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There is a related question here, but it doesn't explain the implications of / on the 2nd Law of Thermo.

One of the effects of the 2nd Law of Thermo is that no matter how many zillion particles travel with a velocity of X they cannot collaborate together to propel even one tiny particle one tiny bit faster than X. So how can air molecules traveling at e.g. 18mph push a sailboat 20mph?

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  • $\begingroup$ The thermodynamics system that powers the sailboat is the sun-Earth-space thermal gradient. Since the sun's temperature is approx. 5800K and the temperature of space is 2.7K, the resulting Carnot efficiency is approx. 99.95%. Do you have examples of sailboats exceeding that efficiency limit? $\endgroup$ – CuriousOne Mar 10 '16 at 6:21
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    $\begingroup$ @Curious. The sailboat and the wind comprise an an isolated system for this question unless you're telling me that some energy other than the wind is propelling the sailboat. $\endgroup$ – Joe C Mar 10 '16 at 13:25
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    $\begingroup$ "The sailboat and the wind comprise an an isolated system for this question [...] " No. They don't. The wind is maintained by contact (energy input) with the wider environment so the system is not isolated. $\endgroup$ – dmckee Mar 10 '16 at 16:41
  • $\begingroup$ @JoeC, the energy available to the sailboat comes from the speed difference between the wind and the water. The keel and the sail work together to extract that energy. $\endgroup$ – BowlOfRed Mar 10 '16 at 16:52
  • $\begingroup$ You can always beat thermodynamics by choosing non-physical system boundaries. That, of course, is not something that mother nature actually cares about. She "knows" where the real thermal baths are. $\endgroup$ – CuriousOne Mar 10 '16 at 23:20
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Levers can modify not only the forces of some input, but also the speed. As an example, a golf club can be used to hit a golf ball with much greater speed than the hands holding it can move. So there is no prohibition in levers making things faster. Only that the total energy or work done does not exceed the input.

The boat can be thought of as an engine that is harnessing the energy present in the velocity difference between the water and the wind. This energy is available to accelerate the boat. It will accelerate until drag losses equal the input energy from the wind-water velocity gradient.

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In a one dimensional world, you'd be correct. But in a two dimensional one (sea) you could be going in any direction relative to the wind. Moving in a different direction then the wind, your speed in the wind's direction remains smaller then the wind's speed, but your speed in the perpendicular direction can increase, increasing your total speed. Of course I'm assuming that the wind is simple and that the drag doesn't limit the boats speed below that of the wind.

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