Quite different from a conventional windmill, more like one that the OP is paying to move through still air to generate power.
Interesting that this question came up. NASA and the Navy have recently developed an underwater system that extracts energy from thermal and buoyancy differences. The essence of the system is a substance that expands or contracts depending on temperature. The change in pressure supplies energy to the device and let’s it go up or down in the ocean and other useful things. It works for an indefinitely long period of time, which is different than having perpetual motion.
I think all the talk of electrolysis is clouding the intent of the OP’s question.
Imagine you have a submarine with a retractable piston coming out of the hull. The sub is just on the edge of neutral buyoancy. When the piston extends, the overall volume of the sub increases just enough so that it has positive buoyancy (sub goes up). When the piston retracts into the hull, the displacement decreases just enough so the sub has slightly negative buoyancy (sub goes down). Piston is powered by an electric motor. Batteries are charged by an spinning paddle wheel/prop that takes energy from the descending sub.
How much energy does it take to extend the piston when the sub is at max depth, in order to make it go up? This is equal to the (water pressure @ max depth) x (volume of the extended piston). (1)
How much energy can theoretically be extracted by the spinning wheel as the sub descends? This is equal to the (net buoyancy force on the sub) x (distance the sub descends to the bottom). (2)
however:
water pressure @ max depth = (distance the sub descends to the bottom) x water density
net buoyancy force on the sub= (volume of the retracted piston) x water density.
When you substitute those in, you’ll find that equation (1) equals equation (2). No surprise. Factor in frictional losses, generator losses & energy storage losses and you come out behind.
Re-reading the OP, it seems to me that what’s going on is trying to combine two different standard perpetual motion cycles: one is electrolyzing water to hydrogen and oxygen, then burning the hydrogen to get the electricity to electrolyze more water; the other is carrying something against gravity, then letting it fall back and using the released energy to carry it back against gravity (typically, it’s thought of as pumping water uphill, then using the water running downhill past a turbine to power the pump, but pushing something down against bouyancy is the same idea).
And in both cases, the thing is you’ll end up with less energy than you started with. In some version of idealized-easy-physics land, where everything is 100% efficient and there’s no friction, both of these would work, so you are getting the basic physics right. But in this imperfect world of friction and heat loss, you’ll always end up with less energy than you started the cycle with.
Now, there’s nothing inherently wrong about the idea of electrolysis to create gas that displaces water in a tank, creating bouyancy. You could even burn the gas later on to get some energy back. It’s just that you’ll always have to add energy at the end of the cycle – you’ll never have as much charge in your batteries at the end of the cycle as you started with. [The other problem with it is that it’s a lot more simple, efficient and quick to bring down a tank of compressed air and use that to displace water, instead of batteries and an electrolysis set-up].
Long ago I started trying to write a humorous novel based upon the laws of thermodynamics. (Imagine Catch-22 crossed with Don Quixote, wordsmithed by Douglas Adams, and you get an idea of what I was trying to shoot for.) It rapidly became apparent for reasons that must be obvious in this thread that most of the jokes and even the basic theme of irreversibility of real world processes would be inaccessible to the vast majority of even the literate public, and I gave up.
Stranger
To directly answer the OP: Perpetual motion is not hard, it’s impossible. Breaking the sound barrier is hard. Making a nuke is hard. Disassembling the planet Jupiter and using the material to build a spherical shell of solar panels completely enclosing the Sun is hard. Perpetual motion isn’t like any of those things: You can’t do it, no matter how hard you try, and no matter how much resources you expend on it.
Not that hard. There is this trick where you take a rectangular parallelpiped with the edges in a ratio of the squares of the first three prime numbers, and the you multiply them…
Stranger
But the first one has to be “Full of stars!” to make it work.
The issue in this and the OP’s previous thread appears to be failing to understand buoyancy and how to calculate energy balance in a system in which substances are changing density. Let’s step back and break this cycle down to its basics and look at the energy balance in each state.
Assume we start with a mass of water. This water occupies a constant amount of space, and is surrounded by an ambient medium that may be water or air, depending on the thought experiment. There may also be submarines, balloons, windmills, electrolysis cells, or other pieces of hardware involved, but we can ignore them for now.
We split the water into hydrogen and oxygen. This requires a fair amount of energy. The energy required is in two parts. First, there’s the basic energy required to split the hydrogen and oxygen into water. Second, as the resulting gas takes up more space than the initial water, there’s the energy required to displace the surrounding air or water environment. In the case of the submarine, when you have split your ballast water into hydrogen or oxygen, you have had to expend the energy required to lift the water displaced by that hydrogen or oxygen out of the way.
Now you allow the less dense hydrogen and oxygen rise against the surrounding medium. As you do this the water or air you lifted in the previous step will descend, and your hydrogen and oxygen will ascend. In theory you can reclaim this energy with some kind of mechanism involving turbines or balloons on a rope turning a generator; the engineering details are not important to the thought experiment. The resulting energy will be somewhat less than the energy spent lifting the water or air out of the way in the first step, because some of the kinetic energy of the falling surrounding medium will have been spent lifting the hydrogen and oxygen to the top of the cycle.
At the top of the cycle, you combine the hydrogen and oxygen back together to make water. This could be done through a fuel cell, or turbine, or Stirling engine, or whatever your preferred means is. We ignore the details and assume perfect recovery of the spent energy. The energy you get back is determined by the basic energy required to split water into oxygen and hydrogen, plus a slight bonus from the ambient pressure since the resulting water will take up less space than the oxygen and hydrogen.
Now you’ve got a mass of water at the top of the cycle. You’re at a slight energy deficit because the energy you spent at the bottom to split the water is more than the energy you got back at the top plus the energy you harnessed from the oxygen and hydrogen rising. If you let the water fall back to the bottom of the cycle, your net overall energy evens out to zero.
In the end, what you’re doing is lifting hydrogen and oxygen up and down, gaining no energy in the process even in theory, and in practice losing energy because no step of the process is 100% efficient. It doesn’t matter if you have a submarine or whatever attached, because the mass lifted when the submarine rises exactly counters the mass lowered when the submarine lowers.
I’ve seen a lot of perpetual motion schemes based on misunderstanding of buoyancy. This isn’t any different. The OP would be best served to read up on previous ideas that have been proposed, or tried and failed, as well as understanding the physics better.
Simplest possible objection: In order to get buoyancy you have to push ballast out. In other words, you must push the entire sea up a minute fraction against gravity. Buoyancy will give you back some of the energy it took to push the sea level up. You won’t get back 100%, and the more convoluted the steps you take to try and accomplish it, the greater your losses will be. There is no get-out clause that states “however, electrolysis of water is a special case, so do as thou wilt”.
It is unlikely that electrical generation followed by electrolysis is actually more efficient than using your kinetic energy on descent to wind a spring which you then use to pump out your ballast tank - it’s just that the OP seems to have this mental image of gases bubbling out of water with irresistible force, so it seems more tempting than the spring idea which is patently idiotic. Moreover, you should not need a giant submarine and the Marianas Trench to test the principle - a small model sub and a swimming pool should do nicely.
Isn’t it the squares of the positive integers? I.e., the ratio in the first three dimensions is 1:4:9, not 4:9:25.
Maybe this will show me an idiot, but, I never did get how the second law of thermodynamics rules out perpetual motion machines of all kinds.
The second law says you can’t extract energy from heat flow if you only have reservoirs of thermal energy that are all at the same temperature. This makes sense from a statistical point of view, because heat flow creates the opportunity to do useful work because in a temperature gradient you can statistically predict which particles will be more stationary than which other particles, so more motional work is done on the more stationary ones by the more vigorous ones. When two particles that are parts of systems of the same temperature interact, on the other hand, there’s no statistical bias to which particle does work on which other particle, because of the complex unpredictability of their motion.
But I don’t know how to extend this to broader statements about perpetual motion machines. My thinking is that I’m just not well informed, and maybe somebody can enlighten me, if it isn’t too much work…
I don’t think that the second law rules out Perpetual Motion machines per se. If one could develop a 100% efficient machine, it could run forever, and would not violate the second law. However, a machine that does work can not run forever, since the second law states that such a machine increases the entropy of the universe, and would therefore eventually run out of sufficient gradient to perform said work.
Those are free as in speech - the OP is looking for free as in beer.
Aren’t you describing Maxwell’s Demon?
A lot of people say “free” when they actually mean “subsidized” by nature.
Maybe (can’t say I’ve encountered it a lot, if at all, in that usage), but if that causes them to misunderstand the laws of physics, it’s their own lookout.
It is not so much about misunderstanding the laws of physics but about asking the wrong question. You can have “free” energy (meaning that you didn’t pay for fuel) without resorting to perpetual motion. In the case of solar energy, nobody gets confused. Once you start having moving parts, and if the energy source is not obvious (such as not seeing the gravity behind the buoyancy), then confusion begins.
Consider a candle sitting under a pinwheel in an insulated chamber. The flame of the candle heats the air around its point of ignition, causing it to rise. This rising blanket of air pushes through the pinwheel and turns it. But as time goes on, the ambient temperature of the chamber has been heated to the same temperature as the ignition point of the candle. There might still be flame, but the air no longer rises because all air in the chamber is of the same configuration.
This is “entropy”. The ability to do work comes from differences in state. But as you utilize that energy, you are removing the differences, until the system has achieved homogeneity. If you are standing inside that system, you can’t return it to the way it was because that takes effort and there is no energy in the system. If you are outside of the system, you are merely in some second system with the same issue.
But so say that your first system does nothing but recharge the second, and the second does nothing but recharge the first. There must be some sort of mechanism which switches the flow. Who powers that mechanism if your two systems are strapped just replenishing each other?