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So, if a mage has to use only the elements/compounds and energy present in a 10mx10m area around them, what are the biggest limitations on their abilities? How much energy would typically be available in that area, presuming an urban centre in the u.k.? How much fire can they throw around before they run out of oxygen?

edit: to expand, that radius goes 10m above and below them as well and is not affected by any matter in the way.

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closed as too broad by 2012rcampion, Ghanima, ArtOfCode, Vincent, James Apr 27 '15 at 1:47

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  • $\begingroup$ Unless they are in a sealed room they shouldn't run out of oxygen. The fire would just cause more air to rush in, like happiness with any fire. $\endgroup$ – AndyD273 Apr 26 '15 at 14:34
  • $\begingroup$ What kind of energy can he use: thermal, electrical energy...? $\endgroup$ – Vincent Apr 26 '15 at 15:47
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    $\begingroup$ Without specifying limits on what they can do... Assuming they're standing on the ground, and have a 10-m diameter hemisphere of dirt to work with, they have access to the mass-energy of 400 tons of matter, which works out to about 8.5 trillion tons of TNT worth of energy. That's the amount of energy released by a magnitude 9 earthquake, or about the tenth of the energy released by the asteroid that killed the dinosaurs. $\endgroup$ – 2012rcampion Apr 26 '15 at 16:04
  • $\begingroup$ They couldn't throw very much fire before running out of life. The amount of energy they have access to is about 350428750 nukes. $\endgroup$ – theonlygusti Apr 26 '15 at 19:19
  • $\begingroup$ Welcome to the site Molua. Magic questions are particularly difficult to ask on the SE format. I am not telling you not to try and that it cannot be done! In fact I would suggest you take a look at this question to get an idea of what it takes to write a good magic question. Take a look and then edit your question and we can get it re-opened. $\endgroup$ – James Apr 27 '15 at 1:50
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I'm not entirely sure of the extent of their power, whether it is limited to simple compound manipulation, but theoretically, the amount of energy in a 10m sphere is more than he will ever need.

Matter can be converted directly to energy, for example, during matter-antimatter collisions, so if we know the amount of matter in the area around him, we know the amount of energy.

Let's say that he is standing on the ground, with a 10m hemisphere of air above him, and a 10m hemisphere of dirt below him.

Well, the density of air (at sea level) is $1.225~\mathrm{kg/m^3}$ and the density of dirt $1000~\mathrm{kg/m^3}$.

The volume of a hemisphere can be calculated as:

$$ V = \frac{\frac43\pi r^2}2 $$

so, with a 10m radius, it is $$ \frac{\frac43\pi 10^2}2 $$ which is about $210 ~\mathrm{m^3}$.

Now, we can calculate the mass of the air around him: $$ 1.225 \times 210 = 257.25 $$ and dirt $$ 1000 \times 210 = 210000 $$

So, in total the mage has $210257.25 ~\mathrm{kg}$ of matter around him.

Plug into equation to get energy: $$ E = mc^2 \\~\\~\\ E = 210257.25 \times (3 \times 10^8)^2 $$ which my calculator tells me is equal to $1.8923152 \times 10^{22} ~ \mathrm J$.

So, your mage has access to $$ 18,923,152,000,000,000,000,000 $$ joules of energy. Hurl a fireball of that and you'd wipe out the planet. To put that into context, the energy released by the Little Boy atomic bomb was $6.276 \times 10^{13}$ joules.

The energy your mage has access to is enormous, equivalent to $301516125$ nukes.

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  • $\begingroup$ I think you may be conflating radius and diameter in your equations. Plus you should show units in your calculations. $\endgroup$ – 2012rcampion Apr 26 '15 at 21:30
  • $\begingroup$ Also, I think some of your numbers are wrong. Your stated energy of a nuclear warhead is only 130 grams of TNT. I did the same calculation and came up with only 8.5 million MT, far less than the 350M warheads you claim (most are in the 100 kT to MT range). $\endgroup$ – 2012rcampion Apr 26 '15 at 21:31
  • $\begingroup$ I agree with 2012rcampion that the question speaks rather about 10 m diameter. The result should be divided by 8, or by $4 \pi/3$ if we interpret shape as a cube. The dirt has also probably bigger density than water. But these are details. This is generally the answer I would give. $\endgroup$ – BartekChom Apr 27 '15 at 7:50
  • $\begingroup$ @BartekChom "that radius goes 10m above and below them as well": I'm pretty sure the question is about a radius; it may be a cube, but I think a sphere with r10 makes more sense. $\endgroup$ – theonlygusti Apr 27 '15 at 14:57
  • $\begingroup$ Ok. I concentrated on "10mx10m". This could be block 10m×10m×20m but "radius" suggests sphere. $\endgroup$ – BartekChom Apr 27 '15 at 17:56

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