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Item 11.
Hot Water Freezes Faster than Cold! updated 11-May-1992 by SIC
----------------------------------- original by Richard M. Mathews
You put two pails of water outside on a freezing day. One has hot
water (95 degrees C) and the other has an equal amount of colder water (50
degrees C). Which freezes first? The hot water freezes first! Why?
It is commonly argued that the hot water will take some time to
reach the initial temperature of the cold water, and then follow the same
cooling curve. So it seems at first glance difficult to believe that the
hot water freezes first. The answer lies mostly in evaporation. The effect
is definitely real and can be duplicated in your own kitchen.
Every "proof" that hot water can't freeze faster assumes that the
state of the water can be described by a single number. Remember that
temperature is a function of position. There are also other factors
besides temperature, such as motion of the water, gas content, etc. With
these multiple parameters, any argument based on the hot water having to
pass through the initial state of the cold water before reaching the
freezing point will fall apart. The most important factor is evaporation.
The cooling of pails without lids is partly Newtonian and partly by
evaporation of the contents. The proportions depend on the walls and on
temperature. At sufficiently high temperatures evaporation is more
important. If equal masses of water are taken at two starting
temperatures, more rapid evaporation from the hotter one may diminish its
mass enough to compensate for the greater temperature range it must cover
to reach freezing. The mass lost when cooling is by evaporation is not
negligible. In one experiment, water cooling from 100C lost 16% of its mass
by 0C, and lost a further 12% on freezing, for a total loss of 26%.
The cooling effect of evaporation is twofold. First, mass is
carried off so that less needs to be cooled from then on. Also,
evaporation carries off the hottest molecules, lowering considerably the
average kinetic energy of the molecules remaining. This is why "blowing on
your soup" cools it. It encourages evaporation by removing the water vapor
above the soup.
Thus experiment and theory agree that hot water freezes faster than
cold for sufficiently high starting temperatures, if the cooling is by
evaporation. Cooling in a wooden pail or barrel is mostly by evaporation.
In fact, a wooden bucket of water starting at 100C would finish freezing in
90% of the time taken by an equal volume starting at room temperature. The
folklore on this matter may well have started a century or more ago when
wooden pails were usual. Considerable heat is transferred through the
sides of metal pails, and evaporation no longer dominates the cooling, so
the belief is unlikely to have started from correct observations after
metal pails became common.
References:
"Hot water freezes faster than cold water. Why does it do so?",
Jearl Walker in The Amateur Scientist, Scientific American,
Vol. 237, No. 3, pp 246-257; September, 1977.
"The Freezing of Hot and Cold Water", G.S. Kell in American
Journal of Physics, Vol. 37, No. 5, pp 564-565; May, 1969.
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Item 12.
Why are Golf Balls Dimpled? updated 14-May-1992 by SIC
--------------------------- original by Craig DeForest
The dimples, paradoxically, *do* increase drag slightly. But they
also increase `Magnus lift', that peculiar lifting force experienced by
rotating bodies travelling through a medium. Contrary to Freshman physics,
golf balls do not travel in inverted parabolas. They follow an 'impetus
trajectory':
* *
* *
(golfer) * *
* * <-- trajectory
\O/ * *
| * *
-/ \-T---------------------------------------------------------------ground
This is because of the combination of drag (which reduces
horizontal speed late in the trajectory) and Magnus lift, which supports
the ball during the initial part of the trajectory, making it relatively
straight. The trajectory can even curve upwards at first, depending on
conditions! Here is a cheesy diagram of a golf ball in flight, with some
relevant vectors:
F(magnus)
^
|
F(drag) <--- O -------> V
\
\----> (sense of rotation)
The Magnus force can be thought of as due to the relative drag on
the air on the top and bottom portions of the golf ball: the top portion is
moving slower relative to the air around it, so there is less drag on the
air that goes over the ball. The boundary layer is relatively thin, and
air in the not-too-near region moves rapidly relative to the ball. The
bottom portion moves fast relative to the air around it; there is more drag
on the air passing by the bottom, and the boundary (turbulent) layer is
relatively thick; air in the not-too-near region moves more slowly relative
to the ball. The Bernoulli force produces lift. (alternatively, one could
say that `the flow lines past the ball are displaced down, so the ball is
pushed up.')
The difficulty comes near the transition region between laminar
flow and turbulent flow. At low speeds, the flow around the ball is
laminar. As speed is increased, the bottom part tends to go turbulent
*first*. But turbulent flow can follow a surface much more easily than
laminar flow.
As a result, the (laminar) flow lines around the top break away
from the surface sooner than otherwise, and there is a net displacement
*up* of the flow lines. The magnus lift goes *negative*.
The dimples aid the rapid formation of a turbulent boundary layer
around the golf ball in flight, giving more lift. Without 'em, the ball
would travel in more of a parabolic trajectory, hitting the ground sooner.
(and not coming straight down.)
References: Perhaps the best (and easy-to-read) reference on this effect is
a paper in American Journal of Physics by one Lyman Briggs, c. 1947.
Briggs was trying to explain the mechanism behind the `curve ball' in
baseball, using specialized apparatus in a wind tunnel at the NBS. He
stumbled on the reverse effect by accident, because his model `baseball'
had no stitches on it. The stitches on a baseball create turbulence in
flight in much the same way that the dimples on a golf ball do.
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Item 13.
updated 4-SEP-1992 by SIC
Original by Bill Johnson
How to Change Nuclear Decay Rates
---------------------------------
"I've had this idea for making radioactive nuclei decay faster/slower than
they normally do. You do [this, that, and the other thing]. Will this work?"
Short Answer: Possibly, but probably not usefully.
Long Answer:
"One of the paradigms of nuclear science since the very early days
of its study has been the general understanding that the half-life, or
decay constant, of a radioactive substance is independent of extranuclear
considerations." (Emery, cited below.) Like all paradigms, this one is
subject to some interpretation. Normal decay of radioactive stuff proceeds
via one of four mechanisms:
* Emission of an alpha particle -- a helium-4 nucleus -- reducing
the number of protons and neutrons present in the parent nucleus
by two each;
* "Beta decay," encompassing several related phenomena in which a
neutron in the nucleus turns into a proton, or a proton turns into
a neutron -- along with some other things including emission of
a neutrino. The "other things", as we shall see, are at the bottom
of several questions involving perturbation of decay rates;
* Emission of one or more gamma rays -- energetic photons -- that
take a nucleus from an excited state to some other (typically
ground) state; some of these photons may be replaced by
"conversion electrons," of which more shortly; or
*Spontaneous fission, in which a sufficiently heavy nucleus simply
breaks in half. Most of the discussion about alpha particles will
also apply to spontaneous fission.
Gamma emission often occurs from the daughter of one of the other decay
modes. We neglect *very* exotic processes like C-14 emission or double
beta decay in this analysis.
"Beta decay" refers most often to a nucleus with a neutron excess,
which decays by converting a neutron into a proton:
n ----> p + e- + anti-nu(e),
where n means neutron, p means proton, e- means electron, and anti-nu(e)
means an antineutrino of the electron type. The type of beta decay which
involves destruction of a proton is not familiar to many people, so
deserves a little elaboration. Either of two processes may occur when this
kind of decay happens:
p ----> n + e+ + nu(e),
where e+ means positron and nu(e) means electron neutrino; or
p + e- ----> n + nu(e),
where e- means a negatively charged electron, which is captured from the
neighborhood of the nucleus undergoing decay. These processes are called
"positron emission" and "electron capture," respectively. A given nucleus
which has too many protons for stability may undergo beta decay through
either, and typically both, of these reactions.
"Conversion electrons" are produced by the process of "internal
conversion," whereby the photon that would normally be emitted in gamma
decay is *virtual* and its energy is absorbed by an atomic electron. The
absorbed energy is sufficient to unbind the electron from the nucleus
(ignoring a few exceptional cases), and it is ejected from the atom as a
result.
Now for the tie-in to decay rates. Both the electron-capture and
internal conversion phenomena require an electron somewhere close to the
decaying nucleus. In any normal atom, this requirement is satisfied in
spades: the innermost electrons are in states such that their probability
of being close to the nucleus is both large and insensitive to things in
the environment. The decay rate depends on the electronic wavefunctions,
i.e, how much of their time the inner electrons spend very near the
nucleus -- but only very weakly. For most nuclides that decay by electron
capture or internal conversion, most of the time, the probability of
grabbing or converting an electron is also insensitive to the environment,
as the innermost electrons are the ones most likely to get grabbed/converted.
However, there are exceptions, the most notable being the
the astrophysically important isotope beryllium-7. Be-7 decays purely
by electron capture (positron emission being impossible because of
inadequate decay energy) with a half-life of somewhat over 50 days. It has
been shown that differences in chemical environment result in half-life
variations of the order of 0.2%, and high pressures produce somewhat
similar changes. Other cases where known changes in decay rate occur are
Zr-89 and Sr-85, also electron capturers; Tc-99m ("m" implying an excited
state), which decays by both beta and gamma emission; and various other
"metastable" things that decay by gamma emission with internal conversion.
With all of these other cases the magnitude of the effect is less than is
typically the case with Be-7.
What makes these cases special? The answer is that one or another
of the usual starting assumptions -- insensitivity of electron wave
function near the nucleus to external forces, or availability of the
innermost electrons for capture/conversion -- are not completely valid.
Atomic beryllium only has 4 electrons to begin with, so that the "innermost
electrons" are also practically the *outermost* ones and therefore much
more sensitive to chemical effects than usual. With most of the other
cases, there is so little energy available from the decay (as little as a
few electron volts; compare most radioactive decays, where hundreds or
thousands of *kilo*volts are released), courtesy of accidents of nuclear
structure, that the innermost electrons can't undergo internal conversion.
Remember that converting an electron requires dumping enough energy into it
to expel it from the atom (more or less); "enough energy," in context, is
typically some tens of keV, so they don't get converted at all in these
cases. Conversion therefore works only on some of the outer electrons,
which again are more sensitive to the environment.
A real anomaly is the beta emitter Re-187. Its decay energy is
only about 2.6 keV, practically nothing by nuclear standards. "That this
decay occurs at all is an example of the effects of the atomic environment
on nuclear decay: the bare nucleus Re-187 [i.e., stripped of all orbital
electrons -- MWJ] is stable against beta decay and it is the difference of
15 keV in the total electronic binding energy of osmium [to which it decays
-- MWJ] and rhenium ... which makes the decay possible" (Emery). The
practical significance of this little peculiarity, of course, is low, as
Re-187 already has a half life of over 10^10 years.
Alpha decay and spontaneous fission might also be affected by
changes in the electron density near the nucleus, for a different reason.
These processes occur as a result of penetration of the "Coulomb barrier"
that inhibits emission of charged particles from the nucleus, and their
rate is *very* sensitive to the height of the barrier. Changes in the
electron density could, in principle, affect the barrier by some tiny
amount. However, the magnitude of the effect is *very* small, according to
theoretical calculations; for a few alpha emitters, the change has been
estimated to be of the order of 1 part in 10^7 (!) or less, which would be
unmeasurable in view of the fact that the alpha emitters' half lives aren't
known to that degree of accuracy to begin with.
All told, the existence of changes in radioactive decay rates due
to the environment of the decaying nuclei is on solid grounds both
experimentally and theoretically. But the magnitude of the changes is
nothing to get very excited about.
Reference: The best review article on this subject is now 20 years old: G.
T. Emery, "Perturbation of Nuclear Decay Rates," Annual Review of Nuclear
Science vol. 22, p. 165 (1972). Papers describing specific experiments are
cited in that article, which contains considerable arcane math but also
gives a reasonable qualitative "feel" for what is involved.
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