Why and how hot water freezes faster than cold water

1. How hot water freezes faster than cold water
Wenqing Wu, Michael Wu, and Gabriel Wu

2. Tackling the impossible
It is well known hot water can freeze faster than cold water
Though not under all circumstances
This is the well known Mpemba effect
Earliest recorded observation dates back thousands of years
Yet it seems impossible to explain
If modeling the Mpemba effect mathematically as
Same governing freezing differential equation
Only difference is initial water temperature
The model will show cold water freezes faster, every time!
£1000 award for the true explanation at the Hermes 2012 event
Organized by the Royal Society of Chemistry
The public are given four weeks to crack the case (deadline 7/30/2012)
Then selected elite young scientists will take on the challenge in London

3. We have got the answers
Short answer for the impatient
Hot water contains less air in comparison to cold water
Assuming all are saturated solution of air in water to start with
Which is the case when water is exposed to air for long enough time
Air in hot water can not reach saturation during quick freeze
Thus hot water contains less air when reaching freezing temperature
Whereas cold water contains more air when reaching freezing
temperature
Air is squeezed out of ice when water freezes
Less air bubbles are produced in ice made from hot water
Majority of air bubble are trapped in ice when freeze from the outside in
More and more air bubbles present in the core as freeze progresses
Air cavities with size of 1cm or smaller are good heat insulator
Hence hot water freezes faster due to less heat insulation from air
bubbles
Long answer for the scrutinizers …

4. Long answer - solubility of air in water
The amount of air that can be dissolved in water
Increases with the system pressure
Decreases with the temperature

Source: engineeringtoolbox.com

5. Long answer – air bubbles in ice
When water is cooled, the solubility of air increases
The solubility stops increasing when water starts freezing
When water freezes, air is separated from ice
Air bubbles are hence formed
They can escape if there are paths to the air
Typically along the edge of ice
They are trapped if closed ice shell is formed
More and more air is pushed to center
Cloudy ice core is formed with more air bubbles closer to the core

6. Long answer – thermal conductivity
Air is 100x less thermally conductive than ice
Air can be very good heat insulator if convection
in air is suppressed
Which is the case for air cavities with vertical
dimension ~1cm or less
That’s why igloo is built with packed snow
Air cavities in porous snow enable igloo to be
resistant to severe cold
Outside temperature −45 °C (-49 °F)
Inside temperature −7 °C (-19 °F)
Temperature
(
o
C)

Thermal Conductivity
(W/mK)
Ice Air
0 2.22 0.0243
-50 2.76 0.0204
-100 3.48 0.0160
Source: engineeringtoolbox.com
Source: wikipedia.org

7. Long answer – the explanation
How to make hot water freezes faster than cold water
1.Aerate cold water (by expose it to air for long enough time)
2.Deaerate hot water (by heating it up, best with boiling)
3.Fast freeze cold water and hot water from outside in
Why hot water freezes faster than cold water
Ice shell will be formed first for cold water
Ice shell will be formed for hot water eventually
The air that is separated from ice is trapped by ice shell
Forming de facto igloo
As hot water does not have enough time to absorb air when cooled down
with fast freeze
The igloo in the ice made from hot water is smaller and thinner
The igloo in the ice made from cold water is bigger and denser
The difference is more significant towards the center of ice core
Eventually the thinner igloo in the ice made from hot water allows hot
water freezes completely first
The explanation can be verified in another way
Melting is more revealing of the igloo effect
Ice made from hot water melts faster than ice made from cold water
If the water from melted ice is drained away promptly

8. Long answer – the experiment (1/8)
To eliminate the effects such as solutes from different
water sources
Cold water was made from the same hot water
Hot water was heat up to 208 °F and kept there
 Cold water was cooled from same hot water in air at room
temperature for ~ 1 day
Both freezing and melting were conducted

9. Long answer – the experiment (2/8)

Michael Wu
7/3/2012 1:39 PM
Gabriel Wu
7/3/2012 1:40 PM
7/3/2012 1:40 PM 7/3/2012 5:56 PM

10. Long answer – the experiment (3/8)

7/3/2012 11:26 PM 7/3/2012 11:27 PM
7/3/2012 9:02 PM 7/3/2012 9:07 PM

11. Long answer – the experiment (4/8)

7/4/2012 11:54 AM 7/4/2012 11:56 AM
7/4/2012 8:19 AM 7/4/2012 8:23 AM

12. Long answer – the experiment (5/8)

7/4/2012 12:26 PM 7/4/2012 2:36 PM
7/4/2012 11:56 AM 7/4/2012 12:24 PM

13. Long answer – the experiment (6/8)

7/4/2012 2:39 PM 7/4/2012 2:40 PM
7/4/2012 2:36 PM 7/4/2012 2:38 PM

14. Long answer – the experiment (7/8)

7/4/2012 3:14 PM 7/4/2012 4:30 PM
7/4/2012 2:40 PM 7/4/2012 3:13 PM

15. Long answer – the experiment (8/8)

7/4/2012 4:50 PM 7/4/2012 4:52 PM
7/4/2012 4:30 PM 7/4/2012 4:50 PM

16. Long answer – the experiment (7/7)

7/4/2012 4:59 PM 7/4/2012 5:00 PM
7/4/2012 4:54 PM 7/4/2012 4:57 PM

17. Long answer – other experiments (1/2)
To verify the igloo effect for water freezing
Cold water was made by cooling oil covered hot water
The experiment showed less difference in cloudiness
between ice made from hot water and ice made from cold
water
To eliminate the effect of vaporization
Both hot water and cold water are covered with ice during
freeze
No noticeable difference was observed

18. Long answer – other experiments (2/2)

Vaporization Effect Study
6/30/2012 1:06 PM
Vaporization Effect Study
6/30/2012 1:15 PM
Air Content Effect Study
7/2/2012 7:55 PM
Air Content Effect Study
7/2/2012 8:02 PM