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Density of Earths inner core = 232.3 g/cm3

no-one-particular

no-one-particular

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density of earth = 5.515 g/cm3
density of ultramafic rock = 3.3 g/cm3
Radius of earth = 6370 km
Radius of core = 6370 - 2890 = 3480 km

Average density of entire core = (5.515-3.3)*(6370^3/3480^3)+3.3 = 16.9 g/cm3
https://www.wolframalpha.com/input/?i=(5.515-3.3)*(6370^3/3480^3)+3.3

Radius of inner core = 1220 km
Density of outer core = density of liquid iron = 7.2 g/cm3

Density of inner core = (16.9-7.2)*(3480^3/1220^3)+7.2 = 232.3 g/cm3
https://www.wolframalpha.com/input/?i=(16.9-7.2)*(3480^3/1220^3)+7.2

Density of iron = 7.87 g/cm3 (bcc) or 8.6 g/cm3 (fcc/close packing)
Density of inner core = 232.3 g/cm3 = 27 * 8.6 g/cm3
Exactly 27 times denser!
This means that the iron atoms in the inner core are exactly three times smaller
This is the expected result if electron shells are evenly spaced.
(Except it isn't clear why the iron atoms go from 3rd to 1st electron shell rather than 3rd to 2nd)
Iron has 4 electron shells but the 4th is already degenerate (which is why its a metal and a conductor)


Gravity at the top of the inner core = (232.3/5.515)*(1220/6370) = 8.067 g's

3/5 of earth gravity is due to density 3.3
Gravity = (0.6 g's * r/6370 km) + (0.4 g's * (6370 km)^2/r^2) for r=3480 to 6370 km

Gravity = 1.668 g's at r=3480 km
1.668*7.2/16.9 = 0.71 g's of that is due to density 7.2
Gravity = ( 0.71 g's * r/3480 km) + (0.958 g's * (3480 km)^2/r^2) for r=1220 to 3480 km
Gravity = 8.04 g's at r=1220 km 

integral of [ (0.6 * r/6370) + (0.4 * (6370)^2/r^2)] for r=3480 to 6370 = 3456 g's * km
integral of [( 0.71 * r/3480) + (0.958 * (3480)^2/r^2)] for r=1220 to 3480 = 7260 g's * km

3456 g's * 1 km * 3.3 g/cm3 = 1.13 * 10^6 bar
7260 g's * 1 km * 7.2 g/cm3 = 5.13 * 10^6 bar

Pressure at top of inner core = 1.13 + 5.13 = 6.26 million bar
 
Bomb#20 said:
no-one-particular said:
Density of inner core = (16.9-7.2)*(3480^3/1220^3)+7.2 = 232.3 g/cm3


Click to expand...
Wikipedia says it's about 13 g/cm3.

It is mostly Iron with some nickel and other stuff. At surface pressure it is about 8 g/cm3. That is an impressive amount of squishing to get it to 13.

https://en.wikipedia.org/wiki/Structure_of_the_Earth
Click to expand...

It is mostly Iron with some nickel and other stuff. At surface pressure it is about 8 g/cm3. That is an impressive amount of squishing to get it to 13.

As a thought experiment, if 1 kg of core (model it as just iron) was transported instantly to the earth's surface what would the effect be? How much pressure energy (ΔPV ?) and heat energy (I know there are more technical aspects to the energy like enthalpy and so on) would it shed to be at 25 Centigrade and 1 atm pressure?
 
Last edited:
repoman said:
As a thought experiment, if 1 kg of core (model it as just iron) was transported instantly to the earth's surface what would the effect be? How much pressure energy (ΔPV ?) and heat energy (I know there are more technical aspects to the energy like enthalpy and so on) would it shed to be at 25 Centigrade and 1 atm pressure?
Click to expand...

I would think it would explode rather violently. Regaining that 40% of it's volume would happen very fast.
 
Loren Pechtel said:
repoman said:
As a thought experiment, if 1 kg of core (model it as just iron) was transported instantly to the earth's surface what would the effect be? How much pressure energy (ΔPV ?) and heat energy (I know there are more technical aspects to the energy like enthalpy and so on) would it shed to be at 25 Centigrade and 1 atm pressure?
Click to expand...

I would think it would explode rather violently. Regaining that 40% of it's volume would happen very fast.
Click to expand...
No it wouldn't. Iron is lazy. Why do you think they have to put carbon to make steel? Because if the carbon isn't there making things happen, the iron just sits there not doing anything.
 
no-one-particular said:
density of earth = 5.515 g/cm3
density of ultramafic rock = 3.3 g/cm3
Radius of earth = 6370 km
Radius of core = 6370 - 2890 = 3480 km

Average density of entire core = (5.515-3.3)*(6370^3/3480^3)+3.3 = 16.9 g/cm3
https://www.wolframalpha.com/input/?i=(5.515-3.3)*(6370^3/3480^3)+3.3

Radius of inner core = 1220 km
Density of outer core = density of liquid iron = 7.2 g/cm3

Density of inner core = (16.9-7.2)*(3480^3/1220^3)+7.2 = 232.3 g/cm3
https://www.wolframalpha.com/input/?i=(16.9-7.2)*(3480^3/1220^3)+7.2

Density of iron = 7.87 g/cm3 (bcc) or 8.6 g/cm3 (fcc/close packing)
Density of inner core = 232.3 g/cm3 = 27 * 8.6 g/cm3
Exactly 27 times denser!
This means that the iron atoms in the inner core are exactly three times smaller
This is the expected result if electron shells are evenly spaced.
(Except it isn't clear why the iron atoms go from 3rd to 1st electron shell rather than 3rd to 2nd)
Iron has 4 electron shells but the 4th is already degenerate (which is why its a metal and a conductor)


Gravity at the top of the inner core = (232.3/5.515)*(1220/6370) = 8.067 g's

3/5 of earth gravity is due to density 3.3
Gravity = (0.6 g's * r/6370 km) + (0.4 g's * (6370 km)^2/r^2) for r=3480 to 6370 km

Gravity = 1.668 g's at r=3480 km
1.668*7.2/16.9 = 0.71 g's of that is due to density 7.2
Gravity = ( 0.71 g's * r/3480 km) + (0.958 g's * (3480 km)^2/r^2) for r=1220 to 3480 km
Gravity = 8.04 g's at r=1220 km 

integral of [ (0.6 * r/6370) + (0.4 * (6370)^2/r^2)] for r=3480 to 6370 = 3456 g's * km
integral of [( 0.71 * r/3480) + (0.958 * (3480)^2/r^2)] for r=1220 to 3480 = 7260 g's * km

3456 g's * 1 km * 3.3 g/cm3 = 1.13 * 10^6 bar
7260 g's * 1 km * 7.2 g/cm3 = 5.13 * 10^6 bar

Pressure at top of inner core = 1.13 + 5.13 = 6.26 million bar
Click to expand...

 
Jimmy Higgins said:
Loren Pechtel said:
I would think it would explode rather violently. Regaining that 40% of it's volume would happen very fast.
Click to expand...
No it wouldn't. Iron is lazy. Why do you think they have to put carbon to make steel? Because if the carbon isn't there making things happen, the iron just sits there not doing anything.
Click to expand...

When you bring that chunk up to the surface the outward pressure will be the same as the inward pressure was when it sat in Earth's core. Nothing is remotely strong enough to hold against that pressure.
 
Loren Pechtel said:
Jimmy Higgins said:
No it wouldn't. Iron is lazy. Why do you think they have to put carbon to make steel? Because if the carbon isn't there making things happen, the iron just sits there not doing anything.
Click to expand...

When you bring that chunk up to the surface the outward pressure will be the same as the inward pressure was when it sat in Earth's core. Nothing is remotely strong enough to hold against that pressure.
Click to expand...

I did very simple inaccurate math saying that for the 1kg iron cube (5x5x5 cm on a side then squished to 60% of normal size) all of the delP (3.3*10^11 Pa) and delV (0.4*1.25*10^-4 m^3) would be used to expand the cube and only on one face. I got that it would be traveling at about 5.7 km/sec from the power of unspringing from this too simple of a model. Escape velocity is about 11.2 km/sec.
 
Loren Pechtel said:
Jimmy Higgins said:
No it wouldn't. Iron is lazy. Why do you think they have to put carbon to make steel? Because if the carbon isn't there making things happen, the iron just sits there not doing anything.
Click to expand...

When you bring that chunk up to the surface the outward pressure will be the same as the inward pressure was when it sat in Earth's core. Nothing is remotely strong enough to hold against that pressure.
Click to expand...
I'm curious what you found in my post that even remotely suggested I was being serious.
 
Density of earth = 5.515 g/cm3
Density of ocean = 1.0 g/cm3
Density of continental crust = 2.7 g/cm3 (granite)
.....2*10^22 kg / (2.7 g/cm3) = 7.4 * 10^9 km3 = 0.34 * volume of moon = 0.25 volume of d'' layer
Density of upper 600 km of mantle = 3.0 g/cm3 (basalt/gabbro)
.....Upper 600 km = 0.3068 * volume of mantle
Density of lower mantle = 3.4 g/cm3 (olivine)
Average density of mantle = 3.27756
.....(5.515*6370^3-(17)*(3480^3))/(6370^3-3480^3) = 3.27756
Density of outer core = density of liquid iron = 7.2 g/cm3


Radius of earth = 6370 km
Average density below 600 km = (5.515-3.0)*(6370^3/5770^3)+3.0 = 6.384 g/cm3
https://www.wolframalpha.com/input/?i=(5.515-3.0)*(6370^3/5770^3)+3.0

Radius of core = 6370 - 2890 = 3480 km
Average density of entire core = (6.384-3.4)*(5770^3/3480^3)+3.4 = 17.00 g/cm3
https://www.wolframalpha.com/input/?i=(6.384-3.4)*(5770^3/3480^3)+3.4

Radius of inner core = 1220 km
Density of inner core = (17.00-7.2)*(3480^3/1220^3)+7.2 = 234.65 g/cm3
https://www.wolframalpha.com/input/?i=(17-7.2)*(3480^3/1220^3)+7.2

Density of nickle =8.90 g/cm3 (fcc)
Density of iron = 7.87 g/cm3 (bcc) or 8.6 g/cm3 (fcc/close packing)
Density of inner core = 234.65 g/cm3 = 27 * 8.69 g/cm3
Exactly 27 times denser!

This means that the iron atoms in the inner core are exactly three times smaller
Iron has 4 electron shells but the 4th is already degenerate (which is why its a metal and a conductor)
Radius of iron atom in core = ((232/(1.2*0.125))*(4/56))^0.3333 = 1/4.79757 helium radii.
And iron atom in the ground electron state would be expected to be 1/13 helium nuclii.
It would appear from this that each electron shell is three times larger than the previous shell


It would appear that all rocky bodies differentiate into an dense core overlaid with a lighter material consisting of whatever is left over after the core has finished settling out.
Earth differentiated into Basalt and Olivine.
I think Theia (and our moon) differentiated into Granite and something even denser than Olivine (Pyrope/Silicate perovskite?).
When Theia struck the Earth the granite became the continental crust and the denser material sank to the core and became the d'' layer.
.....Volume of d'' layer = 4 * pi * (3480 km)^2 * 200 km = 3.0 * 10^10 km3
.....Volume of moon = 2.2 * 10^10 km3
.....Density of d'' layer = 3.5 g/cm3
If, like Ceres, Theia had a large amount of water ice on its surface then that could also explain where our ocean came from.
.....volume of ocean / moon surface area = 35 km

https://en.wikipedia.org/wiki/Theia_(planet)



Gravity at the top of the inner core = (234.65/5.515)*(1220/6370) = 8.1488 g's

3/5.515 of earth gravity is due to density 3.0
solve [ ((3/5.515) * r/6370 ) + ((2.515/5.515) * (6370 )^2/r^2) ] for r=5770 to 6370 km

Gravity = 1.04854 g's at 5770 km
3.4/6.384 of that is due to density 3.4
solve [ ((3.4/6.384) *1.04854 * r/5770 ) + ((2.984/6.384) * 1.04854 * (5770 )^2/r^2)] for r=3480 to 5770 km

Gravity = 1.68416 g's at r=3480 km
7.2/17 = 0.71 g's of that is due to density 7.2
solve [ ((7.2/17)*1.68416 * r/3480) + ((9.8/17)*1.68416 * (3480)^2/r^2)] for r=1220 to 3480 km
Gravity = 8.15 g's at r=1220 km 

integral of [ ((3/5.515) * r/6370 ) + ((2.515/5.515) * (6370 )^2/r^2) ] for r=5770 to 6370 = 613
integral of [ ((3.4/6.384) *1.04854 * r/5770 ) + ((2.984/6.384) * 1.04854 * (5770 )^2/r^2)] for r=3480 to 5770 = 2886
integral of [ ((7.2/17)*1.68416 * r/3480) + ((9.8/17)*1.68416 * (3480)^2/r^2)] for r=1220 to 3480 = 7347

613 g's * 1 km * 3.0 g/cm3 in bar = 180,000 bar
2886 g's * 1 km * 3.4 g/cm3 in bar = 962,000 bar
7347 g's * 1 km * 7.2 g/cm3 in bar = 5,190,000 bar

Pressure at 600 km = 180,000 bar
Pressure at top of outer core = 1,142,000 bar
Pressure at top of inner core = 6,332,000 bar
 
Each electron shell is 3 times bigger than the previous

D5yAI52.png
 
???

At any rate, I will defer for the most part to physicists, material scientists and seismologists. That is empirical and backed up by two or more independent lines of evidence.

The densities you are talking about in the inner core are more like brown dwarf levels.

You seem to be on a mystical, pseudoscience angle. Not saying that with a mean intention. This stuff is pretty simple and actually mundane when it gets down to nuts and bolts. It took a lot of work to get there (knowing what the inner core density is) and it deserve respect and appreciation, but it not insanely complicated and everyone else is not wrong by factor of 18.

Not trying to appeal to authority, but lpetrich is whip-crack smart about this topic and if you want to correct him you have to bring strong evidence.
 
repoman said:
???

At any rate, I will defer for the most part to physicists, material scientists and seismologists. That is empirical and backed up by two or more independent lines of evidence.

The densities you are talking about in the inner core are more like brown dwarf levels.

You seem to be on a mystical, pseudoscience angle. Not saying that with a mean intention. This stuff is pretty simple and actually mundane when it gets down to nuts and bolts. It took a lot of work to get there (knowing what the inner core density is) and it deserve respect and appreciation, but it not insanely complicated and everyone else is not wrong by factor of 18.

Not trying to appeal to authority, but lpetrich is whip-crack smart about this topic and if you want to correct him you have to bring strong evidence.
Click to expand...

not trying to appeal to Authority? That's exactly what you are doing
 
He has a knowledge base that has been proven many times. This is not like him being a preacher.

You are trying to tell me that the inner core of the earth is 18 times higher than seismologists have determined from a model. The model may be wrong and you right, but if I were a betting man I would bet against your calculation.

I have been off in calculations in the past and found out what I did wrong. I learned stuff in the process. Welcome to the club.
 
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