# Query

avalanchethecat
Science 19 Dec '10 12:16
1. avalanchethecat
Not actually a cat
19 Dec '10 12:16
If a planetary sized body of water existed, would the core be solid? This is suggested in Iain M Banks' new novel, but I thought that water was at it's densest as a fluid at around 4 degrees C. I expect he's right, but can someone explain to me why?
2. 19 Dec '10 12:54
Originally posted by avalanchethecat
If a planetary sized body of water existed, would the core be solid? This is suggested in Iain M Banks' new novel, but I thought that water was at it's densest as a fluid at around 4 degrees C. I expect he's right, but can someone explain to me why?
It is also a matter of preassure.
Can you apply a preassure of water so it becomes solid? And if so, which temperature interval is needed?

I think you can, but I don't know about the temp needed.
3. joe shmo
Strange Egg
19 Dec '10 14:57
Originally posted by FabianFnas
It is also a matter of preassure.
Can you apply a preassure of water so it becomes solid? And if so, which temperature interval is needed?

I think you can, but I don't know about the temp needed.
As the pressure inceases, the temperature that solid H20 (saturated) can exist at also increases. So thats promising for the argument. However, the data tables out of my text don't cover pressures as extream as would be experienced by a planetary sized body of water.
4. joe shmo
Strange Egg
19 Dec '10 16:211 edit
Originally posted by joe shmo
As the pressure inceases, the temperature that solid H20 (saturated) can exist at also increases. So thats promising for the argument. However, the data tables out of my text don't cover pressures as extream as would be experienced by a planetary sized body of water.
As the pressure inceases, the temperature that solid H20 (saturated) can exist at also increases. So thats promising for the argument. However, the data tables out of my text don't cover pressures as extream as would be experienced by a planetary sized body of water.

If you want a place to start looking in the realm of pressure its going to be a function of the radius of the planet. I say this is a ball park estimate, but you probably searching for something the size of a quarter in the ball park.

dP/dz = -pg (eq1)

P=pressure
z= elevation
p=density of water
g=acceleration due to gravity

we are going to assume that the density of water is constant ( this is in direct conflict with the objective (ie. the solid core of ice has differing density), and depending on the size of your planet(ie. if really large) compressibility of the fluid could come into play).

To get "g" the acceleration due to gravity, use Newtons Law of Gravitation:

F=G*m1*m2/(r^2)
arbitrarily divide through by one of the masses, and make the mass and the force differential.

dF/m1 = G*dm2/r^2

dm2= p*dV (assuming p is constant)

dV= 4*pi*r^2*dr (assuming the planet is spherical, r being it radius)

combine the above equations by substitution and integrate

1/m1*Int(dF)= 4*pi*G*p*Int(dr)

g= 4*pi*G*p*r (with initial conditions r=0,g=0) (eq2)

substitute eq2 into eq1

dP/dz= -p^2*4*pi*G*r

dz=dr
separate variables and integrate with conditions(r=r_planet,P=0)

P=(p^2*4*pi*G*(r_planet)^2)/2 -(p^2*4*pi*G*(r_core)^2)/2 (eq3)

G=Gravitational constant 6.67428*10^(-11) m^3/(kg*s^2)

everything else you pick( just make sure units are metric)

This would be the(ball park) pressure at the liquid, solid interface.

Using the pressure, and a suitable temp(?) you can define the state the water is in(that is assuming the thermo data can be found in the vicinity of the result).

edit: I remember my Thermo Prof say that ice can be compressed isothermally back to liquid quite easily, this now makes me think that the core temp would have to be really cold(this opposes my first post, and must be because the tables were for solid to vapor).
5. joe shmo
Strange Egg
19 Dec '10 18:35
Originally posted by joe shmo
As the pressure inceases, the temperature that solid H20 (saturated) can exist at also increases. So thats promising for the argument. However, the data tables out of my text don't cover pressures as extream as would be experienced by a planetary sized body of water.

If you want a place to start looking in the realm of pressure its going to be a functi ...[text shortened]... lly cold(this opposes my first post, and must be because the tables were for solid to vapor).
Using to the model above, and a planet the size of earth, with an ice core comprable to that of the earths core. The pressure at the interface is about 16TPa

The following is a phase diagram of water

http://www.lsbu.ac.uk/water/phase.html

using it, I surmise that an ice core of this size would have no trouble exististing.
6. avalanchethecat
Not actually a cat
20 Dec '10 15:54
Originally posted by joe shmo
Using to the model above, and a planet the size of earth, with an ice core comprable to that of the earths core. The pressure at the interface is about 16TPa

The following is a phase diagram of water

http://www.lsbu.ac.uk/water/phase.html

using it, I surmise that an ice core of this size would have no trouble exististing.
Well that all sounds very much like you know what you're talking about! Thanks very much for your efforts Joe, not that I ever doubted Banks, of course.
7. 20 Dec '10 16:47
Originally posted by joe shmo
Using to the model above, and a planet the size of earth, with an ice core comprable to that of the earths core. The pressure at the interface is about 16TPa

The following is a phase diagram of water

http://www.lsbu.ac.uk/water/phase.html

using it, I surmise that an ice core of this size would have no trouble exististing.
Moreover, a ball of nothing but water would have no molten metal core to hold (or even generate) heat from its creation, no rock surface to insulate that core, and a very high albedo, ought to be a lot colder than an equivalent-sized normal planet in the same orbit. I would not be at all surprised if it were as near to zero Kelvin as makes no difference.

Richard