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This question is tied to a previous question:

Cataclysmic event resulting in a region of glass?

In this scenario you have two armies, with a combined strength of roughly 30,000 personnel.

Magicians on both sides cast a ritual spell that feeds off the armies to wreak destruction on their enemies (they cast at the same time, it is essentially the same spell with multiple casters.)

The details:

  1. Everyone dies...they are the source of energy. Average weight is 70.0 kg/humanoid. How much chemical energy is contained in each human?
  2. The spell heats the ground to a depth of 100 meters at the epicenter, at 100 kilometers the depth is 50 meters and at 200 kilometers the depth is 1 meter (or zero..basically that is how far the spell reaches. For the sake of calculations you can consider the terrain completely flat. (basically the area of affect is a big damn cone)
  3. The heat is sufficient that the ground turns crystalline (pick your substrate, meaning sand, stone etc). The result should be a vast obsidian/glass dead land. (shiny and breakable)

    • If anyone can elaborate on the difference in energy requirements for various substrates that is bonus points.
  4. The effect is instantaneous across the whole area of effect (the heat in the entire cone is exactly the same), the area is heated and cooled just to the point of being solid in the span of 5 seconds, though it must cool down from there naturally.

Questions:

  • Is 30,000 humanoids enough to power this spell? If not, how many would it take?
  • Does turning the ground crystalline create more or less volume than before the spell was cast? (does the ground contract or expand)
  • What sort of effects should be expected from the residual cooling process?
  • If chemical energy is insufficient what about the atomic energy in that much matter (how big would the effect be?) per @DanSmolinski 's comment
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  • $\begingroup$ I have a feeling that the effect you're describing is either way too big (if using chemical human energy), way too small (if using the atomic energy of that much mass), or undefinable (if using "magic" energy/lifeforce). $\endgroup$ – Dan Smolinske Oct 20 '15 at 20:35
  • $\begingroup$ @DanSmolinske I am referring to chemical energy...or at least that is what I was thinking. If there is a better option I am all ears. $\endgroup$ – James Oct 20 '15 at 20:38
  • $\begingroup$ I found a unit of measurement called the "foe" today. It blows my mind. $\endgroup$ – Green Oct 22 '15 at 15:07
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If the magicians can react all $30,000$ troops with an equal quantity of anti-matter, then there is enough energy to cause a mass extinction of life on Earth. This is overkill of course.

Establishing Upper bounds

Let's see

$m = 70 \, \text{kg} \cdot 30000\,\text{troops} = 2,100,000 \, \text{kg}$

$c = 299792458 \, \frac{\text{m}}{\text{s}}$

$E = mc^{2}$

$E = 1.88739 \cdot 10^{23} \, \text{J}$

A quick lookup in the Orders of Magnitude table tells us that this amount of energy is roughly equivalent to the impact of a $10 \, \text{km}$ wide asteroid such as Chicxulub. Yes, there is definitely enough energy in $60,000$ people to glass-over the area specified.

This is a cone of effect of $4.18879 \cdot 10^{12} \, \text{m}^{3}$. For simplicity, let's assume that the ground is pure quartz. (Real dirt would have water, organics and a mix of other stuff in there. Let's keep this simple.)

$V_{cone} = 4.18879 \cdot 10^{12} \, \text{m}^{3}$

$D_{quartz} = 2650 \, \frac{\text{kg}}{\text{m}^{3}}$

$M_{quartz} = V_{cone} * D_{quartz} = 1.11003 \cdot 10^{16} \, \text{kg}$

The specific heat equation is $Q = cm\Delta T$ where $Q$ is heat added (in Joules), $c$ is specific heat, $m$ is mass and $\Delta T$ is change in temperature. We know that glass fuses at 1305°C (cone 10 is a common high firing temperature.)

$c_{quartz} = 795.492 \frac{\text{J}}{\text{kg} \cdot \text{K}}$

$Q = c \cdot m\Delta T = c_{quartz} \cdot M_{quartz} \cdot (1305°C - 22°C)$

$Q = 1.13292 \cdot 10^{22} \, \text{J}$

Note this is $33$ times less than the power available by antimatter annihilation. Fusing this much material isn't possible with chemical energy sources. It just isn't.

This calculation also don't explore any explosive effects involved in fusing that much quartz mixed with the organic materials and water surely included in this cone of death.

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    $\begingroup$ Err... isn't it 30,000 people? $\endgroup$ – Malady Oct 20 '15 at 20:50
  • $\begingroup$ @Malandy yep it is $\endgroup$ – James Oct 20 '15 at 20:59
  • $\begingroup$ Green can you elaborate on how many humanoids it would take to do it with chemical energy (and any of the other questions at the bottom you want to take a crack at) $\endgroup$ – James Oct 21 '15 at 20:17
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No antimatter required

If we don't think of introducing antimatter into the equation and instead limit the scenario to hydrogen fusion from the water in the human body, we get:

6.93 MeV per 3 Hydrogen atoms. link

Human body = 60% Water and Water = 1/9 Hydrogen -> 1/15 of total mass being Hydrogen bound in water

2.1 * 10^9 g / 15 * N = 189 * 10^32 particles (N being avogadro's constant).

so total energy E = 189 * 10^32 / 3 * 6.93 MeV = 4.37 * 10^34 MeV = 7 * 10^21 J

Since this is already about 70% of the energy needed according to the other answers, this seems quite plausible (considering there is more fusion potential left into heavier isotopes and also we only use the hydrogen from water).

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Just look at Green's Awesome Answer!


Well, the chemical? energy of 1 human is... 110,000 kcal

Or (4.2 * 110,000) KJ = 502,000 KJ = 502 MJ

(502 * 30,000) MJ = 15,060,000 MJ = 15,060 GJ = 15.06 TJ

15.06 Terajoules... Hmm... Is that sufficient?


Pure sand needs 3,200 Fahrenheit to glass...

Sand plus accelerants needs 2,400 Fahrenheit...

Source: http://www.dailyherald.com/article/20121106/news/711069914/


So... What's the mass to glass? Hmm...

Apparently, the Earth's average density is 5.51 g/cm^3... But I don't know about sand... Which should compress better than Earth Average? Maybe?...

Source: https://www.google.com/search?q=density+of+earth&ie=utf-8&oe=utf-8

Sand has a density of 2-3 g/cm^3?

Source:https://en.wikipedia.org/wiki/Silicon_dioxide

And we're glassing a cone that has a volume of ???... The formula is 1/3 * pi * (radius ^ 2) * height

Source: https://www.google.com/search?q=density+of+earth&ie=utf-8&oe=utf-8#q=cone+volume


How to figure out how many joules is needed to raise that mass of sand/??? to ??? Fahrenheit...:

https://en.wikipedia.org/wiki/Temperature#Heat_capacity

Sand's is 0.290 Joules per Gram for 1 Celsius at 25 Celsius... I'm gonna assume that's true at all Celsiuses...

Source:http://www2.ucdsb.on.ca/tiss/stretton/database/Specific_Heat_Capacity_Table.html


*Leaving...

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If you were able to convert the mass of those humans perfectly to energy, you'd create a nuclear event of sufficient size to extinguish all life on Earth (not enough to disintegrate it but it probably wouldn't be recognizable).

E = mc2

1 human ~= 81kg (worldwide human average)

E = 81000 g/human * 300000000^2 * 30000 humans

E = 7.29 * 1021 J/human * 30000 humans

E = 2.187 * 1026 J

The Tsar Bomba device, the most powerful single nuclear weapon ever test-detonated by humans, released 210 petajoules (2.1 * 1017 J). The perfect, instantaneous conversion of all matter of 30,000 human-sized beings would be roughly equivalent to detonating 1 billion Tsar Bombas simultaneously.

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  • $\begingroup$ The binding energy of the Earth is 2.242 10^32 J. You're short by a factor of at least 2 million. (Actually, more, as you can't expect anything like 100% conversion of the blast into planetary disruption.) $\endgroup$ – Loren Pechtel Oct 20 '15 at 23:43
  • $\begingroup$ Point taken; edited. A blast that big would likely still blow a hole straight to the mantle,. in the process kicking up enough dust to freeze the earth and collapse the food web. $\endgroup$ – KeithS Oct 20 '15 at 23:52
  • $\begingroup$ You are aware that SI units use kg, not g, right? I think you are off by a factor of 10^3. $\endgroup$ – Marius Oct 21 '15 at 11:29

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