| I put 8 oz. of water in a cup and added enough
ice to make it 12 oz. When the ice melted it was
still 12 oz. So if the polar ices melted, would it
not cause flooding because it is all the same volume?|
|Question Date: 2014-08-08|
First, ice is less dense than water which means
that if you have 12 oz of ice-water, when the ice
melts you should get less than 12 oz if you
measure accurately. The density of ice is about
0.9167 g/cm3 whereas the density of
water is about 0.997 g/cm3 if you had
12 fluid ounces of ice and let it melt and warm to
room temperature, you would be left with
12*0.9167/0.997=11.034 fluid ounces of water.
It is important to note that in this
experiment, the total volume of the
ice+water is what is measured. If instead
you put ice in water and record the height of the
water before and after the water melts, you will
see that the water level does not change
significantly. This is because the ice floats and
some of it is above the water line before it
melts. This ice is displacing a volume of water
corresponding to the mass of the ice. When the ice
melts it will then occupy the same volume of water
which corresponds to the mass of the water it
displaced before it was melted. When this happens
you will see no change in volume (neglecting the
small change in the density of liquid water on
warming from 0 C to room temperature). Therefore,
when you conduct an experiment, it is important to
be precise about exactly what you are measuring
and how you are measuring it. In this experiment,
if you are measuring the water level, you will see
no change, but if you are measuring the overall
volume of water+ice, you will see an overall
Second, the reason sea levels are expected to
rise when ice caps melt during global warming is
due to the fact that ice that is not already
floating in the oceans is not contributing to the
height of the sea (such as glaciers sitting on top
of land masses). In other words, the analogous
experiment would be to put a bunch of ice in a
funnel on top of your glass of water and then let
the ice melt and flow into the glass of water.
Obviously the water level in the glass will rise.
This is an interesting observation! Perhaps on a
very small scale melting ice does not
significantly change the volume of liquid water,
but certainly on a large scale it does. Consider
that when water turns to ice, its density
decreases approximately 9% (from about 1
g/cm3 to 0.93 g/cm3).
This reduction in density is why ice floats on
top of water unlike most other materials which
sink to the bottom when they freeze. If you
started with 8 fl. oz. of water and 4 oz. of ice
to make 12 oz. total, when the ice melts to water
the net increase in water should be 4 oz. x 9% =
0.36 oz. Thus you should have 12.36 oz. of water
at the end, where mass is conserved but total
volume has increased just slightly. This small
change is very significant when it comes to
melting polar ice caps—imagine how much water is
stored in those structures!
Your question may be made further challenging by
recalling that solid water (ice) is *less dense*
than liquid water. Therefore, one would expect a
net volume *decrease* upon turning glaciers into
The problem with this line of thinking is that
none of the glaciers in question are currently
submerged! The added volume being discussed is the
volume which is currently occupying the air - not
contributing to the sea level. Take 12 oz of ice
cubes from your ice tray and place them in an
empty cup, then let them melt. The water
level in your cup will rise!
P.S. You may also want to check your
measurements. The difference is slight, but you
should have observed a net decrease in the total
volume of water in your cup after melting (since
ice is less dense than liquid water). Controlling
for evaporation, this is a reasonable way of
calculating the density of ice provided you weigh
the cubes before hand.
Not quite, there are unfortunately two problems
with this experiment. The first problem is that
you probably have some small measurement error.
Ice is about 8% less dense than water, so after
the ice melted you should should have ended up
with about 11.7 oz of water, not 12. But it is a
small different so it can be hard to measure, try
more ice next time. There is also possibly some
small unit confusion, I am assuming you are using
fluid ounces instead of weight ounces.
But even still, this would seem to support your
hypothesis even more strongly - if the ice melts
and then takes up less volume because it is more
dense after melting, then should ice caps melting
reduce ocean levels? The answer is no. The polar
ice caps are floating on top of the water because
they are less dense than the water, so when they
melt a lot of ice that was floating on top of the
ocean and not contributing to the sea level will
end up as water in the ocean, which causes the sea
level to rise.
Archimedes' law: a floating body displaces its
weight, while a sinking body displaces its volume.
The ice cubes were floating in the water, which
means that their weight, not their volume, was
forcing the water level up to the 12 oz.-mark.
When the ice melted, their mass was simply added
to the water, leaving it still at the 12 oz.-mark.
Incidentally, this does have applications to
ice cap melting: the melting of SEA ICE (e.g. the
Antarctic Ross Ice Shelf) does NOT raise global
sea levels, because the ice was floating on the
surface of the ocean, and therefore displacing its
weight and not its volume. The ice that matters as
far as sea-level rise is concerned is the ice that
is actually sitting on continents and not floating
in the ocean. There is quite a lot of ice still on
the continents - enough for about 20 meters of sea
level rise on Greenland, and another 60 m in
Antarctica (the latter of which, thankfully, is
unlikely to melt even in extreme global warming
scenarios, just due to the positions of the
continents and ocean circulation).
Very nice experiment!
This is true - icebergs frozen displace as much
water as they would melted. The real contribution
to sea-level rise would be the ice on Antarctica,
or Greenland. This ice is on land rather than
floating (Antarctica has solid ground under all
the ice). If all the ice on Antarctica melted and
flowed into the ocean, sea levels would rise by
about 200 feet. The ice covering the ground on
Antarctica is around 7000 feet thick! But, most
global warming scenarios suggest the seas will
rise much less than 200 feet, but still enough to
flood many coastal areas of the world.
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