere.. liquid nitrogen, on the other hand, will stay liquid in a normal atmosphere for a while - much better thermal inertia –  warren Feb 17 '11 at 13:01

Take the spoon. Use it to push the coffee over. It will spill out into a large puddle. This has maximal surface area and will cool VERY quickly.

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Just hope the cleaners are doing their job. –  Nick Bedford Feb 17 '11 at 4:47
@NickBedford If they don't, is it the physicist's job to worry about it? :) –  Michael Kjörling Nov 12 '13 at 12:05

With respect to the content in the cup, all Your hampering with the spoon is irrelevant. Cooling of a hot coffee is achieved by vaporisation of water. At temperatures between 100 and say 50 °C the vapor pressure is so big, that the heat carried away by convection of the hot (and much less dense than air!) vapor dominates all other heat transfer mechanisms. (ca 540 cal/g heat of vaporisation!)

So, because You do not "allow/accept" blowing the surface of the coffee, the second best is to wave the spoon over the surface . Blowing/waving will enhance the vaporisation due to quick replacement of the vapour on top of the surface with fresh, cool, dry air.

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Could stirring enhance vaporization in a similar way to your proposed spoon waving? –  Jaime Soto Feb 16 '11 at 15:47
@Jaime, Normally the decisive part of resistance to heat transfer is on the gaseouse side of the barrier. But in doubt, lets compromise, the spoon held a little bit deeper when waving will scratch the suface of the coffee and create some convection there too. :=) –  Georg Feb 16 '11 at 15:59

I can't believe the density or material of the spoon hasn't been considered. If the spoon is very dense you can take it and wave it in the air in a 15° arc and say, "Dear waiter, if you don't put some cold milk in my coffee I will hit you between the eyes with this abnormally dense spoon".

On the other hand, if its made of gold or silver you hold it horizontal to the ground in a north south direction such that it refracts the light and say, "Dear waiter, here I have a brilliant and valuable spoon which I will give you in exchange for placing my coffee cup in a bath of ice til it cools"

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"So that it refracts the light"? Surely you mean "reflects"... –  Floris Jul 1 at 8:52

Well, if you are only allowed to use a spoon, the fastest way to cool the coffee for drinking is to get a spoonful, blow on it, drink it from the spoon, take a next spoonful. Convection does wonders.

If you are allowed a saucer instead of a spoon, pour a bit of coffee in the saucer, blow on it and drink it.

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Are you saying a 98% full cup of coffee cools off faster than a 70% full cup? Because the air is changing less with the coffee lower in the cup? –  corsiKa Feb 16 '11 at 17:48
@glowcoder If the cups are the same size, the fuller one has more coffee, so it will cool more slowly. There's just more heat mass to it. But if the 98% full cup is also thinner radially, so that it has the same amount of coffee, but the coffee is just closer to the rim, then yes: the moving air will cool it more quickly. –  kharybdis Feb 16 '11 at 20:52
@spencer Thank you for the clear explanation of something that isn't intuitive. (Well, maybe it's intuitive to you... I know just enough physics to make people think I know physics :D) –  corsiKa Feb 17 '11 at 8:07
pour a bit of coffee in the saucer ... and while you're at it, why don't you lap it, just like a kitty. The column of coffee between your tongue and the saucer will add to the surface even more. –  Alois Mahdal Nov 19 '13 at 1:47

The answer may depend slightly on the humidity in the room (as that will determine the evaporative cooling rate), but basically your best bet is to increase the surface area of your coffee as much as possible and increase the rate of airflow over the coffee as much as possible (so that the local gradient of partial pressure of water vapor is as steep as possible). I suspect that your best bet would be to pick up spoonfuls of coffee and pour them back into the cup from as high as you can manage without splattering the coffee all over the place--the stream of falling liquid has a high surface to volume ratio and is traveling quickly.

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That's exactly what I was going to say. It's all about evaporation and surface area. –  Keenan Pepper Feb 16 '11 at 16:13
This is exactly what a lot of people do to make very hot liquids drinkable quickly, of course they would use two cups but if all you have is spoon! –  Quaternion Feb 16 '11 at 17:33
This is a good answer and makes sense when the context is cooling a cup that you would like to drink from after cooling. –  DustinDavis Feb 17 '11 at 20:17

The fastest and coolest way to cool the coffee, with only a cup and spoon, that is also theoretically possible, is to throw all the coffee up in the air, and with somewhat well-coordinated movement catch it all in the cup as it falls down. This maximises the total surface area of the coffee with the air per time, and thus also the total heat transfer.

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This is more than hypothetical: wimp.com/hottea –  ide Feb 17 '11 at 22:04

The fastest method for cooling coffee (or hot chocolate, as I'm more likely to drink) I've discovered when I don't have a saucer or second cup is to ignore the spoon altogether.

Without a saucer, spoon, or blowing, I first place my hands around the container without any insulation device and let my hands absorb as much heat as they can stand. I then move my hands to the table to transfer the heat to the table. I then repeat the cupping the cup and transferring to the table as necessary. Within 1-2 minutes I can take a 200+ degree cup down to pleasantly drinkable levels.

This method is all about conducting the heat out of the container to the environment, and has the convenient secondary benefit of warming your hands (and the rest of your body) very quickly while waiting for your drink to cool. Combine it with a swishing of the cup to bring down the overall temperature of the coffee (not just the sides), as well as blowing on the surface (if you are allowed to cheat), and the cup cools even faster.

This works best with glass or metal tables, but wood tables also work well.

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Pre-cool the spoon first (in the freezer, or in your kitchen thermos of liquid nitrogen :) and put it in the cup. Periodically repeat the process with new spoons. Use a silver spoon (some of us were born with one in our mouths.)

Note: If you allow someone to take the spoon in and out of the coffee, the question allows much too much freedom of action--there is nothing in the bounds of the question to rule out cooling the spoon either then---hence, my answer, which was meant ironically, not seriously, for those who have trouble determining the difference...

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@fortran --no one said no cheating ;) But in the rules you say that any other creative methods are welcome, so why the -1? The answer is a joke. I thought I could afford the knock on the rep points. –  Gordon Feb 16 '11 at 18:23

Using the spoon lift some coffee into the air, and let it pour back into the cup. A nice long slow pour is ideal (as high as you can without splashing).

The motion of the water through the air will cool it fastest.

The bigger the spoon the faster it works.

In the real world, to cool coffee fast, get a second cup and pour from one to the other (again, as high as you can). Three pours should be enough to get it from burning hot to drinkable.

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I believe many power stations and indistrial plants have cooling towers that work the same way, by raising the water to a height and letting it fall as a fine mist. –  RedGrittyBrick Sep 29 '12 at 16:41

This question is a classic. On related topics, you can read:

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Both links deal about the question of adding milk asap or alap. This is not the question here! –  Georg Feb 17 '11 at 16:52
@Georg it is still quite interesting anyway... I never thought I'd learn so much thanks to a cup of coffee! :D –  fortran Feb 17 '11 at 17:13

There's also a significant boundry layer on the liquid side, similar to the Sea surface microlayer

The organization of the surface of water is an impediment to the diffusion of gases. For example, an unstirred (~5 ml) oximeter cell will take about 10 minutes to equilibrate with atmospheric oxygen, while a stirred cell will equilibrate in under a minute.

Surface foam, or a monolayer of fatty molecules, such as might be formed by coffee oils or creamer, likely has insulative value. Stirring would minimize that by disrupting the structure.

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Strange question :)

I would say use the room temperature, lift the coffee with the soon and drop it back to the cup repeatedly, this will make a part of the coffee be in contact with the cold room hence getting colder and mixing with the hot one bringing down the overall temperature.

I have (obviously??) no mathematical / physical knowledge about how effective this technique might be, and besides I drink the coffee as hot as I can ;P

Good luck!

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Move the cup. One of the main ways to cool something down is to ensure hot particles that have risen off the surface of the drink don't fall back on it again.

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Stir the coffee with the spoon and blow air into the cup with your mouth. Every few seconds change the direction of the stir (clockwise to counterclockwise and vice-versa). This should cool it quickly than just stirring the coffee with the spoon.

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By leaving the spoon stationary in the coffee, you are only benefiting from the thermal conduction and dissipation of the spoon.

By stirring the coffee, you are not only helping to keep the hottest parts of the coffee in contact with the air & cup, increasing the surface area by introducing abnormalities in the top surface, and helping to move the warm, moist air atop the coffee, but you are also getting all of the benefits of the thermal conduction and dissipation of the spoon.

By dunking the spoon repeatedly, you are not only introducing air into the liquid, which will grab lots of heat and be whisked away as soon as it hits the surface, but you are also getting all of the benefits of the thermal conduction and dissipation of the spoon and all of the benefits of stirring the coffee.

Ignoring the fact that you will probably splash the coffee and make a mess of the counter, the correct answer is repeatedly dunking the spoon. Also, you and your coworkers are nerds!

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"Also, you and your coworkers are nerds" what else can you expect from a bunch of computer scientists? XD –  fortran Feb 17 '11 at 8:12

I stir the coffee in a side to side motion with the spoon bowl parallel to the side of the cup. Due to the angle bernoulli's principle moves the coffee through the center of the cup towards the top. This circulates the liquid much more quickly than you'd expect in a controllable fashion that avoids splashing vigorous stirring can cause. It also has the side effect of removing the dry creamer from the bowl of the spoon far more efficiently than any other possible motion. The liquid coming up from the center and being forced across the top to the sides smoothly and without cavitation gaps stirring causes. The liquid also conducts with the sides better and releases heat both via the wave that forms at the top increasing the surface area contact with air and transferring the heat to the body of the cup/heat radiator. Actually I do stir that way. It cleans the spoon far better and requires less effort. Other than that the above is merely serendipitous inference.

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