Can we actually "blow up" the sea?

tl;dr: Not without killing everything.

Let's do some maths and actually figure this out.

The specific heat capacity of water is $4.186{\text{ kJkg}}^{-1}$. That means it takes 4186 joules of energy to heat 1 kilogram of water up by one degree.

The average temperature of the surface of the sea is 17^oC. It gets a lot colder as you go deeper, so the average temperature overall is more like 0.

The seas contain a volume of 1.3 billion cubic kilometres of water. 1 litre of water = 1 kg. 1 litre of water also = 1 dm³, so there are 1000 litres in a cubic metre and thus a cubic metre of water weighs a ton. (This is assuming freshwater to keep the numbers reasonably nice - salt water is heavier.) Then, there are ${1000}^3=1,000,000,000$ cubic metres in one cubic kilometre. That means 1.3 billion billion or 1.3 quadrillion cubic metres of water and the same number of tons, which in turn is $1.3\times {10}^{21}\text{ kg}$ or 1.3 quintillion kilograms.

Now let's heat all that up by one degree.

$$(1.3\times {10}^{21}\text{ kg})\times 4186{\text{ Jkg}}^{-1}=5.4418\times {10}^{24}\text{ J}$$

Multiply by 100 so we can heat the water to boiling:

$$=5.4418\times {10}^{26}\text{ J}$$

Finally, you need around 6x the energy to actually boil it:

$$=3.2651\times {10}^{27}\text{ J}$$

Now while that's not quite on the order of blowing up the Earth, that's a hell of a lot of energy. You're in the perfect region for an asteroid impact. We can work out how big and fast it needs to be:

$$\text{KE}=\frac{1}{2}m{v}^2$$ $$2\text{KE}=m{v}^2$$ $$6.5301\times {10}^{27}=m{v}^2$$

We can play around with mass and velocity. Let's say this asteroid is a perfect 10km cube with 5000kg/m³ density, thus giving it a weight of $5\times {10}^{12}\text{ kg}$. That means its velocity has to be:

$$v=\sqrt{\frac{6.5301\times {10}^{27}}{5\times {10}^{12}}}$$ $$v=36138898.71{\text{ ms}}^{-1}$$

or around $0.12c$. That speed isn't insignificant, and while an impact from an asteroid of this size and speed wouldn't destroy Earth, it would most likely make a massive crater, not vaporise the oceans because the energy isn't distributed easily, and kill all life on Earth.

And that's before we start on the water cycle dropping all that steam straight back where it came from.

posted about 10 years ago

ArtOfCode‭ staff

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