Cooling a cup of coffee with help of a spoon During 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 a greater surface than the flat coffee, so it is better for heat exchange with the air.

*Due to the difference in 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 another 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:
The reasoning for this is that the spoon cools off faster when it's outside.
(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).
 A: 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.
A: 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.
A: 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. 
A: Heat flows into a cooler condition; cold does not flow into a warmer condition. The 'rate' of cooling is dependent upon the difference between the coffee and the surrounding, ambient temperature. That is, a very hot cup of coffee will cool "faster" than a just warm cup of coffee. As the very hot cup of coffee starts to approach room temperature the rate of cooling will slow down too. 
  Just touching the spoon with an ice cube will allow the 'heat' to flow into the ice cube faster. However, the addition of the ice cube may violate the parameters of the experiment. 
By letting the spoon remain at room temperature you will be able to know the temperature of the coffee. It'll be the same as the room temperature---no colder.   
A: 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.
A: 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.
A: 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.
A: 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...
A: 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.
A: 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.
A: 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!
A: 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.
A: 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!
A: If the only apparatus is a cup of hot coffee and a (metal) spoon, the best way to cool the coffee is to stir the coffee in a 'random' manner rather than circular motion. The reasons are as follows:

*

*Choice of metal spoon: The metal spoon is at a lower temperature than the coffee and it acts as as a heat sink so that heat flows from coffee to the spoon.

*Stirring the coffee: Stirring increases the surface area of the coffee in contact with the atmosphere and through convection the heat currents rise up to the surface and cool due to the temperature difference between atmosphere and coffee.

*Stirring in a 'random' manner:  If the stirring is done circularly, then, roughly each portion of the coffee moves in a circular pattern and parts that start out below the surface stay below the surface. But, if the stirring is random, then any portion of the coffee has a greater chance to move to the surface layer. Moreover, heat transfer coefficient depends on the Reynold's number; more the turbulence, more is the Reynold's number and more is the heat transfer. So, random stirring can increase the turbulence of the flow resulting to enhanced heat transfer between the coffee and the atmosphere.

N.B.: One should stir the coffee randomly within a limit, otherwise the coffee would get spilled leaving no coffee in the the cup to drink at all.
A: 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.
A: I recently made a slightly different test, also testing temperature in a cup of coffee:

Where: 


*

*Green area is where I think the coffee is in a drinkable temperature

*Purple is no cooling. It's simply showing a cup of coffee with a spoon standing in room temp.

*Orange is blowing on the coffee. Yes I did it for 20 min (go physics).

*Red is lifting spoon, similar to "insert and removing the spoon repeatedly", but i lift some coffee up and drop it down into the cup as well (about 5 cm drop).

*Blue is stirring the coffee with a spoon.


Test was made by using an arduino to save temperature every 2 seconds. 
Results show blowing is way faster! Blowing is faster because you blow away humid and hot air just above the cup. Then you replace it with cold and dry air. The old equilibrium will form again causing much more evaporative cooling.
Using a saucer or ice cubes are still faster, but my test focused on the best you can do when you sit at a cafe. 
I made it for this video, where I explain more about the setup and the results.
A: drhodes did the experiment, got the data, and demonstrated that my hypothesis was incorrect. That's real science.
Saucering your coffee is still old-school cool.

Previous (refuted) version:

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.
A: Use a large and thick copper spoon.


*

*Put the spoon in the coffee for 3 seconds.

*Remove it and insert the spoon in your mouth. (beware it will be hot)

*Use the tongue and palate to cool spoon pushing hard. When the spoon is close to the temperature of your mouth (feels tepid) remove it and reinsert the spoon in the coffee by another 3 secondos plus 0.5 multiplied by the times you have inserted the spoon.

*Repeat until the spoon has the temperature you want.

*Drink coffee. (but do not share it, is unhealthy)

A: With the movement of the spoon you give energy to the particles and molecules.In this way the molecules increase their kinetic energy and many of them escape from the cup of the tea.Therefore the use of a spoon for cooling a cup of tea is valid!
A: There are many answers and even experimental data, but there is no mathematical model. I will fill this gap, add a few models explaining the experimental data. The simplest model is laminar convection, which describes heat transfer from coffee to the surrounding air. This model describes the cooling of coffee without a spoon and without blowing. Here we assume that heat is removed from the top and through the side walls, and the bottom is insulated. Figure 1 shows the convective current flow lines (upper left) and temperature changes with time in the volume (right) and at three points $1 - (0.5,0.5),2 - (0.5,0), 3-(0.25,0)$ (lower right).

Figure 2 shows the same parameters in the presence of blowing. Comparing the data in Figs. 1 and 2, we see that airflow reduces cooling time to an acceptable temperature at the bottom of the cup (but not in the center). That's why we still need a spoon to mix hot and cold liquid.

A: If you hold a spoon firmly and move it back and forth perpendicular to the face of the spoon at a certain rate you will cause stable cavitation and extreme turbulence that does not splash from the cup.  I do this all the time when dissolving sugar in kool-aid but with practice I think it might cool the coffee faster.  Might be a close second to the spoonful-lift-pour technique.  
A: How about this:
Before putting the coffee into the cup, pour the hot coffee directly onto the spoon, allowing the excess to drizzle into the coffee cup. The goal here is to make the coffee flow downstream onto the spoon and then into the cup, with as much distance as possible.
The more distance there is between the spoon, cup, and source of coffee, the more it can cool down from the air.
You can feel this effect when taking a shower. If you adjust the heat of the water, and lift the showerhead closer and farther from your body, you can feel the temperature change the more it travels through the air.
A: According the fastest way would be keep a flat rectangular thick strip in the coffee with an ice cube at the other end the heat will flow by conduction. And since the temperature difference between the two is large a lot of heat energy will be absorbed by the ice cube to melt.(Taking perhaps a colder object might be better).
This heat is deducted from you coffee and it is cooled down. I think it is quite similar to dropping some ice cubes in a coffee just without diluting the coffee.
