Is there a way to calculate the energy required to reduce the heat of oceans?
Am I wrong in thinking it is not as simple as reversing the calculation for specific heat of sea water?
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The question is slightly confused, because reducing the temperature of the oceans, in a direct sense, doesn't require energy - it releases it. The amount that is released is simply related to the mass and specific heat capacity of seawater, as you suggest.
The missing question, though, is why the ocean is cooling. For it to happen naturally and simply release energy, it would need to be because its surroundings (e.g. the air) were cooler. If you want to actively cool the sea, then yes, that is going to consume energy. If the cooling has approximately the same level of performance as building-sized air conditioning, the power used by the cooling apparatus will be about 40% of the rate at which the energy is removed (and remember that this is not just the total energy divided by the time, because more heat will be leaking back in while you do it).
Leaving aside the, uh, engineering challenges of this scale of cooling, this leads to a question as to why one might want to do this. Remember that unless you devise some complex system to radiate this heat into space from above the atmosphere, you're going to be releasing the same heat into the same global climate system, plus the additional 40% that you've used to move it around.
Assuming a surface ocean temperature of 288 K and a deep ocean temperature of 277 K, let's assume a mean temperature around 282.5 K.
The specific heat capacity of seawater at constant pressure is 3,890 joules per kilogram per kelvin.
The mass of the ocean is 1.39 x 1021 kg.
Therefore the "thermal content," if I can call it that, of the ocean is 1.528 x 1027 J. At 281.5 K, it would be 1.522 x 1027 J. The difference is 5.407 x 1024 J using all the significant figures Excel gives me. That's a lot of energy!
Heat capacity is the amount of thermal energy it requires to heat a gram of "A substance" one Kelvin degree. Salt water of oceanic variant average salinity (3.5%) has specific heating of 3.993 J/(g K) or 3.993 Joules of energy per gram of water to raise it ONE degree kelvin.
using Metric; Water has a specific heat capacity of 4.186 J/g°C, meaning that it requires 4.186 J of energy (1 calorie) to heat a gram by one degree Celsius. With an Oceanic volume of 321 Million Cubic miles (1.338 Quintillion! cubic meters) with roughly one million grams of water per cubic meter it would take the removal of nearly a Yottajoules worth of energy, 500 TIMES current human annual energy consumption.