[alancalverd (OP)]

As an aside from the discussion on energy transfer between ice and water, consider a cube of ice immersed in water, all at 0 deg C.

All the molecules are jiggling about at random. Those at the edges and corners of the cube have the fewest bonds to other members of the cube so are most likely to acquire sufficient kinetic energy to leave the solid and enter the liquid.

It takes 334 joule/gram (latent heat of fusion)  x 3 x 10^-23 gram (mass of a water molecule) to release one molecule from ice. So by leaving, our exceptionally energetic molecule reduces the temperature (the average kinetic energy of all the remaining molecules) of the ice by a tiny amount.

So a water molecule could now attach itself to the ice to restore thermal equilibrium. But the most probable place for the impact to occur is on a flat surface, not an edge.

Thus if we maintain absolute equality of temperature between the ice and the water, the cube will gradually turn into a sphere!

[Bored chemist]

The pressure is slightly higher at the bottom of the sphere than at the top.
So the melting point should be slightly lower.
Ice should melt at the base of the sphere and re-freeze at the top.

The rate of change of melting point with depth is measurable and you need to consider it in the highest accuracy temperature calibrations.
https://www.bipm.org/documents/20126/28439029/working-document-ID-1785/b55e5aa5-5e8d-5d6b-8c8d-4d1ae0024d97/
More importantly, ice will actually form crystals.
Forming crystals with a lower surface area is favoured- much as Alan says.
He has recognised a fairly well known phenomenon.
https://en.wikipedia.org/wiki/Ostwald_ripening

[Eternal Student]

Hi.

  Yeah, I quite like it.

   The sad thing is, in reality it's more like a shape change with a small energy release (and hence energy transfer) that you just can't avoid.  This small amount of energy released would tend to elevate the temperature of the mixture slightly.  You'd have to keep it in a fridge and extract heat to stand any chance of keeping everything at 0 deg. C.

    As outlined by @Bored chemist 's  and the Ostwald ripening article,    molecules at the centre of an ice cube have more bonds with other particles around them.   Molecules on the surface have the least.   Hence, unavoidably there is some energy released by forming a shape with a lower surface area to volume ratio.
    The liquid should also behave the same way, those water molecules also want to maximise the number of bonds they can sustain by being surrounded more often and having the least molecules at the surface with the ice.

Best Wishes.

[alancalverd (OP)]

The sad thing is, in reality it's more like a shape change with a small energy release (and hence energy transfer) that you just can't avoid.  This small amount of energy released would tend to elevate the temperature of the mixture slightly.  You'd have to keep it in a fridge and extract heat to stand any chance of keeping everything at 0 deg. C.

So global warming is caused by the polar ice melting, not the other way around? And if I have a bucket of ice and water at 0 deg C I can extract energy from it with a heat engine attached to another bucket at 0 deg C ? The perpetual  motion ice bucket has arrived!

You have to extract energy from water to get it to freeze. So it can't be possible that the ice contains more energy than the water we started with.

I smell a conundrum!

[alancalverd (OP)]

The pressure is slightly higher at the bottom of the sphere than at the top.

Not in the International Space Station. Or if you rotate the ice cube.

I'm talking physics, not engineering!

[Eternal Student]

Hi.

   I don't know.  The following seems reasonable.

So global warming is caused by the polar ice melting, not the other way around?

   Global warming is caused by many things.   I wouldn't have thought ice cubes reforming is a huge contributor.  There's also a density thing, ice floats on the top of the water and forms sheets, there's not much you can do to force it down under the water and keep all surfaces in contact with the liquid.   This is a bit different to Ostwald's crystal ripening where the crystals were dense enough to be in the solvent.

The perpetual  motion ice bucket has arrived!

    Why is there an endless amount of energy available?  There is a single most energetically favourable shape.  Once you've reached that shape, it stops, you would have thought.   

...it can't be possible that the ice contains more energy than the water we started with.

  It's sufficient if the ice (in Shape B) contains more energy than the ice (in shape A),  A < B.
Both bits of ice can have less energy than the liquid water if they want to.   A < B < C.

Best Wishes.

[Bored chemist]

I'm talking physics, not engineering!

And you have solved the problem for a spherical cow in a vacuum.
Do you not realise that gravity is part of physics?

[Bored chemist]

What Alan seems not to realise is that exactly the same thing can be said about a crystal forming.
He thinks it should be a sphere.
That's not what happens.

[Bored chemist]

So global warming is caused by the polar ice melting, not the other way around?

No. That's just silly.

What you are saying- and it's  correct- is that an sphere of ice is a more stable shape than a cube of ice.

Well , if a system changes from a less stable state to a more stable state, it will release energy- typically as heat.
So, in order to keep the temperature constant you need to either remove that heat- with a fridge or whatever- or you have to accept that the ice sphere will be a tiny bit smaller than the ice cube was. Some of the ice will have been melted by the heat released.

[chiralSPO]

some crystals grow fastest at their edges (like bismuth), or along a single axis (like rutile).

It shouldn't be surprising that oversimplified models predict oversimplified outcomes.

Depending on the exact conditions, water will form all kinds of shapes (including spheres).

see here: https://www.its.caltech.edu/~atomic/snowcrystals/class/class-old.htm