Re: Superman

From: David Lee (davidlee_malvern_at_dont.use.this.bit.hotmail.com)
Date: 10/11/04 

Date: Mon, 11 Oct 2004 19:09:09 +0100

Darren Dunham wrote in-line...(so I'm staying at the top)

You haven't the first clue about Archimedes principle! There is absolutely
NO loss of mass implied in my argument - your problem is that you have
entirely ignored the difference in density between brine and fresh water.

The average density of surface seawater is about 1027 kg per cubic metre.
Consider an iceberg with a mass of 1 metric tonne (1000kg). This will
displace 1 tonne of seawater - a volume of 0.974 cubic metres. If we remove
this iceberg from the ocean then the ocean's effective volume will be
reduced by just this amount. Now imagine we melt the iceberg - it will
produce a volume of water of exactly 1 cubic metre. If this water is
returned to the ocean then there will be a net INCREASE in volume of 0.026
cubic metres.

Of course these numbers are a simplification since the density of seawater
varies with salinity and temperature and brine is not an ideal solution so
the volumes will not add linearly. However the principal is sound - melting
an iceberg will cause a small increase in the sea level.

A similar, counter-intuitive, argument is the answer to the question: A boat
is floating on a pond. In the boat is a large rock. If the rock is thrown
into the water, what will happen to the level of the water in the pond?
'Common-sense' suggests that the water level will rise whereas in actual
fact it will fall. When in the boat the rock will displace its mass of
water and when submerged, its volume. Since the specific gravity of the
rock is greater than that of water it will displace more water when floating
than when submerged. I think that it is easier to see the truth of this
argument than in the case of the iceberg because its volume doesn't change
during the experiment. However, the principal is exactly the same except
that the relative densities are reversed, leading to an increase in water
level.

David

Darren Dunham wrote in-line...
> David Lee wrote:
> > That's true for fresh water but not for sea water. Floating ice
displaces
> > its MASS of the surrounding water but when it melts it adds its
> > VOLUME.
>
> Anything floating displaces a volume of water equivalent to its mass.
> The volume of the floating object is irrelevant. After it melts, it's
> the same mass.
>
> > When sea water freezes the salt is excluded and the floating ice is
almost
> > fresh water which is much less dense than brine.
>
> Yes. That means that the ice will float higher in the brine than it
> would in fresh.
>
> > Hence the water level will
> > rise when the sea-ice melts
>
> Huh? Lets run that backward. Are you saying that if I can freeze fresh
> water out of a salt solution that the water level would drop? Where did
> the mass go to cause the drop? I'd have to remove mass to drop the
> level, wouldn't I?
>
> , but I've no idea, off the top of my head, how
> > large this effect is. Should be easy to get a rough estimate though -
from
> > the density of brine, the average salinity of the ocean and enough
> > enthusiasm to do the sums!
>
> No.
>
> --
> Darren Dunham ddunham@taos.com
> Senior Technical Consultant TAOS http://www.taos.com/
> Got some Dr Pepper? San Francisco, CA bay area
> < This line left intentionally blank to confuse you. >

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