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CRSC calc 2, melting boogaloo: Scraping the Surface of the Planet

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In a last-ditch attempt to take out Saitama, Boros tried to release all his energy with his surface-scraping "Collapsing Star Roaring Cannon" attack, which he claimed would ruin earth's surface(https://archive.vn/GVxO8#selection-2867.35-2867.130). Previous calcs have tried to calculate this feat as a generic explosion, but looking closer at Boros's attacks in this fight we can see that they are melting the surface of the ship. Examples here, here and here, original chapter here if you want a clearer look at the damage. Extrapolating these effects onto the rest of the planet, it makes sense to calculate CSRC as an attack that melts the surface of the planet (causing devastation that way). What exactly does that mean? My hope is that we can come to a consensus on roughly how much energy melting the planet's surface would involve and then calculate it.
 
My first question is this; what counts as the surface? Are we treating it as a near flat surface (1 meter depth) or the crust of the planet? I don't know if anyone knows Japanese here, but I'd like to know if the word Boros used for surface implies crust or some other measurable depth. I think a good baseline for melting would be enough energy to melt the entire planet's uppermost surface (just one meter for volume's sake) as if it were all solid (and not 71% water like it is in real life). Using concrete as a substitute (since I've struggled to find the joules/cm^3 for melting clay), and using the earth's surface area of 510.1 million kmยฒ, we get a result of 6.2395432ร—10^27 joules or 149 petatons. Clay is probably about a tenth that, so for our baseline, ruining the uppermost meter of the earth's surface on land and the upper reaches of the ocean would be about 10 petatons using this rudimentary calc. However, if we calced melting the topmost kilometer or the earth's crust I would expect a result of about 10 exatons or 300 exatons respectively. Could be wildly wrong with this but I'm trying my best to establish a ballpark of possible outcomes
 
I think the Japanese quote was, Shaving the Earth! or ruining the planet surface! or something like that.

By that, I'd assume everything looks like destroyed and every part of the planet's surface is desecrated in some sort.
 
I agree on that, I'm asking about depth. Desecrating the surface could easily mean melting the topsoil or turning the entire crust into molten slag. I guess we could do high and low ends, but I suspect that would just end up with the low end being accepted
 
@Damage3245 @DMUA Hey guys, how would you calculate melting the surface of the planet? Our first question is theoretically, what depth should you use to calculate the volume of the melted area (e.g. 1 meter of topsoil, 10 meters of soil, 1 km of earth, 30 km of crust)? I know that science guy video that got 5-C results for CSRC assumed the entire crust would be destroyed, but I don't know if that will fly here. Once we answer that and assume a baseline of energy required, we can take boiling in account for the seas and the material being melted on land
 
I don't know if anyone knows Japanese here, but I'd like to know if the word Boros used for surface implies crust or some other measurable depth.
The kanji used can be read here. The implication with his manga statement leads more to destroying the crust (or at least the upper crust) with the CSRC.
 
Yeah, the shaving and ruining part leaves me to believe CSRC would melt the upper layers of the crust rather than the entirety of the crust, Low-End I would say is melting the crust at 1cm^3 depth (already calced by Ourosboros). Mid-End maybe 6-17ish km? (crust can go down from 6 to 35km depending on the area, hence 17km being the midpoint) High-End would be melting all of the crust leaving only the mantle and vaporising the ocean.
 
Actually, if the kanji implies that the attack would destroy the crust, you can disregard my earlier calc because CSRC would be melting some portion of the crust as opposed to the top soil. I think you could make the Low-end 6km and the high end 35km since we seem to be talking about the crust of the planet and not the surface. For the LE, we can assume that the energy required to melt 6 vertical kilometers of earth is being applied equally across the planet's surface so that all the exposed upper crust will be destroyed.

I would calc the LE like this; find the energy required to melt 6 km2 of earth by determining the energy required to melt granite (the primary component of continental crust). I will assume the landmass of OPM earth is the same as our own, as we have no proof that OPM earth is an entirely different celestial body outside of that one anime scene with multiple satellites. Assuming the energy distribution is equal, we just have to multiply that result by the earth's 510.1 million km^2 surface area to find the results across the planet.
 
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Since the continental crust is overwhelming made of Granite, I found the melting value per ccm^3 and worked from there. Here is what I found:

Melting Granite: 4358.9475 J/cm^3 x 10^15 = 4.3589475ร—10^18 J/km^3 x6 (LE)= 2.6153685ร—10^19 Joules per km of surface area,

4.3589475ร—10^18 J/km^3 x 35 (HE) = 1.52563162ร—10^20 Joules per km of surface area,

LE, destroying the upper crust (6 km on average): 2.6153685ร—10^19 Joules per km of surface area x 510.1 million (surface area of earth in sq^km) = 1.33409947ร—10^28 joules or 3.19 exatons, High 6-A

HE, destroying the entire crust (35 km on average): 1.52563162ร—10^20 Joules per km of surface area x 510.1 million = 7.78224692x10^28 Joules or 18.60 exatons, High 6-A
 
Since the continental crust is overwhelming made of Granite, I found the melting value per ccm^3 and worked from there. Here is what I found:

Melting Granite: 4358.9475 J/cm^3 x 10^15 = 4.3589475ร—10^18 J/km^3 x6 (LE)= 2.6153685ร—10^19 Joules per km of surface area,

4.3589475ร—10^18 J/km^3 x 35 (HE) = 1.52563162ร—10^20 Joules per km of surface area,

LE, destroying the upper crust (6 km on average): 2.6153685ร—10^19 Joules per km of surface area x 510.1 million (surface area of earth in sq^km) = 1.33409947ร—10^28 joules or 3.19 exatons, High 6-A

HE, destroying the entire crust (35 km on average): 1.52563162ร—10^20 Joules per km of surface area x 510.1 million = 7.78224692x10^28 Joules or 18.60 exatons, High 6-A
Did you account for the energy to raise the temperature to melting point in that calc?
 
To get an "acceptable" number you would need to find the composition materials of the crust and go from there.
 
I just used the site's predetermined value for melting granite, which is just E = m*c*delta T, so it's included in there.
That is the equation for heating granite. Thermal energy has two components: temperature change, and phase change, if the granite does not start at its melting point then both have to be considered.
 
That is the equation for heating granite. Thermal energy has two components: temperature change, and phase change, if the granite does not start at its melting point then both have to be considered.
The wiki says the heat of fusion for granite is 947657.98 joules per kilogram, which I'm assuming is the phase change happening here.
 
This equation would have granite starting at 20c and going up to 1215c (granite's melting point) so I suppose the heat fusion is not included. To be honest, I thought the heat of fusion would be included in the change in temperature. But if it is not as you say, then I should calc the heat of fusion separately and add that to the numbers I already have? This sounds like it would get moon level results, interesting.

To get an "acceptable" number you would need to find the composition materials of the crust and go from there.

About the crust's composition- it's overwhelmingly granitic rocks and the 2.7 kg/cm density used in the melting equation is the aggregate density of granitic rocks (rhyolite, etc), so breaking the numbers down into compositional materials would involve alot of backtracking and guessing (we only have a rough idea of how much of each type is where) and would presumably produce near similar results. The one question I have, and I hope someone has an answer, is what percentage of the continental crust is not granitic? If it's more than 1% I will recalc accordingly
 
Oxygen based materials meaning silicate crystals (as well as other oxygen-based minerals like Feldspar or Mica) in Granite. Oxygen is a very important component in Silicate (Si0^2) crystals which make up about 77% of Granite, and it also figures prominently in the other components of granite. That's why it's best to use the aggregate sum for granite, if you just looked at the elements you'd get skewed results because it'd be impossible to account for the varying melting points of different crystalline compounds and (molecular) mineral formations

That all being said, some of that oxygen might be in non-granitic rock. The thing is I can't find many statements about the mineral composition of crust beyond A) a list of the elements involved (which is not very useful when it comes to melting point) or B) that the crust is overwhelmingly granitic, but whether that means 80, 90 or 99.9% granitic rock is unclear to me
 
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That is the equation for heating granite. Thermal energy has two components: temperature change, and phase change, if the granite does not start at its melting point then both have to be considered.
So if we starting at 20c and go up to melting point, just raising the temperature to that point- we need to put extra energy in to push the granite over melting point? In that case, what I've calced so far (the energy required to raise the temperature to melting point) is just half the equation? In that case, should I just add the phase change energy on top of that?
 
So if we starting at 20c and go up to melting point, just raising the temperature to that point- we need to put extra energy in to push the granite over melting point? In that case, what I've calced so far (the energy required to raise the temperature to melting point) is just half the equation? In that case, should I just add the phase change energy on top of that?
Yes, yes and yes.
Using water as example, you can have both Water (liquid) at 100 celsius and Water (vapor) at 100 celsius
The energy required to change the state from liquid -> gas (or solid -> liquid, were it at 0 celsius), when the water (or any other material) is at 100 celsius (or its melting/boiling point) is the phase change energy.
A material doesn't simply change its state at its melting/boiling point, they need extra energy for that. If you search for graphs where temperature is plotted based on energy added to the system, you will see plateaus where, even though energy is being added, temperature is constant - those are phase changes, and that added energy is trying to fulfill phase change energy requirements of the material.
 
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Yes, yes and yes.
Using water as example, you can have both Water (liquid) at 100 celsius and Water (vapor) at 100 celsius
The energy required to change the state from liquid -> gas (or solid -> liquid, were it at 0 celsius), when the water (or any other material) is at 100 celsius (or its melting/boiling point) is the phase change energy.
A material doesn't simply change its state at its melting/boiling point, they need extra energy for that. If you search for graphs where temperature is plotted based on energy added to the system, you will see plateaus where, even though energy is being added, temperature is constant - those are phase changes, and that added energy is trying to fulfill phase change energy requirements of the material.
Exactly. If you just raise a material to its melting point, it won't change phases unless you continue to heat it past that point. The temperature will stop changing, because the energy is now being absorbed to change its phase, in the case of melting the earth's crust, from solid to liquid. You simply calculate the energy needed to heat the material to its melting point using:
joules of energy = specific heat capacity * mass in kilograms * change in temperature in degrees kelvin
then add this value to the heat of fusion equation:
joules of energy = (mass in kilograms * specific latent heat of fusion)*1000
The second is multiplied by 1000 because the equation is given in kilojoules.
 
Just throwing this scan in here because I forgot to include in the original post and I might as well bump the thread. Busy with projects at work right now, I won't be able to calc CSRC until this weekend
 
Just calculated the energy required to boil 3.7 km^3 of water + melt 1 km^3 of basalt and multiplied it by 510100000 km^2 (earth's surface area), so that every inch of the earth's surface is getting hit with energy sufficient to "scrape" the top km of oceanic crust as well as the top few km of continental crust.

Low End Results: 6.63593495ร—10^27 joules or 1.586 exatons, High 6-A.

But as you can see, this is just the low end, now I'm going to calculate how much energy it will take to melt 35km of continental crust and multiply it by the earth's surface area for a high end.
 
Before I can finish, however. I need to know four things, which I couldn't find anywhere during my research
1) the melting point of shale, 2) the specific heat of shale, 3) the latent heat of fusion for shale, and the 4) the latent heat of fusion for sandstone.

Anyone know where I could find that information?
 
I was not able to find the melting point of Shale, but I was able to find that shale is primary made out of quartz , feldspar and some minor minerals. I don't know if that helps at all.
 
It does, I have been looking through the mineral compositions of these rocks and am using the latent heat of fusion of the most common materials (quartz for sandstone and shale, calcite for limestone) as substitutes. I will have results very soon.
 
Still in High 6-A, so lower than the 5-C calc from the video, but we have Boros in the exatons yesssss
 
The final results are in the blog, it's got all the math, some of the sources (I probably looked at over 100 sites today while researching).

LE: 1.586 exatons
HE: 13.27 exatons


So now Saitama and Boros are in the exatons, strong enough to one shot most High 6-As. It's not moon level OPM, but at least Saitama and Boros will be much more competitive now (assuming the calc is accepted).
 
If anyone sees an issue in the calc, please let me know. I have a calc group member reviewing it now, I'd like to get this ironed out as soon as possible if it has any rough edges
 
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