Why and how hot water freezes faster than cold water

How hot water freezes faster than cold water

Wenqing Wu, Michael Wu, and Gabriel Wu

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

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 …

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

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

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 (oC)

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

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

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

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

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

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

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

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

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

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

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

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

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