What would happen if you concentrate all of Earth's heat into one area and how hot would it be?

Answer 1

Unfortunately the question is poorly phrased and cannot be answered the way it is asked:

1) In thermodynamic terms, "heat" is energy in motion, moving between a warmer system and a cooler system. What you are probably thinking of is probably "enthalpy", which is a combination of the internal energy and the product of pressure times volume. To use analogy, when water is falling from the sky, we call it "rain". When it is just sitting around, not moving anywhere - in a glass, in a bottle, in the tub, THEN we just call it "water".

2) How hot the area would be depends on how big the area was and what it was composed of. It takes about 2 1/2 times as much energy to warm a cubic meter of water by 1 °C as it takes to warm a cubic meter of concrete and more than a hundred times as much energy to warm a cubic meter of water as it does to warm the same volume of wood by the same amount. Water takes more than 3000 times the amount of energy to warm that the same volume of air would take. If you concentrated all the enthalpy of the earth in 1 cubic meter of something it would be far hotter than concentrating it in 1 cubic kilometer of the same material since you would be distributing it in 1 billionth the amount of mass.

With all that said, and realizing the extreme amount of energy beneath the mantle and core of the earth, if you concentrated it all into something like a cubic kilometer of rock, the rock would be converted to plasma - if you could contain it long enough to get that hot...

Answer 2

There is really no reasonable way to do that - and you would require extra energy to move the heat around; the heat energy itself can't be used for that (Second Law of Thermodynamics!). Assuming you could really do that, it would really depend on the size of your "area" (which should really be a "volume"). Roughly speaking, and forgetting about differences in specific heat, if you transfer all the heat into a volume half the size, the temperature of that volume would be double the original temperature; if you transfer all the heat into a volume 1/100 of the size, the temperature of that volume would be 100 times as much, etc. - if you express temperatures in an absolute scale, such as Kelvin.