myoarin-ga ,
that is an interesting question.
The answer, like your question, will be purely theoretical. I have
not attempted to verify, by experiment, the reasoning behind this
answer. However, to compensate for that, I will add a practical tip
as well.
Not the same tip which thx1138-ga has in a comment. That tip is
true - as water evaporates, so surface gets cooler, but it is not
ecologically correct, because your fridge will have to add defrost
cycles, which wastes energy.
The tip, first: If you are ever in a hurry, put the bottles in the
freezer for a carefully determined interval of time.
That, the timing, will also give you control over the temperature,
which is essential. A typical freezer will cool beer so much that one
cannot taste it.
The correct cooling of beer was well documented in the Czech movie
http://www.imdb.com/title/tt0090257/
where one of the heroes, after many years of experimenting,
determined that right temperature was obtained by placing bottles on
the seventh step of the stairs leading to the typical Czech country
cottage cellar. Counting from the top, of course. The result was so
well accepted, that Czechs to this day will sometimes say 'let's have
something from the seventh step' when suggesting a beer. As
documented here, Czechs do understand beer.
http://www.radio.cz/en/article/46095
Now to your real question - the theory of cooling:
The limiting factors would be the thermal conductivity of liquid.
The surface (be it can or bottle) will equilibrate quickly with the
fridge atmosphere, and the thermal gradient inside the container will
slowly transport the heat to the walls of the container. But we said
'would' - because there is another effect, which will speed thing up:
convection.
Currents will form in the container, and cooling will be faster than
they would be without this factor (which you can check by shaking the
containers a bit from time to time yourself, but not opening them
right away after that, of course :-).
So - how will the position of the container affect the convection
currents? Quite a bit.
Horizontal bottles will cool faster.
The currents depend on gravity. A long narrow , closed, vertical
tube will have a hard time developing currents, compared with the same
volume of the same liquid on, for example, a (covered) plate.
To explain this, we will simplify the cooling (which, as we said, is
transporting heat from the center):
Imagine a tube with cold water at the top, and warm water at the
bottom (which can be achieved by placing a pot of water on the burner
for a short time).
Such situation is unstable, obviously, and eventually currents do
develop, a pattern of up and down currents in a pattern
of hexagonal cells. These are called
Bernard Cells
http://staff.science.nus.edu.sg/~parwani/c1/node63.html
This site has some pictures of the effect (these are not hexagonal,
due to the flow)
http://physics.ust.hk/penger/turb_ray_Ben_con.html
Here is a simple picture, within a more technical explanation. The
size of cells depends on the properties of the liquid,
and a large horizontal area allows more cells, and therefore better
heat transport.
http://www.ldeo.columbia.edu/users/jcm/Topic3/Topic3.html
So, in summary: horizontal bottles will equilibrate faster. But do
not over-cool your beer. Either set your fridge on low cooling,
or let them stand outside for a while. Happy drinking!
SEARCH TERM: Bernard cells
Hedgie |
Request for Answer Clarification by
myoarin-ga
on
22 Mar 2005 16:06 PST
Hedgie,
That is all very enlightening, also your tip about wet bottles in the
fridge, and especially the Czech film. I missed anything about the
seventh step, but believe you, and Czech film comedies are really
great, trans-cultural delights.
Of course I know that in an emergency I can use the freezer, and in an
emergency I won't forget the bottles long enough for them burst. Once
had a freezer full of champagne snow, however.
But - sorry - the comparison of a standing bottle with anything but
one lying down confuses me. Obviously the greater the surface area
exposed to cooling will increase the speed of cooling, and my
experiment is different from one that applies heat only at the bottom.
(Yeah, I seem to remember that cooling is the removal of heat - or
that the heat gets transferred/reduced, that coolness isn't a thermal
force, but I'll stick to my beer-trinker terminology.)
My bottles are being cooled on the total surface of the glass, mainly the "tube".
I would have thought that with a standing bottle, once the convection
flow starts - sliding down next to the glass - that the beer's
longer contact with the cooler glass would allow it to cool faster,
and that the convection flow would be faster than in a horizontal
bottle, in which - my supposition - the convection flow would be
slower to develop because the beer would first be cooling all along
the horizontal "tube" and the effect of gravity on it would be less
than in the case of the standing bottle, where a gravity could
increase the circulation due its effect for a longer period of time as
beer at the top slid down the length of the bottle, increased
momentum. Whereas in the horizontal bottle this effect would be less.
But thx1138-ga is right, for a can, then the top would also be in
contact with beer to add cooling surface. With bottles, I am not so
sure. Seems like there would then be more beer in contact with the
air in the bottle - the long surface ... Don't know ...?
This may call for an empirical test: warm up my last two bottles of
beer to increase the temperature change, get the thermometer, and give
them, say, fifteen minutes ...
This is what I wanted to avoid.
I still accept your answer, even if I end up thinking I have proved
you wrong, but will wait till later to rate it.
Of course, if you have any further comments now, I'd love to hear them.
|
Clarification of Answer by
hedgie-ga
on
22 Mar 2005 20:08 PST
myoarin-ga
You are right in the following:
"the comparison of a standing bottle with anything but one
lying down confuses me"
and answers should not be confusing. So I will clarify and I
appreciate that you are waiting with the rating.
1. I have introduced an example of a long sealed tube fully filled
with water. Forget the plate. Imagine one standing up,
and laying down. That is just focusing on one important aspect of
your bear bottle question. The currents will develop
differently in these two cases.
2. Indeed you are not heating (or cooling) container at the bottom.
Pot of cold water on the burner is just a standard setup to
explain the concept of conductive currents, which develop in the
containers, when there is an non-uniform temperature
distribution.
I do not follow the reasoning in
...effect of gravity on it would be less
than in the case of the standing bottle ...
sorry. Momentum does not really matter in this type of experiments.
The formation of the convection currents has been studies in detail
both experimentally e.g.
http://faculty.pnc.edu/gvandegr/publications/bohan2.pdf
and theoretically,
http://staff.science.nus.edu.sg/~parwani/c1/node63.html
and even if they do not always agree exactly
http://chaos.ph.utexas.edu/research/schatz/hexonset.html
it is an established fact, that the convection cells do form, do
form differently
in a horizontal and vertical tube, and that they affects the rate of cooling.
If you would want to argue with that, by some reasoning about
effect of gravity being less or more,
you may have yo get a bit more quantitative than 'effect of
gravity on it would be less'.
Effect of gravity is described by the fundamental equations, as done e.g. here
http://www.pma.caltech.edu/Courses/ph136/yr2002/chap17/0217.1.pdf
All I am adding to well known and 'scientifically established' facts
is an educated guess, that this,
the effect of large horizontal area, will dominate the experimental
result in case of beer bottles,
compared to effect of size of a contact are between the wall and the liquid.
And for practical purposes, John in his comment is right:
The liquids will always carry the heat more effectively then gases.
Hedgie
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