I suggest that the origin of the Mpemba effect (the freezing of hot water before cold) is due to freezing-point depression by solutes, either gaseous or solid, whose solubility decreases with increasing temperature so that they are removed when water is heated. The solutes are concentrated ahead of the freezing front by zone refining in water that has not been heated, reducing the temperature of the freezing front, and thereby reducing the temperature gradient and heat flux, slowing the progress of the freezing front. I present a simple calculation of this effect, and suggest experiments to test this hypothesis.
REFERENCES
1.
D.
Auerbach
, “Supercooling and the Mpemba effect: When hot water freezes quicker than cold
,” Am. J. Phys.
63
, 882
–885
(1995
).2.
M.
Jeng
, “Hot water can freeze faster than cold?!?
,” Am. J. Phys.
74
, 514
–522
(2006
).3.
G. S.
Kell
, “The freezing of hot and cold water
,” Am. J. Phys.
37
, 564
(1969
).4.
B.
Wojciechowski
, I.
Owczarek
, and G.
Bednarz
, “Freezing of aqueous solutions containing gases
,” Cryst. Res. Technol.
23
, 843
–848
(1988
).5.
P. K.
Maciejewski
, “Evidence of a convective instability allowing warm water to freeze in less time than cold water
,” J. Heat Transfer
118
, 65
–72
(1996
).6.
M.
Freeman
, “Cooler still - an answer?
,” Phys. Educ.
14
, 417
–421
(1979
).7.
8.
9.
10.
J. A.
Burton
, R. C.
Prim
, and W. P.
Slichter
, “The distribution of solute in crystals grown from the melt. I. Theoretical
,” J. Chem. Phys.
21
, 1987
–1991
(1953
).11.
H. E.
Huppert
and M. G.
Worster
, “Dynamic solidification of a binary melt
,” Nature (London)
314
, 703
–707
(1985
).12.
J.
Stefan
, “Über die Theorie der Eisbildung, insbesondere über die Eisbildung im Polarmeere
,” Ann. Phys. Chem.
42
, 269
–286
(1891
).13.
G.
Lamé
and B. P.
Clapeyron
, “Mémoire sur la solidification par refoidissement d’un globe solide
,” Ann. Chem. Phys.
47
, 250
–256
(1831
).14.
L. G.
Longsworth
, “Diffusion in Liquids
,” in American Institute of Physics Handbook
, 3rd ed., edited by D. E.
Gray
(McGraw-Hill
, New York
, 1972
).15.
A. V.
Eletskii
, “Diffusion
,” in Handbook of Physical Quantities
, edited by I. S.
Grigoriev
and E. Z.
Meilikhov
(CRC Press
, Boca Raton, FL
, 1997
), pp. 465
–487
.© 2009 American Association of Physics Teachers.
2009
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.