We both made mistakes. First, yours:
1) The atlantic is a lot bigger than 1.4 trillion cubic meters of water and 7 billion cubic meters at 100m thick. I looked up the precise size, and it's even larger than I listed (although area actually cancels out in the equation). It's 1.057e8 km^2, not my 8e7 estimate. That's 1.057e14 m^2. Given an average water depth of 4000 meters and heat transfer zone depth of 100 meters, V0=4.228e17m^2, and V1=1.057e16m^2 You're
waaaaay off.
2) "heat loss by other means"? What sort of possible explanation could you have? Losing heat *into the earth*?
It's easiest to calculate in calories like I did, BTW, since 1 cal heats 1 gram of water 1 degree at STP. Of course, that's for pure water, but it's not too different for salt water.
Try again, using the right numbers this time!
Now, mine: I used the wrong number of cubic meters in the water. Let's place the formula out here.
T=temperature, dT=difference in temperature from the ocean.
A=area of the atlantic
Da=average depth of the atlantic
Dm=depth of magma that we're considering
Va=volume of the atlantic
Vm=volume of magma
Sm=specific heat of magma
Sw=specific heat of water
Dm=density of magma
Dw=density of water
Em = heat energy of magma
Ew = heat energy of water
dTw = change in temperature in water
dT=1000K
A=1.057e8km^2
Da=4000m
Dm=100m
Va=A km^2 * (1000m/km)^2 * Da=4.228e17m^3
Vm=A km^2 * (1000m/km)^2 * Dm=1.057e16m^3
Sm=0.3 cal/g
Sw=1.0 cal/g
Dm=2.5 g/cm^3
Dw=1.0 g/cm^3
Em=dT K * Vm m^3 * (Sm cal/g * Dm g/cm^3 * (100 cm/m)^3) = 7.9275e24 cal
Ew=Em cal = 7.9275e21
dTw=Ew cal * (1 K*g/cal) / (Dw g/cm^3 * (100cm/m)^3 * Va m^3) = 18.75 K
Of course, this uses the preposterous estimate that only 100 meters of magma transfer their heat energy to the water over the course of an entire *year*.
Now, while the current number would still be spewing huge amounts of steam into the atmosphere (and trapped gasses making the entire ocean horribly acidic and toxic, etc) (i'd also doubt a laden boat could sail in water bubbling like that, unless you expect somehow that all steam bubbles will collapse before they get to the surface), let's look at how quickly magma *actually* dissipates heat into water. Even pretending that the Atlantic heat can just go into the other oceans (do you know how fast conveyors go? What, do you expect conveyors moving hundreds of miles per hour, but Noah riding just fine?), there's still another problem. Heat transfers *much* more quickly than the values that I used that under water, especially due to pillowing (which would be happening on a *massive* scale here). How quickly? Well, the mid-atlantic ridge with the magma in a thin line transfers about 2.3e19 cal/yr. It manages such a heat transfer with *very* minimal exposure due to two things: a) cracks in the cooled rock due to pillowing extend for hundreds of meters deep in places, and b) the lower reaches are rapidly cycles through by magma. With this, you're going to be looking at what could only reasonably be *kilometers long* cracks from pillowing (have you ever seen an underwater volcano before, out of curiousity? the rate that they transfer their heat is tremendous). The effect would be, really, staggering. Even if you scale the 100 meters of magma's worth of heat up to only 1 km, all of the oceans would be boiling.
Just the immediate quench of exposed magma is almost unthinkable, the wave of steam it would release... talk about causing a megatsunami. Every freshly exposed area of magma will release a huge bubble of steam shooting to the surface. And if the mantle isn't nice and smooth, but is erupting due to trapped gasses, the situation becomes far, far worse.
I really don't think you've thought about the heat situation very much.
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"Illuminant light,
illuminate me."