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How much energy would be obtained from the seawater with a second type perpetual motion machine if it were cooled by $\Delta T = 1° C$? The mass of the seawater is $m\approx1.4 \cdot 10^{21} \mathrm{kg}$. How long would this energy supply last with an average power requirement of mankind of around $P\approx13\mathrm{TW}$ per year?

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The question is moot, as a PMM type II is impossible because it violates the Laws of Thermodynamics.

If you want to know how much heat energy $Q$ would have to be extracted from the Earth's seas and oceans to lower their temperatures by $\Delta T = 1° C$ then:

$$Q=mc_p\Delta T$$

where $c_p\approx 4200\mathrm{Jkg^{-1}K^{-1}}$

So:

$$Q=1.4 \cdot 10^{21} \times 4200$$ $$=5.88\cdot 10^{24}\mathrm{J}$$

As regards the duration $\Delta t$, first convert $P\approx13\mathrm{TW}$ to $\text{Joule/year}$:

$$13 \cdot 10^{12} \times 365 \times 24 \times 60 \times 60=4.1 \cdot 10^{20}\mathrm{J/year}$$

$$\Delta t=\frac{5.88\cdot 10^{24}\mathrm{J}}{4.1 \cdot 10^{20}\mathrm{J/year}}\approx 14000 \text{years}$$

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