|MadSci Network: Earth Sciences|
If there's one thing an oceanographer loves, it's a back of the envelope calculuations! I'll use scientific notation because the numbers are going to be pretty large.
Lets's take your 10 by 10 kilometer square patch of ocean, so a hundred square kilometers. Next, lets say that we want to decrease the temperature in the top metre of water by 3 degrees celcius. The amount of water in that 10 km by 10 km by one metre is 10000 metres times 10000 metres times 1, or 108 cubic metres. A cubic metre of water weighs 1000 kilograms (we'll ignore salt in this example), so that volume of water will weigh 108m3 times 1000 kg/m3, which equals 1011 kg. That's a lot of water, it's equivalent to the mass of almost 50 000 statues of liberty.
The amount of energy required to heat or cool a parcel of water is calculated
by multiplying the specific
heat by the mass of water, and the temperature change. The specific heat
of water is 4.186 kJ/kg oC (in other words, 4.186 kilojoules
must be removed to cool one kilogram of water by one degree).
So in our example, the amount of energy required is 4.186 kJ/kg oC times 1011 kg times 3 oC, which works out to 1.3x1012 kJ. That is a lot of energy - Little Boy, the atomic bomb dropped on Hiroshima, released about 1.8x1010 kJ, so we are talking about an amount of energy roughly equivalent to about 70 Little Boys.
Moving on, the heat of solution of ammonium nitrate is 26.2 kJ/mole (i.e., 26.2 kJ is removed for every mole of ammonium nitrate that is dissolved). So we will need 1.3x1012 ÷ 26.2 kJ/mole, which equals 4.8x1010 moles. The molar mass of ammonium nitrate is 80.04 grams per mole (equivalent to 0.08004 kilograms per mole), so that works out to a grand total of 4.8x1010 moles times 0.08004 kilograms/mole, which equals 3.8x109 kilograms of ammonium nitrate required, or a little under 4 million metric tons.
I think you'll agree that that is a lot of ammonium nitrate! I can see a few problems with this plan:
So, in short, I think we're just going to have to put up with the weather for the forseeable future.
I hope that helped!
Rob Campbell, MAD Scientist
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