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
A Brief Introduction
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 will
usually freeze first, if all other conditions are equal and
remain so during cooling.
Freezing and melting
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.
Heating water
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.
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
Up to 8 vials
DAQ
Experimental set-up
Up to 8 vials
DAQ
4 "identical" glass vials; Nucleation agents unknown
80
90
70
80
70
Vials 3 & 4
50
40
Vials 1 & 2
30
40
20
Hot 1 to freeze
10
Vials 1 & 2
30
st
st
Hot 1 to freeze
#3 Last to freeze
20
#3 Last to freeze
10
0
0
-10
-10
-20
-20
0
20
40
60
80
100
120
140
0
80
80
70
70
60
60
o
Trmperature C
Vials 3 & 4
60
50
o
Trmperature C
60
Vials 1 & 2
50
20
40
Vials 3 & 4
30
20
Cold 1 to freeze
#2 Last to freeze
10
0
-10
-10
-20
100
120
st
Cold 1 to freeze
#3 Last to freeze
10
0
80
Vials 1 & 2
30
st
20
60
Vials 3 & 4
50
40
40
-20
0
20
40
60
80
Time (min)
100
#3
120
0
20
40
60
80
Time (min)
100
120
140
Experimental set-up
Top
thermocouple
Bottom
thermocouple
“Spontaneous ice-nucleation temperature”
HOT
COLD
Added
Bottom
thermocouple
Top
Thermocouple
Hot water freezing before very cold water
“Spontaneous ice-nucleation temperature site”
*
*
Photos of freezing water (2 ml of water)
The speed of the ice front depends on how low the water is supercooled
freezing
If T=0
At 35 msec
At 70 msec
At 105 msec
15 freeze/thaw cycles
-10.8±0.3
15 freeze/thaw cycles
Loss of
water apparent
[-14.3o C] The vial was cracked by the ice during the 1st freeze cycle
~70 hrs.
Shaking water in a container may
change the
“spontaneous ice-nucleation temperatures”
Latent heat released at oC
Vial #
1
2
3
4
5
6
7
8
Initially
-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
13 cycles
After shaking
-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
13 cycles
Net difference
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
Latent heat released at oC
0
Graphic display of the ice nucleation temperatures
Vial # 2
-2
-4
A spontaneous change in the ice-nucleation temperatures.
Reason unknown.
-6
-8
Vial shaken
-10
-12
Before shaking
After shaking
-14
-16
-18
-20
0
5
10
15
20
25
30
35
Freeze/thaw cycle
40
45
50
55
Graphic display of the ice nucleation temperatures
0
Latent heat released at oC
Latent heat released at oC
0
Vial # 6
-2
-4
-6
-8
Vial shaken
-10
-12
-14
-16
-18
15.1±0.1
15.1±0.4
Vial # 1
-2
-4
-6
Vial shaken
-8
-12
-14
-16
-18
0
5
10
15
20
25
30
35
40
45
50
0
55
5
10
15
Freeze/thaw cycle
25
30
35
40
45
50
55
0
Vial # 5
-2
20
Freeze/thaw cycle
0
Vial # 8
-2
A spontaneous change in the ice-nucleation temperatures
Latent heat released at oC
Latent heat released at oC
5.1±1.3
16.1±0.2
-20
-20
-4
?
-10
-6
-8
Vial shaken
-10
-12
-14
-16
-18
-4
-6
Vial shaken
-8
-10
-12
-14
-16
-18
-20
0
5
10
15
20
25
30
35
Freeze/thaw cycle
40
45
50
55
-20
0
5
10
15
20
25
30
35
Freeze/thaw cycle
40
45
50
55
Hot water never cools to 0oC first
Conclusion
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
Acknowledgments
• I wish to thank Cara Walkin, Julie
Galluccio and Mark Stephens for
comments and suggestions.
• 4 March 2010