Due to popular request, I am going to recalculate CSRC by finding the energy required to melt the earth’s crust, oceanic and continental. CSRC has been previously calced as a generic explosion covering the earth's surface, but we here in the OPM community on vsbattles have agreed that it would be better to calculate CSRC as a burst of energy that melts the earth's crust. Discussion here:[1]
Boros says he will “shave the crust” according to the Kanji here(https://jisho.org/word/%E5%89%8A%E3%82%8B). Since he’s referring to the crust as a whole, I will calculate the low end according to how much energy it would take to “shave” both the continental and oceanic crust, meaning the top kilometer of the oceanic crust and the oceans above it and however much continental crust that would destroy. The high end will be the energy required to “shave” most of the thicker (but less dense) continental crust.
For our low end we will calculate the energy per sq km2 required to melt the upper layer of oceanic crust, because if Boros is going to shave the earth's crust, even just the uppermost crust (1 km for example), he has to shave both the continental crust and the oceanic crust. Since the oceanic crust is harder to melt by virtue of being denser and underneath several km of ocean, I chose the energy to do so for a low end. If Boros can cover the planet with enough energy to melt the average uppermost km3 of seabed, he can effectively shave most of the upper crust (BONUS! I calculate boiling the oceans too, to see if my numbers are good). To clarify, this equation assumes that energy is being equally distributed in every sq km2 of the globe, so both upper oceanic and upper continental crust (about 4 km's worth) will be melted.
For our high end we are going to approximate the energy required to melt most of the crust, upper and otherwise. Since the continental crust is much thicker than the oceanic crust, so if we want to melt the entire crust we have to melt the thicker parts of the continental crust. The continental crust is on average 35 km deep, so I will calculate the energy required to melt it and spread that energy around the world, so that the overwhelming majority of crust (lithosphere not included) is melted.
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Boiling the Ocean(LE part 1)
Since 71% of the Earth’s surface is ocean and roughly 71% of earth’s crust is oceanic crust, in order to shave the earth’s crust Boros must first boil away the oceans and then melt the top km^3 of oceanic crust. To calculate the energy required to boil away a cubic kilometer of ocean, we will find the volume of water and multiply it by the temperature change and specific heat, which will be added to the volume multiplied by the latent heat of vaporization.The average ocean depth is 3.7 km and the density of water is 998.23kg/m^3 at 20C. So, 998.23 *1000m(width)*1000m(depth)*3700m(height) = 3.693*10^12 kg per km^2 of surface area on average
Boiling point for water is 100C (temperature change of 80C)and the specific heat of water is 4,200 joules per kilogram. The latent heat of vaporization of water is 2257000j/kg.
(3.693*10^12) * 80 *4182 =1.235*10^18 joules,
(3.693*10^12) * 2257000 =8.336*10^18 joules,
(1.235*10^18) + (8.336*10^18) = 9.571×10^18 joules per average km^2 of ocean (assuming average ocean depth), Mountain level
Now to calculate melting a cubic km of oceanic crust.
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Melting the top 1 km of the oceanic crust(LE part 2):
We will repeat the same process for the basaltic crust, but with melting instead of vaporization. So we will first find the volume per km^3, then multiply that volume by the temperature change necessary to melt basalt and the specific heat of basalt, which will be added to the volume multiplied by the latent heat of fusion for basalt.
The density of the oceanic crust is 3011 kg/m^3, which is also the density of basalt which overwhelmingly composes it. 3011 kg/m^3 * 10^9 = 3.011*10^12 kg/km^3. Basalt melts at 984C to 1260C, we will use the low end for a temperature change of 784C (oceanic crust is 200 to 400C), multiplied by the 840j/kg specific heat of basalt. The latent heat of fusion for basalt is 15.4 kJ/mol or 481250 j/kg.
(3.011*10^12) * 784 * 840 = 1.449*10^18j
(3.011*10^12) * 481250 = 1.98310^18j
(1.449*10^18) + (1.98310^18) = 3.432*10^18j, Mountain Level
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Melting the top 1 km of Basalt + Boiling 3.7km of ocean (LE part 4)
(3.43196792*10^18) + (9.57153008*10^18)=1.3003498×10^19 joules, High 7-A ________________________________________________________________________________________________________________________________
Multiplying the combined results by the earth’s surface area (LE part 5)
I’ll multiply the energy used to melt the average km^2 of oceanic crust/ocean water by the earth’s surface area. I will not calculate the effect of this energy on the continental crust because I will assume the energy distribution is relatively equal, so that every square km of earth’s surface is getting High 7-A amounts of melting energy sufficient to boil most of the oceans and melt most of the oceanic crust.
The earth’s surface area is 510100000km^2.
(1.300*10^19)*510100000=6.63308433×10^27 joules or 1.586 exatons, High 6-A,
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Bonus points: Boiling the Ocean(BONUS)
The ocean’s surface area is 361132000 km^2.
(9.577*10^18)* 361132000= 3.010*10^27 joules or 719.51 petatons, High 6-A
Alternatively, the ocean’s volume is 1.4 x10^21 kg of water, repeating the steps with did earlier with this new holistic volume we get…
(1.4*10^21) * 80 *4182 =4.6838*10^26 joules,
(1.4*10^21) * 2257000 = 3.160*10^27 joules,
(4.6838*10^26) + (3.1598*10^27) = 3.628*10^27 joules, 867.64 petatons, High 6-A
So we can see that our results for scraping most of the ocean crust would involve boiling most(if not all the ocean) and melting most of the upper oceanic crust.
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Melting the Granite(HE part 1)
To find the high end, we are going to calculate how much energy it would take to melt the average of the thicker continental crust down to the mantle. In other words, how much energy would it take to melt km^2 of continental crust and how much energy would that be if duplicated for every square km^2 of the earth’s surface. So, the composition of the continental crust is a little more diverse: 95% Granite, 4%shale, 0.75% sandstone, 0.25% limestone. We just have to calculate the energy required to melt 35km^3 of this rock composition and multiply accordingly.
Granite: Since 95% of the continental crust is granite, it will be our first stop. Average density of granite is 2.7g/cm^3.
2.7 *10^6 *10^9 *0.95*35 = 8.978×10^13kg per km^3
We will multiply the volume by the specific heat of 790j/kgK and the average temperature change of 915C. The crust ranges in temperature from 100 to 600C, with an average of roughly 300 C, since the melting point of granite here is said to be 1215 to 1260C, subtracting 300 from 1215 gets an average difference of 915C. We then multiply the volume by the 418680j/kg latent heat of fusion and add this to the first total for the energy required to melt all the granite in our 35km^3 cuboid.
(8.978*10^13) * 915 * 790 = 6.489*10^19 joules,
(8.978*10^13) * 418680 = 3.759*10^19 joules,
(6.489*10^19) + (3.759*10^19) = 1.02480856×10^20 joules, 6-C.
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Melting the Shale(HE part 2)
Shale: Shale is 4% of the crust, so it comes next. Crustal shale typically has a density of 2675 kg/m^3, so:
2675 * 1000 * 1000 * 35000 * 0.04 =3.745*10^12kg,
Like Sandstone and Limestone, shale is a sedimentary rock, albeit with higher clay mineral content. The specific heat is 1043j/kgK and since I could not find its melting point, I will borrow that of sandstone. The latent heat of fusion is also unknown, so that of quartz (common in shale) will be used as an approximation.
Melting point; 1500- 300C = 1200C
Specific heat: 1043j/kgK
Latent heat of fusion:8.9 ± 1.0 kJ mole−1,
8900 joules per mole, 16.67 moles per kg, 148,333 j/kg
(3.745*10^12) * 1200 * 1043 = 4.687*10^18 joules,
(3.745*10^12) * 148333 =5.555*10^17 joules,
(4.687*10^18) + (5.555*10^17) = 5.243*10^18 joules, high 7-A
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Melting the Sandstone (HE part 3)
Sandstone: Sandstone is 0.75% of the crust, so it comes third in our equation. Crustal sandstone typically has a density of 2600kg/m^3, so:
2600 * 1000 * 1000 * 35000 * 0.0075 =6.825*10^11kg,
Melting point is 1500 c and specific heat is 780. I could not find the latent heat of fusion, so I will again that of quartz as a substitute as it is one of the most common components of sandstone.
Melting point: 1500C-300C=1200C
Specific heat: 780j/kgK
Latent heat of fusion: 148,333
(6.825*10^11) * 1200 * 780= 6.388*10^17 joules,
(6.825*10^11)*57500= 1.012*10^17 joules,
( 6.388*10^17) * (1.012*10^17) = 7.401×10^17 joules, 7-A
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Melting the Limestone (HE part 4)
Limestone is our last component as 0.25% of the crust. Crustal limestone has a density of 2711 kg/m^3, very close to granite. So:
2711 * 1000 * 1000 * 35000 * 0.0025=2.372*10^11kg,
Melting point: 1339C-300C=1,300
Specific heat: 840j/kgK
Latent heat of fusion: 57500j/kg (calcite)
(2.372*10^11) * 1300 * 840 = 2.590*10^17 joules,
(2.372*10^11) * 57500 =1.353*10^16 joules,
(2.590*10^17) * (1.353*10^16) = 2.727*10^17 joules, 7-B
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Combining the Granite, Shale, Sandstone and Limestone results (HE part 5)
Now that we have the individual values for melting the proportions of granite, shale, sandstone and limestone, we will combine them for the final tally for 35km^3 of vertical continental crust.
(2.727*10^17) + (7.401×10^17) + (5.243*10^18) + (1.025 6×10^20) = 1.087*10^20 joules per km^2 of surface area.
Like before, we will multiple this tally by the surface area of earth under the assumption that energy and corresponding destruction will be relatively equal.
(1.087*10^20) * 510100000 = 5.54664061×10^28 joules or 13.27 exatons, High 6-A
In resume, our final results are:
LE: 6.63593495×10^27 joules or 1.586 exatons, High 6-A, (ACCEPTED)
HE:5.54664061×10^28 joules or 13.27 exatons, High 6-A
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Cited Sources
While calculating this, I had to refer to dozens, possibly a hundred difference sources to determine everything from crustal temperature to the latent heat of fusion for minerals like quartz and calcite.
Crust composition: http://butane.chem.uiuc.edu/pshaple...n minerals are,sandstone, and 0.25% limestone.
Crustal temperature: https://www.nationalgeographic.org/encyclopedia/crust/#:~:text=The%20upper%20crust%20withstands%20the,Celsius%20(752%C2%B0%20Fahrenheit).
Melting points of Granite/Basalt: http://www.minsocam.org/msa/collectors_corner/arc/tempmagmas.htm#:~:text=Basalt%20melts%20at%20about%20984,open%20crucible%20in%20the%20laboratory
Specific heat for various rocks:
https://www.engineeringtoolbox.com/specific-heat-solids-d_154.html
Boiling the oceans:
https://www.ck12.org/physics/heat-temperature-and-thermal-energy-transfer/rwa/Boiling-Water/#:~:text=Phase%20changes%20in%20pure%20water,water%20is%202257%20kJ%2Fkg.
Ocean depth:
Ocean volume and surface area:
https://en.wikipedia.org/wiki/World_Ocean
Melting Granite: https://vsbattles.fandom.com/wiki/User_blog:The_Causality/Orochi%27s_Kamehameha_-_One_Punch_Man?commentId=4400000000001054701#comm-3072272