The Mpemba effect(im-PEM-bah)

When Hot Water Freezes Before Cold Water

James D. Brownridge

Department of Physics, Applied Physics and Astronomy

State University of New York at Binghamton

Binghamton University

An experimental explanation for why hot water will sometimes freeze more rapidly than cold water is offered. Two specimens

of water from the same source will often have different spontaneous freezing temperatures; that is, the temperature at which freezing begins. When both specimens supercool and

the spontaneous freezing temperature of the hot water is higher than that of the cold water, then the hot water willusually freeze first, if all other conditions are equal and

remain so during cooling.

A Brief Introduction

Under normal conditions, ice that is warmed from less than 0o C will always begin melting when its temperature reaches 0o C. However, when liquid water is cooled from

above 0o C, it often will not begin freezing until it has supercooled to several degrees below 0o C. This is why

hot water can freeze before cooler water when all experimental conditions are identical except for the initial temperatures of the water. Hot water will freeze before cooler water only when the cooler water supercools, and then, only if the nucleation temperature of the cooler

water is several degrees lower than that of the hot water.

Freezing and melting

Heating water may lower, raise or not change the spontaneous freezing temperature. The keys to

observing hot water freezing before cold water are supercooling the water and having a significant

difference in the spontaneous freezing temperature of the two water specimens.

Heating water

Freezing water

Clean water that is setting undisturbed in a freezing environment (freezer) will not freeze when its temperature falls to 0o C. It will supercool to well below 0o C before

heterogeneous nucleation initiates freezing. Small volumes of very pure water with no “ice nucleation agents” (foreign

agents) can be supercooled to ~ -40o C; at this temperature it is homogeneous nucleation that initiates freezing.

When freezing is initiated by heterogeneous nucleation the water will freeze when its temperature reaches the “ice

nucleation temperature” of the foreign agent with the highest “ice nucleation temperature”

Experimental Results

Most outstanding cases of hot water freezing first

(Slide 7, 8 and 9)

A few silver iodide crystals were added to 3 of 6 vials

Experimental set-up

DAQ

Up to 8 vials

Experimental set-up

DAQ

Up to 8 vials

0 20 40 60 80 100 120 140-20

-10

0

10

20

30

40

50

60

70

80

#3

Vials 3 & 4Vials 3 & 4T

rmpe

ratu

re o C

Vials 1 & 2

Last to freeze

Hot 1st to freeze

0 20 40 60 80 100 120-20

-10

0

10

20

30

40

50

60

70

80

90

Hot 1st to freeze#3 Last to freeze

Vials 1 & 2

0 20 40 60 80 100 120-20

-10

0

10

20

30

40

50

60

70

80

Trm

pera

ture

o C

Cold 1st to freeze Cold 1st to freeze

#3

#2 Last to freeze

Vials 3 & 4

Vials 1 & 2

Time (min)

0 20 40 60 80 100 120 140-20

-10

0

10

20

30

40

50

60

70

80

Last to freeze

4 "identical" glass vials; Nucleation agents unknown

Vials 1 & 2

Vials 3 & 4

Time (min)

#3

Experimental set-up

Top thermocouple

Bottom thermocouple

Hot water freezing before very cold water

“Spontaneous ice-nucleation temperature”

HOT COLD

Top Thermocouple

Bottom thermocouple

Added

“Spontaneous ice-nucleation temperature site”

*

*

If T=0 At 35 msec At 70 msec At 105 msec

freezing

The speed of the ice front depends on how low the water is supercooled

Photos of freezing water (2 ml of water)

15 freeze/thaw cycles

-10.8±0.3

15 freeze/thaw cycles

~70 hrs.

Loss of water apparent

-14.3o C the vial was cracked by the ice during the 1st freeze cycle

[-14.3o C] The vial was cracked by the ice during the 1st freeze cycle

-11.0 ± 0.5 -3.3 ± 1.7 -10.5 ± 0.9 -9.1 ± 0.8 -9.9 ± 0.3 -7.5 ± 1.2 -3.4 ± 1.7 -9.8 ± 0.8

-11.3 ± 0.3 -13.8 ± 0.1 -14.3 ± 0.1 -11.3 ± 0.1 -10.8 ± 0.3 - 9.7 ± 0.1 -1.2 ± 1.1 -9.9 ± 0.2

0.3 ± 0.6 10.6 ± 1.7 3.8 ± 0.9 2.2 ± 0.8 0.9 ± 0.4 2.3 ± 1.2 -2.2 ± 2.0 0.1 ± 0.8

Initially After shaking Net differenceVial #

12345678

Shaking water in a container maychange the

“spontaneous ice-nucleation temperatures”

Latent heat released at oC

13 cycles 13 cycles

0 5 10 15 20 25 30 35 40 45 50 55-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

A spontaneous change in the ice-nucleation temperatures.

Reason unknown.

Vial shaken

Freeze/thaw cycle

Late

nt h

eat r

elea

sed

at o C

Vial # 2

Graphic display of the ice nucleation temperatures

Before shaking After shaking

0 5 10 15 20 25 30 35 40 45 50 55-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Freeze/thaw cycle

Late

nt h

eat r

elea

sed

at o C

Vial shaken

Vial # 8

0 5 10 15 20 25 30 35 40 45 50 55-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

A spontaneous change in the ice-nucleation temperatures

La

tent

hea

t rel

ease

d at

o C

Freeze/thaw cycle

Vial shaken

Vial # 5

0 5 10 15 20 25 30 35 40 45 50 55-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

5.1±1.316.1±0.2

Late

nt h

eat r

elea

sed

at o C

Freeze/thaw cycle

Vial # 1

Vial shaken ?

0 5 10 15 20 25 30 35 40 45 50 55-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

15.1±0.4

Vial shaken

Late

nt h

eat r

elea

sed

at o C

Freeze/thaw cycle

Vial # 6

15.1±0.1

Graphic display of the ice nucleation temperatures

Hot water never cools to 0oC first

We have determined that when water is added to a container there may be many “ice nucleation sites” with different nucleation temperatures. The temperature of a given site

can often be changed by heat, stirring or jostling water inside the container. Heating water may lower, raise or not

change the spontaneous freezing temperature, however, heating water will not necessarily cause it to freeze faster

than water that was not heated. The nucleation temperature of the “ice nucleation agent” in a sample of water is

responsible for the temperature at which the sample will freeze

Conclusion

Acknowledgments

• I wish to thank Cara Walkin, Julie Galluccio and Mark Stephens for

comments and suggestions.

• 4 March 2010