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The feat

Ingrid freezes Arendelle with a gesture.

This is the size of the country she froze.

Assumptions

  • The average temperature on Earth is 15 C.
  • I'll use the Red Sea and the Sea of Cortés as two parameters for the sea of Arendelle. The Sea of Cortés is a low-end.
  • I'll completely ignore the rest of the country and assume only Arendelle's sea was truly frozen. It is obviously not what happened, but it'll make the calculation easier and keep it a low-end.

The calculation

Freezing Arendelle's sea

  • Red Sea
    • Part 1 - Mass

The Red Sea's water volume is 233000 km³, which means 233000000000000 (or 2,33x10^14) . Density of water is 1000 kg/m³.

So, its mass is 233000000000000000 (or 2,33x10^17) kg.

    • Part 2 - Temperature

Specific Heat Temperature

Q1 = m * c * ΔΤ

ΔΤ = 15C

Q1 = 233000000000000000 * (4186 j/kg) * 15

Q1 = 1463007000000000000000000 (or 1,463007x10^24) joules.

Latent Heat of Fusion

Q2 = ML

Q2 = (233000000000000000 kg)(333.7 J/kg)

Q2 = 77752100000000000000 (or 7,77521x10^19) joules.

    • Part 3 - Adding them together

Q1 + Q2 = 1463007000000000000000000 + 77752100000000000000 = 1463084752100000000000000 joules or 349.7 teratons (High 6-B; Small Continent level)

  • Sea of Cortés
    • Part 1 - Mass

Volume of the Sea of Cortés is 145000 km³, which means 145000000000000 m³.

Density of water is 1000 kg/m³, which means: m = 145000000000000000 kg (or 1,45x10^17).

    • Part 2 - Temperature

Specific Heat Temperature

Q1 = m * c * ΔΤ

ΔΤ = 15C

Q1 = 145000000000000000 * 4186 * 15

Q1 = 9104550000000000000000 joules

Latent Heat of Fusion

Q2 = ML

Q2 = 145000000000000000 * 333.7

Q2 = 48386500000000000000 joules

    • Part 3 - Adding them together

Q1 + Q2 = 9104550000000000000000 + 48386500000000000000 = 9152936500000000000000 joules or 2.2 teratons (Low 6-B, Small Country level)


The Result

Freezing Arendelle's sea

  • With the Red Sea: 349.7 teratons (High 6-B; Large Country level)
  • With the Sea of Cortés: 2.2 teratons (Low 6-B, Small Country level)
    • More consistent with the verse's 6-C feats.
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