
Cooling a cup of coffee with help of a spoon - jyro2080
http://physics.stackexchange.com/questions/5265/cooling-a-cup-of-coffee-with-help-of-a-spoon
======
rgrieselhuber
The two cup trick is also used in Japan when making green tea, because the
fragile tea leaves can be damaged if the water is too hot.

I once heard a tea master say that every time you pour the water from one cup
to another, it cools down by 10 degrees (celsius). I'm not sure I fully
believe him because pouring the water between cups 10 times didn't freeze the
water. ;-)

~~~
wisty
It won't be a fixed "10 degrees". More like dt = (T_cup - T_room) x cooling
factor.

I'll leave it as an exercise, as to what 10 pours will do, but it won't freeze
the water; as I don't remember how to solve it and I don't have a piece of
paper handy.

And that's not accounting for the specific heat in the state change.

~~~
sp332
Entropy is logarithmic with respect to degrees of freedom, and since degrees
of freedom is (usually but not always) proportional to the energy of the
system, the temperatures of the tea and of the room will approach each other
faster when the difference between them is greater, but the heat exchange will
slow down when the temperatures are similar.

EDIT I meant to say that entropy is _proportional_ to degrees of freedom,
which is logarithmically related to heat energy (except in some weird cases).
Anyway, the conclusion was right :-)

------
edge17
<http://www.youtube.com/watch?v=-surEvJXj34>

~~~
kingsley_20
This is the traditional way of serving coffee in south India:
[http://farm4.static.flickr.com/3499/3281237995_091cdeac67.jp...](http://farm4.static.flickr.com/3499/3281237995_091cdeac67.jpg).
Basically, you get a cup and a bowl to pour it back and forth with.

------
ern
I also remember my grandfather using saucering to cool hot tea down, I finally
have an explanation for why it works.

I wonder why the practice went out of fashion. Do paper doilies send a signal
that the saucer is not to be used to hold liquids?

~~~
samatman
From reading the Laura Ingalls Wilder books, when I was a young'n, I remember
that 'saucering' was considered rural, unrefined behavior. That kind of thing
goes out quick; I bet none of the Silver Screen movie stars were seen
saucering their tea.

------
JonnieCache
I always stir my coffee in a random way so that you see turbulent movement in
the cup as opposed to the whirlpool you get from moving the spoon in smooth
circles.

My intuition tells me that this should give more efficient cooling. I
basically have nothing to back this up. Thinking about it, it probably makes
more sense for dissolving the sugar than cooling the coffee.

~~~
gjm11
Your aim is to make sure that every bit of the coffee eventually makes it to
the surface (so that the highest-energy molecules there can escape and cause
cooling). If you stir regularly then (roughly) each bit of the coffee just
moves in a circle, and parts that start out below the surface stay below the
surface. If you stir it at random, then (this is probably a theorem, if you
define "random" with a bit of care, and it probably doesn't require all that
much randomness) any portion of the coffee ends up eventually at any given
place.

So I think your intuition is doing pretty well.

~~~
khafra
Surely there are some regular motions which could be approximated using a
spoon which would more efficiently move the hottest parts of a liquid to the
surface than random turbulence? My intuition says sliding the spoon down the
side of the mug, then turning the flat side upward and lifting it in the
middle of the mug would be one such more efficient motion.

Does anybody have a supercomputing cluster we could use to run an optimizing
search across a whole bunch of fluid flow simulations?

~~~
apl
I got one, but unfortunately it's still working on the milk-or-tea-first
conundrum.

~~~
JonnieCache
_> milk-or-tea-first_

Ahhhhh, the one debate more divisive than emacs-or-vim.

------
gus_massa
I think that the explanation is wrong (or at least it is a
oversimplification.)

The main problem is that the explanation ignores completely the air. Static
air is a good isolator, therefore much of the heat must be transported by
thermal convection or forced convection (blowing). If the air doesn't move, it
wouldn't be useful to make each part of the coffee visit the surface.

The second problem is that the it says that most of the heat is lost by
evaporation of the water molecules (latent evaporation heat). I think that
this is true when the temperature is over 195 F/90 C. But when the water is
cooler I think that thermal conduction is more important, and it is not
related to the "high-kinetic-energy outlier water molecules". And also some
heat is lost by the floor and walls of the cup, but I think that most of the
heat is lost by the surface. [More details in "experiment" bellow.]

The third problem is more an oversimplification. It is incorrect imagine that
some of the molecules of the water are "high-kinetic-energy outlier". Let
imagine that we mentally "paint" the fast molecules at initial time. Very soon
these molecules will bounce with other molecules and change their velocity, so
a few instants later the fast molecules will be other molecules. To estimate
the time that we have to wait until the fast molecules bounce we can use the
"mean free time". This time is useful in a gas where the molecules are far
apart, and for air in usual conditions it is ~5E-10seg. Obviously water is not
a gas, but the molecules are more close together, so this the time we should
wait is much smaller. But the time that a drop of water needs to go from the
bottom to the top of the cup is ~.1 seg (rough estimation). So the molecules
have time to bounce and bounce. Moreover, while the drop is traveling though
the surface the molecules have time to bounce and reach thermal equilibrium
after some of then evaporate. So I think that a macroscopic model that only
consider the temperature should work.

[experiment]

A few yeas ago, I worked at a school and we need an experiment for a physic
olympiad. We measure the cooling of a plastic cup of water in different
conditions. The idea was that the temperature follow a law like:

    
    
      Temp = Constant * exp(-time/tau) + Temp_external
    

Taking logarithms

    
    
      log(Temp-Temp_external) = - time/tau + Konstant 
    

So it is possible to make a graphic of the log(Temp-Temp_external) and from
the slope get the value of tau. In an ideal case, tau is a constant (or almost
constant) that depends on the materials and the sizes of the experiment.

Really tau is not constant. When the temperature if below 195 F/90 C the value
of tau is almost constant and the graphic of the log is a nice line.

But when the water is hotter tau is not constant, the bigger the temperature,
the bigger is tau (IIRC perhaps like twice the cold value). So the graphic of
the log is curved and the water cooled faster than expected.

When the temperature if above 195 F/90 C something strange was happening.
Looking at the cups we see that above that temperature there was a lot of
steam over the cups and bellow that temperature the seam almost disappear.
Looking at the graphics of the vapor pressure of water we saw that above 195
F/90 C the vapor pressure is bigger than the value bellow 195 F/90 C. So we
expect to have a lot of evaporation when the water is hot and few evaporation
when it is cold.

So the conclusion was that when the water is cold most of the heat is
exchanged by conduction and convection, but when the water is hotter the
evaporation is and additional important part of the cooling effects.

Note 1: We did some additional experiments that are consistent with this
explanation, but perhaps there is something we forgot to check.

Note 2: The change between the "hot" and "cold" water above and bellow 195
F/90 C was not sharp. While the water was cooling the steam get thiner softly,
tau get lower softly and the vapor pressure gets null softly. So the number
195 F/90 C is only an approximation. (And it was a few years ago.)

Note 3: Heat flow is difficult to modelate in paper, so better measure it
experimentally. "In theory, practice is the same as theory. In practice, it
differs."

------
spullara
Reminds me of a correction I sent to The Straight Dope many years ago:
[http://www.straightdope.com/columns/read/851/why-do-you-
blow...](http://www.straightdope.com/columns/read/851/why-do-you-blow-on-
coffee-to-cool-it-but-on-your-hands-to-warm-them)

------
kschua
The indian drink stall sellers in Malaysia and Singapore have a good way to
cool it down. It is called Teh Tarik

Picture here [http://3.bp.blogspot.com/_0o2-S1p2MUo/Sm-
YjNyRfpI/AAAAAAAAAd...](http://3.bp.blogspot.com/_0o2-S1p2MUo/Sm-
YjNyRfpI/AAAAAAAAAd4/Xo3Ga1M7J3s/s1600/TEH+TARIK.jpg)

Description of what it is here <http://en.wikipedia.org/wiki/Teh_tarik>

Edit : Found a video of it here <http://www.youtube.com/watch?v=WPuIybnQemc>

------
phaedrus
Similarly I've often wondered if it results in hotter coffee to mix your milk
with the coffee when it goes into the thermos, rather than when it comes out.
I'm pretty sure it is better to do it this way - my reasoning is that the
hotter black coffee, because of a greater temperature difference with the
surroundings, loses heat more rapidly through the thermos walls than the milk
+ coffee mixture. But I'm unsure how significant the effect is. Perhaps I'll
measure it some time.

~~~
maxbRuns
Yeah, that's interesting. I always do it the same way as you, but I decided to
do a quick analytical calculation. I wrote it up here:

[http://maxbrunsfeld.wordpress.com/2011/02/17/on-the-
mixing-o...](http://maxbrunsfeld.wordpress.com/2011/02/17/on-the-mixing-of-
milk-and-hot-coffee/)

my result agrees with your intuition.

------
thesz
This is related to the phenomena that tea leaves tend to group in center of
cup when you stir it with spoon.

Due to centrifugal forces the level of water near the border is higher that at
the center so the water start to flow from borders to center at the bottom of
the cup.

This speed up heat exchange as the water gets constantly mixed in addition of
usual thermal exchange flow.

------
indrax
Assume a spherical spoon...

~~~
maxbRuns
in an infinite region of coffee...

------
eps
I remember similar physics puzzle from high school days. Given a cup of hot
tea and few spoons of sugar how does one go about sweetening the tea so that
it would cool off the most in the process.

~~~
neworbit
First, remove your sugar crystals from the thermos of liquid nitrogen...

~~~
pbhjpbhj
Should you crush the sugar crystals (to promote rapid cooling) or should you
use the largest possible crystals so there are more bonds to be broken?

I'm going to guess that there's a sweet spot in there somewhere; _a priori_ it
seems you want the maximum size that will dissolve completely.

~~~
eps
If I remember the answer correctly, it went something like this. Dump all
sugar into the tea at once and wait for the temperature to settle. Now split
sugar in two halves, dissolve first half, wait for the temperature to
stabilize, dissolve second half. Through math it worked out that the second
method cooled the tea more. So the answer was to go with the infinitely small
pieces of sugar :)

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

Reminded-me of this xkcd strip: <http://xkcd.com/435/>

~~~
juiceandjuice
I didn't understand that comment... was he insinuating physicists don't know
thermodynamics? The original question is pretty basic.

~~~
maxbRuns
I think he was saying that although physicists generally understand the
principles involved, a chemist might have a better sense of the relative
magnitudes of the different effects that come into play in cooling a solution,
since chemists have to perform this task routinely.

~~~
juiceandjuice
I suppose, but any physicist worth anything should be able to remember enough
high school chemistry to deduce the answer.

~~~
dandelany
Fluid dynamics aren't exactly high school chemistry...

------
JoeAltmaier
Feynman would get a cup of coffee, a spoon and a thermometer.

~~~
gus_massa
Why the downvotes? I usually don't like oneliners and reference to
Feynman/Einstein, but I think that this comment has an important point. I will
try to expand it.

Some topics in physics are easy to model and get a closed formula but some are
not. In particular, fluids flow and heat flow are very difficult (if the
system is not very symmetric).

To make an industrial heat exchanger, the chemical engineers use "books" that
have a lot of examples for different chemical products and different
geometrical configurations and try to find the more similar to get some
experimental constants. These constant can be placed in formulas to get the
required size of the new heat exchanger, but are only reliable if the new one
is similar to the original example.

A few yeas ago, I worked at a school and we need an experiment for a physic
olympiad. We measure the cooling of a plastic cup of water in different
conditions. One of the ideas was to measure the effect of a metal spoon, but
in the pretesting we found out that the effect is negligible. We got the
bigger difference using a thin plastic lid, the cooling time was much longer.

So, to find out the best method to cool a cup of coffee you can't use a pencil
and a peace of paper. You should measure it experimentally wit a thermometer.
(Perhaps a computer model simulator might work.)

And in one of the Feynman books, he was trying to see if jelly gets hard if
you stir it while cooling. He waited for a freezing day, got a pan with hot
jelly, something to stir and a jacket. In another book someone told him that a
piece of rubber from the Challenger shuttle would become hard when cold. He
got some water, ice cubes and somthing to hold the rubber to test it. So
probably Feynman Feynman would get a cup of coffee, a spoon and a thermometer.

------
ramki
on a completely different note, I like my coffee hot :)

~~~
hencq
Hahaha yes, while I liked the thought exercise I kept thinking: "Why would I
want to cool it?" In fact, I often pre-heat my cup with hot water before I put
coffee in it, so it doesn't cool down as fast.

------
BoppreH
That`s why I love plastic ice cubes. Keep in the freezer for some time so the
water inside will freeze and enjoy your non-watered down drinks!

------
51Cards
I smell an episode of Mythbusters coming on.

------
nivertech
try putting cooling heat-pipe into your hot cup of coffee - your fingers will
burn instantly.

------
Pooter
1) Find person nearby with a drink that has ice in it

2) Use spoon to extract the ice from their glass

3) Put ice in coffee

Also, you may need to threaten the person with the spoon to get the ice.

~~~
harshpotatoes
But now you've added a non negligible amount of water to your coffee. Nothing
worse in the morning than watered down coffee.

------
drstrangevibes
bend spoon into a u-shape and stick the other end in a cup of liquid nitrogen

