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05/23/2007
Hot Ice
A few weeks ago (5/2/2007), I wrote about the discovery of a
planet termed “super-Earth” orbiting Gliese 581, a red dwarf star.
This past week, the same team of Swiss-based astronomers
announced another planet orbiting another red dwarf star 33
light-years from Earth. As opposed to super-Earth, which may
be a candidate for hosting some form of life, the newly
announced planet seems way too hot for any life as we know it.
This is a Neptune-size planet that whips around its star, GJ 436b,
in only 3 days and sports toasty temperatures approaching 250
degrees Centigrade (about 470 degrees Fahrenheit). Its
discovery was a lucky one in that its orbit carries it between its
star and our Earth. The researchers could observe the decrease in
the amount of light from the star when the planet passed across
the face of the star. From the decrease in the amount of starlight,
they could calculate the diameter of the planet and, I’m
assuming, from the orbit of the planet and the mass of the star
they could calculate the mass of the planet.
The surprise came when the mass turned out to be consistent
with the planet being mostly hot solid water – ice! Of course,
my natural tendency was to think these guys and/or gals are out
of their mind. How can ice exist on such a hot body with temps
way above the boiling point of water? Then I read an article on
the discovery by Maggie Fox posted on the Scientific American
Web site. The reason that ice can exist at such temperatures is
that the pressures on this Neptune-size planet are quite high.
This didn’t seem right when I recalled that I’ve heard that the
reason ice skaters glide so smoothly across the ice is that the
weight of the skater on the thin blades is sufficient to melt the ice
under the skates. In other words, increasing the pressure lowers
the freezing/melting point of water/ice. Hence, the slippery
skating. But if pressure lowers the melting point of ice what
about that high-pressure hot planet? Clearly, I had to look more
deeply into the subject.
Accordingly, I turned to my shopworn 1944 edition of my
battered physical chemistry textbook by Frederick Getman and
Farrington Daniels. Sure enough, on page 157 (heavily
underlined by me in 1945), is a calculation using an equation
derived by a fellow named Clapeyron back in 1834. The
equation shows that the effect of pressure on the melting point of
ice depends on the heat needed to melt the ice and on the volume
change when water freezes to form ice. Those of us old enough
to have had our milk delivered in bottles know that water
increases in volume when it freezes, as witnessed by the milk
pushing the cap off the top of the milk bottle when left outside in
freezing weather.
The Clapeyron calculation says that it takes 133 atmospheres
pressure to lower the melting point of ice 1 degree Centigrade.
(An atmosphere is about 14.7 pounds per square inch.) But wait
a minute. The high pressures on that hot planet should be high
enough to lower the melting point significantly, so how can there
be any ice? Well, turning to page 311 of my old textbook, I
found the key to the answer. At high pressures, in 1944, there
were seven different known forms of ice having different crystal
structures. All of these high-pressure ices are denser than water,
unlike the ordinary ice we skate on or add to our drinks. If water
froze to form any of these high-pressure ices, the volume would
decrease and the cap would stay on our bottle of milk.
If the volume decreases on freezing, Clapeyron’s equation tells
us that the freezing point will increase, not decrease, with
increasing pressure. My textbook being over 60 years old, I went
online to see if there was anything new in the way of ice. Sure
enough, there are now at least 13 or 14 different forms of ice that
have been found at high pressures. I found a reference to the
existence of one high-pressure ice being solid at 175 degrees
Centigrade, way above the boiling point of water (100 degrees
Centigrade) and approaching the nearly 250 degree temperatures
possible on the planet orbiting GJ 436b. My search was not an
exhaustive one and now I’m willing to accept that there is an ice
(or ices) that can exist on a toasty hot planet.
Oh, about that ice skating bit, in the course of searching the Web,
I encountered conflicting views on the subject. The argument
that the pressure of the skate on the ice causes the ice to melt,
forming a film of water, seems rather dicey. I looked up the
thickness of the typical blade of an ice skate and found that it
was about an eighth of an inch for hockey and about half that for
speed skating. Taking the hockey example, if the blade is a foot
long I calculate it has an area of about 1.4 square inches. For
convenience, let’s say our hockey player weighs 140 pounds, a
bit light I admit. However, that translates to 140/1.4 = 100
pounds per square inch, or about 7 atmospheres. Remembering
that Clapeyron said it takes 133 atmospheres to lower the melting
point 1 degree, our hockey player, skating flat on his skate, only
lowers the melting point by 7/133 = 0.05 degrees C.
If the temperature of the ice is more than a degree or so below 0
degrees C (32 degrees F) lowering the melting point a degree
won’t melt the colder ice. Another urban myth down the drain?
Possibly. On the other hand, water is a crazy substance and I’ve
seen some work suggesting that, even when water ice is
significantly below the freezing point, the surface molecules are
more like a liquid than in the solid bulk ice. Even if true, skaters
can skate on ice that’s much colder than the melting/freezing
point where even those surface molecules ought to be tied down
to the rest of the molecule in the ice. Even today, water in both
solid and liquid forms is not a done deal and papers on its
structure and properties will continue to appear for some time to
come.
I just happened to think. What will happen to that hot icy planet?
Will it eventually get so close to the red dwarf star that it just
evaporates or will it get sucked into the star with its icy core still
intact? If the latter, that should be some spectacular explosion
when all that hot ice becomes superheated steam!
Allen F. Bortrum
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