1,000,000 m^3 of rock:
1,000,000 m^3 = 1,000,000,000,000 cm^3
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Rock = 2,700 kg/m^3
1,000,000 m^3 = 2,700,000,000 kg
1) Energy to Melting Point (Using silicon dioxide values for lack of better options due to rock being complex)
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^ Heat Capacity at 300K, J/kg·K = 733
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^ Melting point = 1600-1725°C (= 1662.5C = 1663C)
2,700,000,000*(1663-20)*733 = 3,251,661,300,000,000 J
2) Energy of phase change
latent heat of fusion
(8) 0.529107 (0.444 kJ mol)
(14) 0.337021 (50.21 kJ mol)
(13) 0.033872 (10.71 kJ mol)
(20) 0.044000 (8.54 kJ mol)
0.529107 x 0.444 = 0.234923508
0.337021 x 50.21 = 16.92182441
0.033872 x 10.71 = 0.36276912
0.044000 x 8.54 = 0.37576
0.234923508 + 16.92182441 + 0.36276912 + 0.37576 = 17.895277038 kJ/mol = 17,895.277 J/mol
Atomic Masses :
16 x 0.529107 = 8.465712
28 x 0.337021 = 9.436588
27 x 0.033872 = 0.914544
40 x 0.044000 = 1.76
8.465712 + 9.436588 + 0.914544 + 1.76 = 20.576844
2,700,000,000,000 g / 20.576844 g/mol = 131,215,457,530.8 moles
131,215,457,530.8*17895.277038 = 2,348,136,964,181,589.4 J
2,348,136,964,181,589.4 J + 3,251,661,300,000,000 J = 5,599,798,264,181,589.4 J
5,599,798,264,181,589.4 J / 1,000,000,000,000 cm^3 = 5599.798 J/cm^3
Just by eyeballing the rock that 5% Katsuyu melted, it was no bigger than Manda's body width. Because Manda is no more than 15 meters wide, using 15 meters is a very generous dimension.
Melted Rock Volume ≈ (1/3)*(15^2)*15 = 1,125 m^3
1,125 m^3 = 1,125,000,000 cm^3
1,125,000,000 cm^3 * 5599.798 J/cm^3 = 6,299,763,750,000 J
100% = 20 5%
6,299,763,750,000 J * 20 = 125,995,275,000,000 J = 30 kilotons of energy
So yeah, the slug is overrated as all hell.