Die is Cast firepower

In Die is Cast fleet destroys 30 % of planetary crust in single salvo (previously, we know that crust should be destroyed in 1 hour, and mantle within 5). Volume of crust could be around 1.5 x 10e10 km^3 or 1.5 x 10e19 m^3. We see 10 to 12 torpedoes and around 16 beams fired. 30% of crust equates 4.5 x 10e18 cubic meters.

Here is table of elements of crust, along with calculated volume of each element in area of crust melted in attack:

60.2 % silicium - 2.709 x 10e18 m^3
15.2 % aluminium - 6.84 x 10e17 m^3
5.5 % lime - 2.475 x 10e17 m^3
3.1 % magnesium - 1.395 x 10e17 m^3
3.8 % iron (II) oxide - 1.71 x 10e17 m^3
3 % sodium oxide - 1.35 x 10e17 m^3
2.8 % potassium oxide - 1.26 x 10e17 m^3
2.5 % iron (III) oxide - 1.125 x 10e17 m^3
1.4 % water - 6.3 x 10e16 m^3
1.2 % carbon dioxide - 5.4 x 10e16 m^3
0.7 % titanium oxide - 3.15 x 10e16 m^3
0.2 % phosphorus pentoxide - 9 x 10e15 m^3

So we now have exact volume of each of major elements of crust melted during attack. Now only thing needed to calculate exact firepower is to do 12 calculations for each element separately, then calculate sum of involved energy and calculate how much of energy is done by torpedoes and how much by energy weapons. That I will do at later time.

We know that they planned to melt both crust and mantle. Given that temperature of mantle is in range from 1400 to 3000 ° Celzius, we can assume temperature produced is at least 1400 ° C. Given that calcium oxide melts at 2572 ° C, temperatures in excess of 2600°C are possible. So temperatures produced are around 2600 ° C.


Silicium

Specific heat capacity of silicium is 1.547 J(cm^3 x K). Volume is 2.709x10e24 cm^3; that means that energy required to melt it is 1.08961398 x 10e28 J.

Aluminium

Specific heat capacity of aluminium is 2.422 J(cm^3 x K). Volume is 6.84 x 10e23 cm^3. So we have E = 4.3072848 x 10e27 J.

Magnesium

Specific heat capacity of magnesium is 1.773 J(cm^3 x K). Volume is 1.395 x 10e23 cm^3. So we have E = 6.430671 x 10e26 J .

Water

Specific heat capacity of water is 4.1796 J(cm^3 x K). Volume is 6.3 x 10e22 cm^3. So we have E = 6.8461848 x 10e26 J .

(unfinished)

I currently do not have specific heat capacities for remainder of elements, but so far we have 1.653 x 10e28 J or 3.95 exatons of firepower (3 950 000 000 gigatons). If we take torpedoes to be 5 times stronger than beams, then 1 beam has little less than 52 000 000 Gt of power and one torpedo has around 260 000 000 Gt of firepower (52 and 260 petatons).

NOTE: Some claim that visuals, which show no ejecta, no fire etc. contradict that, and that sensors were fooled by Dominion. However, such argument is nonsense. Dominion already had fleet lying in its trap, so fooling them to think attack was succeeding is actually contraproductive, since any false, over-inflated readings woud have warned Tain and his officers about Dominion plan - fleet was "manned by combat veterans", and any combat veteran would notice if destruction levels were so much out of scale. Yet, officer which read sensor report wasn't surprised at all until sensor showed no changes in lifeform readings, and only at that point they realized it was trap. And even if inflating readings was not actually contraproductive, they weren't exactly helpful - fleet was already in Dominion trap at that point. So that firepower is canon. About contradicting visuals - show did have budget after all. For other possibility look at Note 2 below.

Also, in "The Chase" one Klingon Bird of Prey can obliterate all life on a planet, to the point where no DNA would be recoverable from any of the remains. This is, to put it bluntly, impressive, however it is some sort of chain reaction. Not only that, but we know about Starfleet General Order 24 - order to destroy all life on planet. A last resort.

NOTE2: It is possible that petaton-range effective yield of weapons was not actually true yield of weapons, but rather included some form of chain reaction/NDF. Given evidence from "Chase" and visual evidence from episode, that seems most likely.

NOTE 3:
Enterprise season 3 episode 20 "the forgotten".


TUCKER: "HELL, it would take at least (he stops to think/calculate) a thousand starships like enterprise to blow up a entire planet".

Based on 1x10e29 J requirement for blowing up planet calculated by (someone) for Death Star, that quote would put firepower for each ship at 1x10e26 J or 23.9 petatons which fits with DE requirements for stated "Die is Cast" firepower.