Mpemba Effect

I was already rather sick when I came across the Mpemba Effect competition by the Royal Society of Chemistry. Even though my background is limited to CHEM 100 from decades ago, I was so inspired by the challenge, I strived through my illness to complete a paper for submission.

Unfortunately, my paper was buried under an avalanche of haphazardous submisssions, by every Joe, Dick and Harry going for a joy ride, making mockery of a respectable worthy contest, ruining my chance at a fair review. Afterwards, I was too sick even to make sense of the finalists' paper. But deep down in my bones, I feel like I have a better paper, which just never got to see the lights of day. Am I being too narcistic to wish for a second chance at a proper review?


Mpemba Effect Explained, the Amateur Way...
Comparing the time it takes to freeze water in 2 equal sized containers, 
one hot and one cold.
(For brevity, I'll only refer to the freezing process within a freezer.  
But this can take place just as well in any freezing cold environment).


I am a fractured alien soul from the 11th Dimension Parallel Universe.
Our people, the Ggrowbyyans, communicate via brain waves.
Alas, I am rather awkward with your language. 
Moreover, the human form I am entrapped in is quite brain-damaged, 
and in volatile health, which definitely complicates my attempt at any task.

Obviously, I lack the academic background of your other more distinguished 
contestants.  But for the same reasons, my submission should inspire a novel 
perspective.  Yet without precise mathematics or vigorous experimentation under perfectly controlled environment, my feeble attempt is at best interesting conjecture.  I sincerely hope there is some sort of consolation prize for my ingenuity/creativity/originality or shamelessly persevering effort.



(2.1) Current Acts as the Catalyst

For the hot water container:
As hot water collides with the cold (such as inside the freezer), 
a current is generated - the bigger the contrast in temperature, 
the higher the (thermal-turned-)kinetic energy - the faster the current.

[We're talking about micro current here (and thus micro movements and actions), 
as opposed to the macro ocean current.]

Just as stirring hot water will cool it down faster,
the current (stimulated stirring) generated by the hot-cold collision 
dynamically expands the surface areas to dissipate heat, in order to achieve (temperature) equilibrium faster.

For the cold water container:
As there is much less temperature contrast, there would be negligible current generated in the cold container, thus much less heat dissipation.

(2.2) Team Effort (Division of Labour and Cooperation) Speeds up the Work

For the hot water container:
Frost (tiny ice crystals) continues to form on the walls of the cooled down 
container, inside and outside.  (The inside "frost" is not noticeable 
as it is obscured by the liquid water.)
These crystals get swept away by the "speedier" current, rotating while rapidly circulating, and due to their polar nature, 
align and adhere to nearby crystals, forming bigger crystal chunks.
As the "polarised" ice chunks grow in size, their "magnetic" force also grows stronger, thus attracting each others even faster, forming even bigger chunks, 
till eventually they all merge into one whole ice block.

For the cold water container:
When compared to the hot container mentioned above, there are little 
activities happening, other than the much slower thermal transfer.


(3.1) Matters seek equilibrium

[Newton's Law of Cooling, see (4.1) below, is a subset of this theory.]

The bigger the imbalance 
(in our case: the temperature contrast between the hot water in the container 
versus the cold freezer) 
the more vigorously matters try to restore back to equilibrium.

In our case, more energy is expanded, through heat transfer - thereby speeding up the process (to compensate for time) - such that the time it takes to equilibrium "remains" the same.

(3.2) Affinity of Like Matters and Team Effort

Like substances have more affinity for each others (than unlike ones).

As ice crystals grow, ice tends to be attracted to ice (as in the hot container), much faster than ice to water (as in the cold container).  The freezing process becomes more of a team effort of like substances (see 2.2) cooperating, rather than the much slower thermal transfer, "sequentially". 

More affinity translates to speedier process to (temperature) equilibrium.
[In our case, "equilibrium" is the freezing temperature, 
since the freezer keeps on consuming more electric power (energy) 
to stay that cold, on top of supplying latent energy for freezing its contents.]

(3.3) Viscosity Decreases with Increasing Temperature

The increasing kinetic energy in the hot water container overcomes the attractive forces (viscosity) and water molecules can move more easily past each other, 
(frost crystals circulating amongst themselves to "team" up with those with the closest "affinity", i.e. similar-shaped ice crystals)
contributing to the "current", which is negligible in the cold water container.


(4.1) Newton's Law of Cooling 

The law states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient (surrounding) temperature.

Instead of messing with differential equations, natural logarithms, etc., 
we shall assume the number μ is so huge (with magnitude in the vicinity of 
mole or Avogadro's Number) that we can approximate/substitute our 
differential "time function" ƒ(t)
with simple linear formula...

For 2 equal sized containers of dimension μ³,
each containing μ³ micro-units of water:

Assuming it takes t amount of time for each water unit 
to transfer one degree of heat to its neighbouring water unit, 

it would take ½μt 
to transfer that heat from the centre to all 6 sides of the container
(ignoring any diagonal directions, for simplicity).

But for the hot container, the movement of the "current" 
makes the "sequential" heat transfer time almost unnecessary.  
All water units are transferring heat simultaneously, everywhere, 
in all directions, 
instead of from the centre to container walls, one unit at a time.

In t amount of time, the hot container transfers more heat 
than what the cold container can accomplish in time ½μt
[with μ being a very huge number, thus t << ½μt]

(4.2) Temperature Catch-Up 

If the difference in temperature between the hot and cold containers is σ 
(degree Celsius), probably in the range:
           30 < σ < 60
           σ << μ
the time for the hot container to catch up with the cold container in temperature 
is negligible:
           σt << ½σμt

(4.3) Dropping Water Temperature to Zero

Similarly, we can assume the same negligibility.

(4.4) Latent Heat of Fusion

By the time the cold water container reaches 0°C, the freezer still has to work hard to absorb 80 calories of heat per gram of water, in order to freeze it into ice.
This phase transition requires much more time (in thermal transfer) than lowering the temperature to zero.

However, with the hot water container, the "current" effect, as stated in (2.2), 
has been mobilizing the already-frozen crystals to merge into the final ice block, right from the beginning, and all through the "freezing" process, essentially bypassing much of the most time-and-energy-consuming (phase transition) step.


There are many more "minor" details and contributing factors.
But the less said, the better to conceal my ignorance and inadequate 
communication skill.  However, should you find my babbling "micro-dissertation" 
have merit, I'll endeavour to fill in any omissions, if necessary.
After all, I'm only vying for a consolation prize, 
please be lenient.
(I regret overlooking the possibility of doing a video.) 


Mpemba Effect Explained, the Amateur Way...
Sorry I'm such a scattered-brain.  It dawns on me belatedly that 
there should be a summary/conclusion to organise my random thoughts.
So please accept the following as an addendum to my
original submission on July 24th.


the freezing process involves the (negative/reverse) thermal transfer 
from freezer to container walls to the water in container centre 
(conveyer-belt-style, i.e. "sequentially").

The expected sequence of events involves 2 steps:
[1] degree by degree, until water temperature drops to zero
[2] latent heat of fusion
step [2] is a far more energy-and-time-consuming step than step [1]
(80 calories per gram versus one calorie per gram per degree)

Whereas with a container of hot water, 
there exists a "current" (catalytic) effect, 
which circulates tiny ice crystals, 
until they all merge, first into various chunks, 
then eventually into one solid block of ice.

We take advantage of the ice crystals formed on the container walls, 
essentially bypassing much of the "sequential" thermal transfer.

Imagine many colonies of bees, all busy depositing honey into their hives.
Then the bee-keeper just collects all the honey into one big pot.
This simultaneous team work is definitely faster than the conveyer-belt model.

Aug 1/2012 %%%%%%%%%%%%%%%%%%%%

Mpemba Effect Explained, the Amateur Way... (3)
Sorry, sorry, sorry... I'm terrible at making myself understood.
I don't know how to write a paper.
So se to include the following FOOTNOTE as an addendum to my
previous addendum submitted on July 26th.

I suspect this teetering may disqualify me from winning the Grand Prize. 
But life is never fair.  It is more to have the satisfaction of having 
given my best, and hopefully at least receive the acknowledgement that 
my solution is very close to the truth.

So here goes:

(6) Postscript / Footnote


Hope u'd post & archive all entries by categ: 
creative, comic, off base, finalists
(Good mtl for PSYCH study)

Aug17/2012 %%%%%%%%%%%%%%%%%%
Too late for me to figure out how to do a video.
But I think adding a FOOTNOTE to my SUMMARY 
may clarify my messy explanation a bit better.
                                                       Aug. 17/2012
So here goes:

... etc ...


The Honey-Bees (HB) Model "defines (approximately)" the gaseous state.  
The Conveyer Belt (CB) Model "defines" the solid state.
Whereas the liquid state is "defined" by a combination of both models.
The HB Model dominates in hot water; and the CB Model dominates in cold water.

Latent Energy serves as a "buffer" to prevent (or slow down) 
the ice crystals from melting in the hot water, 
giving them a chance to "team" up with neighbouring crystals, 
to fortify themselves, ... and so the story goes ...

[OK, those are lousy examples, but I don't have much artistic talent 
to come up with more illustrative imagery...]


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