Re: suppose there was an earth sized watermelon?

From: Peter Webb (webbfamily-diespamdie_at_optusnet.com.au)
Date: 11/19/04 

Date: Fri, 19 Nov 2004 22:07:36 +1100

4 j/degree
4 kJ/degree/kg

400 metres increase 1 degree

40 kms = boiling point

"Gerry Quinn" <gerryq@DELETETHISindigo.ie> wrote in message
news:MPG.1c06aa336cc65cd5989b11@news.indigo.ie...
> In article <1d7e2eb0.0411171825.1c48dc2b@posting.google.com>,
> cerebureaucracy@hotmail.com says...
>> i know such a thing is not possible of ever existing, but suppose...
>>
>> with a snap of a finger, planet earth turned into a giant watermelon.
>>
>> what would happen?
>>
>> this is my prediction. tell me if you think i'm right.
>>
>> gravity would immediately collapse the watermelon and the center would
>> turn very hot due to the sheer pressure of the damn thing.
>
> Not due to the 'pressure' as such, but due to the work done in
> compressing the central parts. (Note that the Earth's rocks are already
> compressed, though water would compress more. The Earth-size watermelon
> would shrink to be smaller than the Earth is now, even a bit smaller
> than the Earth would shrink if it were somehow uncompressed and left to
> settle.)
>
>> as the watermelon collapses, the liquid in the melon would burst out
>> of the cracked rinds and evaporate into gas. planet melon would keep
>> shrinking and shrinking until all the water boiled and evaporated and
>> only bits of burnt rinds would remain which would then drift off into
>> space like asteroids.
>
> Wrong. Let's assume for the sake of argument that we start with a ball
> of water. How much it shrinks will depend on the equation of state of
> water at high pressures. As it shrinks it will heat up, indeed - to
> find out how much you would have to integrate pressure x area /
> distance, and the distance in turn depends on the pressure of H2O at a
> given density. Probably the latter would have to be estimated as some
> pressures involved would be greater than testable in a laboratory.
>
> My guess is that the core of the Earth would convert into a form of Ice
> that is stable at relatively high temperatures and pressures (there are
> about nine known forms of ice, all but one denser than water and stable
> only at pressure). This would be quite hot. Outside it would be a
> layer of water at boiling point (some miles deep - 50-100 perhaps?),
> surrounded by a dense atmosphere of steam. If there was enough steam,
> some would escape into space due to the Solar Wind or the gravitational
> pull of other bodies. I would guess this would be a very small part of
> the total water.
>
> The temperature of the boiling sea would depend on the atmospheric
> pressure. Whether heat from the centre would transmit as convection or
> huge eruptions of steam, I can't say.
>
> Pure energy conservation should tell you that the planet could not *all*
> boil into space!
>
> This would be an interesting physics problem and given a few hours I
> could probably make ballpark estimates. However, I'm pretty sure of the
> general trend as described above.
>
> - Gerry Quinn
>
>

To elaborate slightly on the heat part of this.

We can assume that almost all the energy deriving from the contraction goes
into heat - a small part will be retained as potential energy resulting from
compression, but the relative incompressability of water means this will be
a small component.

Each gram of water requires 4 Joules of energy to raise it 1 degree; a kg
requires 4 kJ. The energy generated from a kg falling under gravity is 9.8
K/metre, say 10J/metre, so every metre the surface drops raises the
temperature by 1/400 degree. A drop of 400 metres gives you a degree, so to
raise it to boiling (+80 degrees) requires about a 30 kms fall.

This is very roughly 1/200th of the earths radius. A contraction in volume
of x% causes a contraction in radius of (x/3)%. So if the water compressed
by only 1/70th, there would be sufficient energy released to boil the top
layers. Nobody knows what the actual contraction would be, but 1/70 is only
a (cough) drop in the ocean ... a drop of say 10% would increase the surface
water temperature to about 600 degrees C ... thats a lot of steam.

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