Friday, February 26, 2010

The Science of Global Warming

(continuing from part one)

We have seen that the Earth could potentially be quite cold (5 C). The atmosphere plays a large part in keeping the temperature comfortable.

Another part is the oceans.
"the ocean can store as much heat in its top three meters (10 feet) as the entire atmosphere does"
That is an interesting statement, which I would like to walk through...

The atmosphere contain 5e18 kg of gases. The surface area of all the oceans is 3.61e18 cm^2.

One liter of water is 10 cm deep under 100 cm^2 surface area (1e3 cm^3). 3 meters deep gives us 1.08e19 cm^3, or 1.08e16 L. One liter of water weighs 1 kg (at the temperature and pressure we care about).

The heat capacity of water (in the temperature range we are interested in - 5 to 30 C) is 4.2 J/gK (this should be familiar as the value of one calorie).

That gives us a total heat capacity of 4.54e19 J/K. That is a lot. Total world consumption of energy is 4.74e20 J per year. That's enough to raise surface ocean temperatures 10 degrees.

The total amount of water in the hydrosphere is 1.4e21 kg (about 100,000 times that amount). One part in 100,000 is in the atmosphere (the rest being in the oceans). The temperature varies from 12-20 C near the top (1,000 m) to 4 C in the depths.

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